2x(x)=5
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La altura inicial del objeto lanzado desde una plataforma es de 60 metros, representando la altura de la plataforma. Esto se obtiene al evaluar h(x) cuando x = 0.

La altura del objeto en el momento del lanzamiento se refiere al valor de la función h(x) cuando x = 0, ya que x representa el tiempo en segundos después del lanzamiento. Para determinar la altura inicial, simplemente sustituimos x = 0 en la función h(x):

h(0) = -5(0)^2 + 20(0) + 60 = 60

Por lo tanto, la altura inicial del objeto en el momento del lanzamiento es de 60 metros.

En términos físicos, esto tiene sentido, ya que el término cuadrático (-5x^2) representa la aceleración debida a la gravedad, y el término lineal (20x) representa la velocidad inicial. Cuando x = 0, no ha pasado tiempo después del lanzamiento, y la altura es simplemente la altura inicial de la plataforma, que es 60 metros.

En resumen, la altura del objeto en el momento del lanzamiento es de 60 metros.

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The object will land on the ground 6 seconds after launch.

To determine when the object will land on the ground, we need to find the time [tex]\( x \)[/tex] when the height [tex]\( h(x) \)[/tex] is zero. The height of the object is given by the equation:

[tex]\[ h(x) = -5x^2 + 20x + 60 \][/tex]

Set [tex]\( h(x) = 0 \)[/tex] to find the time when the object lands on the ground:

[tex]\[ -5x^2 + 20x + 60 = 0 \][/tex]

This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \),[/tex] where [tex]\( a = -5 \), \( b = 20 \),[/tex] and [tex]\( c = 60 \).[/tex] We can solve this using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

Substitute the values of [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex] into the formula:

[tex]\[ x = \frac{-20 \pm \sqrt{20^2 - 4(-5)(60)}}{2(-5)} \][/tex]

Simplify inside the square root:

[tex]\[ x = \frac{-20 \pm \sqrt{400 + 1200}}{-10} \][/tex]

[tex]\[ x = \frac{-20 \pm \sqrt{1600}}{-10} \][/tex]

[tex]\[ x = \frac{-20 \pm 40}{-10} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{-20 + 40}{-10} = \frac{20}{-10} = -2 \][/tex]

[tex]\[ x = \frac{-20 - 40}{-10} = \frac{-60}{-10} = 6 \][/tex]

Since time [tex]\( x \)[/tex] cannot be negative, we discard [tex]\( x = -2 \).[/tex] Therefore, the object will land on the ground [tex]\( 6 \)[/tex] seconds after launch.

So, the object will land on the ground 6 seconds after launch.

The translated question is:

An object is launched from a platform. Its height (in meters), x seconds after the launch, is modelled by:

[tex]h(x)=-5x^2+20x+60[/tex]

How many seconds after launch will the object land on the ground?

Answer:

Belinda can expect to make $1 more with option B.

Step-by-step explanation:

The expected value for every option is calculated as:

[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)[/tex]

Where [tex]x_1[/tex] and [tex]x_2[/tex] are the posibles money prize and [tex]p(x_1)[/tex] and [tex]p(x_2)[/tex] are their respective probabilities.

Option A:

Belinda has 12 possibilities: 1-3, 1-4, 1-5, 3-1, 3-4, 3-5, 4-1, 4-3, 4-5, 5-1, 5-3 and 5-4

From that 12 possibilities, there are 6 that have a sum greater than 6. That possibilities are: 3-4, 3-5, 4-3, 4-5, 5-3 and 5-4

So, the probability that the sum of the two spins is greater than 6 is:

[tex]P=\frac{6}{12} = 0.5[/tex]

At the same way the probability that the sum of the two spins is lower or equal than 6 is 0.5.

So, the expected value for this option is:

[tex]E_A(x)=(8*0.5)+((-2)*0.5)=3[/tex]

Option B:

Belinda has 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH and TTT

Where T means Tails and H means Heads.

Form that 8 possibilities, there are 4 which heads appear twice. That possibilities are: HHH, HHT, HTH and THH.

So, the probability that head appear twice is:

[tex]P=\frac{4}{8}=0.5[/tex]

At the same way, the probability that head doesn't appear or appear once is equal to 0.5

So, the expected value for this option is:

[tex]E_B(x)=(10*0.5)+((-2)*0.5)=4[/tex]

Finally, Belinda can expect to make $1 more with option B.

[tex]E_A(x)-E_B(x)=4-3=1[/tex]

Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.

To find the option with the greater mathematical expectation, we need to calculate the expected value (or mean) for each option.

Option A:

Step 1:

- The spinner has numbers 1, 3, 4, and 5.

- There are a total of 16 possible outcomes when spinning the spinner twice (4 outcomes for each spin).

- We need to find the probability of getting a sum greater than 6 and multiply it by $8, and then find the probability of getting a sum less than or equal to 6 and multiply it by -$2.

Step 2:

Let's calculate the probabilities:

1. Probability of getting a sum greater than 6:

- Possible outcomes: (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5) (total of 8 outcomes)

- Probability: [tex]\( \frac{8}{16} = \frac{1}{2} \)[/tex]

- Winning amount: $8

2. Probability of getting a sum less than or equal to 6:

- Possible outcomes: (1, 1), (1, 3), (1, 4), (1, 5), (3, 1), (4, 1), (5, 1) (total of 7 outcomes)

- Probability: [tex]\( \frac{7}{16} \)[/tex]

- Losing amount: -$2

Step 3:

Now, we calculate the expected value for Option A:

[tex]\[ \text{Expected value (Option A)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]

[tex]\[ \text{Expected value (Option A)} = \left( \frac{1}{2} \right) \times (8) + \left( \frac{7}{16} \right) \times (-2) \][/tex]

[tex]\[ \text{Expected value (Option A)} = 4 - \frac{7}{8} \][/tex]

[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \][/tex]

Option B:

Step 1:

- There are 2 ways to get heads twice out of 3 coin flips: (HHH, HHT, HTH, THH)

- There are a total of 8 possible outcomes when flipping a coin three times.

- We need to find the probability of getting heads twice and multiply it by $10, and then find the probability of not getting heads twice and multiply it by -$2.

Step 2:

Let's calculate the probabilities:

1. Probability of getting heads twice:

- Possible outcomes: (H, H, T), (H, T, H), (T, H, H) (total of 3 outcomes)

- Probability: [tex]\( \frac{3}{8} \)[/tex]

- Winning amount: $10

2. Probability of not getting heads twice:

- Possible outcomes: (H, H, H), (T, T, T), (T, T, H), (T, H, T), (H, T, T), (H, T, H) (total of 5 outcomes)

- Probability: [tex]\( \frac{5}{8} \)[/tex]

- Losing amount: -$2

Step 3:

Now, we calculate the expected value for Option B:

[tex]\[ \text{Expected value (Option B)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]

[tex]\[ \text{Expected value (Option B)} = \left( \frac{3}{8} \right) \times (10) + \left( \frac{5}{8} \right) \times (-2) \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{30}{8} - \frac{10}{8} \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} \][/tex]

Step 4:

To find out which option has the greater mathematical expectation, we compare the expected values of Option A and Option B:

[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \approx 3.625 \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} = 2.5 \][/tex]

Since [tex]\( \frac{29}{8} \)[/tex] is greater than [tex]\( \frac{20}{8} \)[/tex], Belinda should choose Option A.

To find out how much more money she can expect to make by choosing Option A over Option B, we calculate the difference in expected values:

[tex]\[ \text{Difference} = \text{Expected value (Option A)} - \text{Expected value (Option B)} \][/tex]

[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} \][/tex]

[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} = \frac{9}{8} \][/tex]

[tex]\[ \text{Difference} = \frac{9}{8} \][/tex]

Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.

Answer:

  B. is dependent

Step-by-step explanation:

The denominator determinant will be zero when the coefficients of the variables are dependent. One of the numerator coefficients will be zero when the coefficients involved are dependent. Hence using Cramer's Rule will result in the ratio 0/0 when the system is dependent.

___

The ratio will be 1/0 if the system is inconsistent (has no solution).

Answer: 17 containers

Step-by-step explanation:

Debbie bought 8 1/2 lb of ground turkey and she packed the turkey in 1/2 lb containers before put the turkeys in the freezer.

To calculate the number of containers she used for packing the turkey, we divide 8 1/2lb by 1/2 lb.

= 8 1/2 ÷ 1/2

We change 8 1/2 to improper fraction

= 17/2 ÷ 1/2

= 17/2 × 2/1

= 17

Debbie would need 17 containers to pack the turkey.

Answer:

Debbie will need 17 containers to pack the turkey.

Step-by-step explanation:

Debbie bought 8 1/2 lb of ground turkey

she packed the turkey in 1/2 lb containers

To know the number of containers she used for packing the turkey,

we divide 8 1/2lb of ground turkey by 1/2 lb containers.

[tex]=8\frac{1}{2} \div \frac{1}{2}[/tex]

[tex]= \frac{17}{2} \div \frac{1}{2}[/tex]

[tex]= \frac{17}{2} \times \frac{2}{1}[/tex]

[tex]=\frac{34}{2} \\\\= 17[/tex]

Debbie will need 17 containers to pack the turkey.

Answer:

Option B. 1024(0.5)^x

Step-by-step explanation:

From the question given, we were told that half (1/2) the players are eliminated at the end of each round.

If T is the total number players, then after round one it becomes:

T x (1/2)^1 = T x 0.5

After round x, the the numbers of player remaining will be:

T x (1/2)^x = T x (0.5)^x

From the question given, the total number of players are 1024. Therefore, the above expression can be written as:

T x (0.5)^x => 1024(0.5)^x

Answer:

The answer is A.

Answer:    The Answer is A

Step-by-step explanation:

Answer:

9 cards

Step-by-step explanation:

he originally had 36 cards before giving 5 away, 36 divided by 4 is 9

Final answer:

Tony originally had 9 cards in each of the 4 equal sets before he gave 5 cards away.

Explanation:

The question asks how many cards were in each set originally when Tony had 4 equal sets of sports cards, gave away 5 cards, and now has 31 cards left. To find the number of cards in each set, we add back the 5 cards Tony gave away to the total number he has left, which gives us 31 + 5 = 36 cards. Since these 36 cards were divided into 4 equal sets, we divide 36 by 4 to find the number of cards in each set. Therefore, each set originally had 36 / 4 = 9 cards.

a = (1+0.2)p

This equation is used to calculate the quantity of lemonade.

Step-by-step explanation:

Let the quality of lemonade in lans glass be 'a'

Quantity of lemonade in patricias glass = p ounces

Lan pours 20% more than Patricia

a = (1+0.2)p

This equation is used to calculate the quantity of lemonade

Answer:

Patricia poured P ounces of lemonade in her glass. Ian poured 20% more than P ounces in his glass; that is, he poured 0.20p or .2p ounces more than Patricia.

ANSWER: 0.20p

Step-by-step explanation:

Answer:

i think it is E

Step-by-step explanation:

Answer:

T = sin(6572t)

Step-by-step explanation:

A pure tone is a sine-wave and sine-waves are defined by ω (omega) and t (time)

For a sine model:

Amplitude of wave form = sin(ωt)

A sine model that gives the Tone, T, as a function of time, t, for this key:

T = sin(ωt)

Sin is a mathematical operator in trigonometry

ω = 2πf

π = 3.14

The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz.

f = 1046.5 hertz

ω = 2×3.14×1046.5

ω = 6572.02

T = sin(6572t)

The sine model for the 64th key on a standard 88-key piano with a frequency of 1046.5 Hz is represented as T(t) = A sin(2π(1046.5)t + φ), where A is the amplitude, φ is the phase shift, and t is the time.

The student has asked for a sine model that represents the Tone, T, as a function of time, t, for the 64th key on a standard 88-key piano, which has a frequency of 1046.5 hertz. A sine function that models the tone can be written as:

T(t) = A sin(2πft + φ)

For this example, since frequency (f) is given as 1046.5 Hz and we don't have information about amplitude (A) and phase shift (φ), we can write the model as:

T(t) = A sin(2π(1046.5)t + φ)

This model can be used by piano tuners to ensure that the piano is properly tuned by comparing the accurate frequency with the sound coming from the piano and making adjustments as needed.

Answer:

6750

Step-by-step explanation:

There are 1000g in a single kilogram. Therefore, [tex]\frac{6.75kg}{1}\cdot \frac{1000}{1kg}=6750g[/tex]. Hope this helps!

Answer:

6750

Step-by-step explanation:

The 36% of the students in the sample prefer cats. Hence, 36% is correct answer.

The step-by-step calculation to determine what percent of students in  sample prefer cats:
1) Find the total number of students who prefer cats:

Add the number of male students who prefer cats (10) to the number of female students who prefer cats (26). 10 + 26 = 36
2) Find the total number of students surveyed:

Add the number of students who prefer dogs (36 + 20), the number of students who prefer cats (36), and the number of students with no preference (2 + 6). 36 + 20 + 36 + 2 + 6 = 100
3) Calculate the percentage of students who prefer cats:

Divide number of students who prefer cats (36) by the total number of students surveyed (100) and multiply by 100%. 36 / 100 * 100% = 36%
4) Round the answer to the nearest percent:

36% rounded to nearest percent is 36%.

Complete and correct question is in the image:

According to the given sample, 36% of students in the sample prefer cats.

To find the percentage of students in the sample who prefer cats, we need to sum up the number of students who prefer cats, which is 26 for females and 10 for males.

Total number of students who prefer cats = 26 (females) + 10 (males) = 36.

Now, let's find the total number of students in the sample:

Total number of students = 36 (males who prefer dogs) + 20 (females who prefer dogs) + 10 (males who prefer cats) + 26 (females who prefer cats) + 2 (males with no preference) + 6 (females with no preference)

= 36 + 20 + 10 + 26 + 2 + 6

= 100.

Now, we can calculate the percentage of students who prefer cats:

Percentage of students who prefer cats = [tex]\frac{Number \ of \ students \ who \ prefer \ cats}{Total \ number \ of \ students}[/tex] × 100

= ([tex]\frac{36}{100}[/tex]) × 100 = 36%.

So, approximately 36% of students in the sample prefer cats.

The question is:

Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.

Preference  Male  Female

Prefers dogs  36  20

Prefers cats  10  26

No preference  2  6

Approximately what per cent of students in the sample prefer cats?

Answer:

51

Step-by-step explanation:

Just did it on edgu

Final answer:

Based on the circle graph, 34 percent of the 150 surveyed people completed college, which translates to 51 individuals.

Explanation:

The question asks how many people completed college based on a circle graph showing the education levels of 150 surveyed individuals. To answer this, we use the percentage given for those who completed college and apply it to the total number surveyed. With 34 percent having completed college, we calculate the number of people by multiplying 34 percent (or 0.34 as a decimal) by the total survey number, 150 people.

The calculation is as follows: 0.34 × 150 = 51. Therefore, 51 people surveyed completed college.

Answer:

Step-by-step explanation:

2376

Answer:

48 in each bus

Step-by-step explanation:

divide 192 by 4

Answer: 48

Step-by-step explanation:

If there are 4 buses and 192 students you divide 192 by 4 and get 48

Answer:

n=438

Step-by-step explanation:

-Given the sample proportion [tex]\hat p=0.24[/tex] and the confidence level is 95%.

-The sample size can be calculated using the formula;

[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

#Substitute parameters in the formula and make n the subject of the formula;

[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\n=(\frac{z_{0.025}}{ME})^2\hat p(1-\hat p)\\\\\\=(\frac{1.96}{0.04})^2\times 0.24\times 0.76\\\\=437.94\approx 438[/tex]

Hence, the desired sample size is n=438

"The correct answer is C. The statement If these probabilities are correct, 12%is the probability that it will rain both days

To find the probability that it will rain both days, we need to multiply the probability of rain on Saturday by the probability of rain on Sunday, assuming that the events are independent.

The probability of rain on Saturday is 30%, which can be expressed as 0.30 or[tex]\(\frac{30}{100}\)[/tex].

The probability of rain on Sunday is 40%, which can be expressed as 0.40 or[tex]\(\frac{40}{100}\)[/tex].

Now, we multiply these two probabilities to find the probability of both events occurring:

[tex]\[ P(\text{Rain on Saturday}) \times P(\text{Rain on Sunday}) = \frac{30}{100} \times \frac{40}{100} \][/tex]

[tex]\[ \frac{30}{100} \times \frac{40}{100} = \frac{30 \times 40}{100 \times 100} \] \[ \frac{30 \times 40}{100 \times 100} = \frac{1200}{10000} \] \[ \frac{1200}{10000} = \frac{12}{100} \] \[ \frac{12}{100} = 0.12 \][/tex]

Converting this decimal to a percentage, we get 12%.

Therefore, the probability that it will rain both days is 12%."

Answer:

w=(x-6)

Step-by-step explanation:

x^2-4x-12=(x + 2)(w)

a=wl (area equals width times length)

x^2-4x-12=(x + 2)(w)

(x-6)(x+2)=(x + 2)(w)

(x-6)=w

Answer:

Table A

Step-by-step explanation:

It's only Table A because if you look at Table B at the top it says

Topping 1 and Topping 2

You're only supposed to have Crust and Topping, not 2 toppings

Answer:

Table A

Step-by-step explanation:

Khan

Answer:

[tex]\frac{2}{3}[/tex] or [tex].666666666[/tex] or [tex]\%66.66[/tex]

Step-by-step explanation:

Answer:

Each person would get 2/3

Step-by-step explanation:

Split the two circles and each person gets one portion of it.

Answer:

The horizontal shift from point A to point A’ is -2. The vertical shift from point A to  point A’ is 5. Since in a translation all points shift the same distance, the coordinates of  point B’ are (5, 7 ).

Step-by-step explanation:

A moved two units to the left.

1 - 3 = -2

A also moved 5 units up.

12 - 7 = 5

The translation rule is: [tex](x,y) -> (x - 2, y + 5)[/tex]

Apply the translation rule to point B.

[tex](7 -2, 2+5) = (5,7)[/tex]

B' should be (5,7).

Answers and Step-by-step explanations:

1. The horizontal shift from point A to point A' will simply be the difference in the x-coordinates. The x-coordinate of A is 3 and the x-coordinate of A' is 1. So, we take 1 - 3 = -2. The horizontal shift is 2 units to the left.

2. The vertical shift is the difference in the y-coordinates. The y-coordinate of A is 7 and the y-coordinate of A' is 12. So, we take 12 - 7 = 5. The vertical shift is 5 units up.

3. Basically, we want to move the coordinates of B 2 units to the left and 5 units up. B is currently (7, 2). When we move 2 units to the left, we subtract 2 from the x-coordinate 7, and when we move 5 units up, we add 5 to the y-coordinate 2: B' = (7 - 2, 2 + 5) = (5, 7)

Hope this helps!

Answer:

A

Step-by-step explanation:

just took the quiz on edgen

The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

The property of the logarithm is found as;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)}[/tex]

Given equation;

[tex]\rm log_4(x+3) = log_2(2+x)[/tex]

LHS;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_4(x+3) \\\\ y_1 = \rm y_1 = \frac{log(x+3)}{log 4}[/tex]

RHS;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_2(2+x) \\\\ y_2 = \frac{log(2+x)}{log 2}[/tex]

The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.

Hence, option A is correct.

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Answer:.5

Step-by-step explanation:

.5

Answer:

y= -11/144(x-8)^2+6

Step-by-step explanation:

This equation can be represented in vertex form, which is:  

y=a(x-h)^2+k

If we plug in 8 as h and 6 as k we get the following equation:

y=a(x-8)^2+6

Now we have to plug in x and y. We can use the other point (-4,-5) and plug it into the equation and get:

-5=a(-4-8)^2+6

Once we solve this we get a= -11/144

Now we have to plug in -11/144 into the original equation to get

y = -11/144 (x-8)^2 + 6

Answer:

50m per 1 minute

Step-by-step explanation:

250m/5 min=50/1

pls mark brainliest!! i only need one more!

Answer: Fraction= 3 3/4kg

Decimal= 3.75kg

Step-by-step explanation:

15 kilograms of rice are separated equally into 4 containers. To get the number of kilograms of rice are in each container, we divide the total kilograms of rice by the number of containers. This will be:

Kilograms of rice in each container=

15/4 =3 3/4kg as a fraction.

To convert the fraction to decimal, we divide 3 by 4 and add to 3. 3/4 equals 0.75. We then add 3 to 0.75. This will be:

Decimal of 3 3/4 = 3+0.75 = 3.75kg

Answer: shameeka sold 20 hamsters to the store.

Step-by-step explanation:

Let x represent the number of hamsters that shameeka sold to the store.

Let y represent the number of hamsters that the pet store had initially.

Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. It means that

x + y = 2y

x = 2y - y

x = y

Then the store got six more hamsters. If the pet store has 46 hamsters now, it means that

2y + 6 = 46

2y = 46 - 6

2y = 40

y = 40/2

y = 20

Since x = y, then

x = 20

Answer:

Step-by-step explanation:

45

Answer:

34

Step-by-step explanation:

1+4=5 2+5=12 3+6=21 5+8= ??

It is noticed that the previous solution is added to the unknowns and the cycle continues.

The previous solution is 5 which is added to 2 and 5 to give 12

5+2+5=12

12 is then added to the next set of unknowns 3+6 to give 21

12+3+6=21

21 is then added to the 5+8 to give 34

21+5+8= 34

Answer:

3

Step-by-step explanation:

3 even numbers 2,4,6

or 1/2

or 50%