A student bikes 5.00 km East to school in 30.0 min, realizes he forgot his calculator for physics, spends 30.0 min going back going home, and then races back to school in 27.0 minutes. 1. What is the students total displacement ?2. Determine the students average velocity ?

Answer:

A, C,D,E,F

Step-by-step explanation:

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

For more such questions on ratio of the sides

https://brainly.com/question/31529028

#SPJ8

The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

For more questions on fraction

https://brainly.com/question/78672

#SPJ8

Answer:

The answer for the first one is 1 and the second answer is 12i.

Step-by-step explanation:

The value of the given imaginary number i¹² will be 1 thus option (A) is correct.

A complex number is the sum of a real number and an imaginary number.

The idea of a complex number has come by solving a quadratic equation that has root as negative under root.

If we solve x² + 1 = 0 ⇒ x = √(-1) which is called as iota(i).

The value of iota(i) is given as i = √(-1).

By the law of indices,

i¹² = (i²)⁶

⇒ (-1)⁶

Since the even exponents of a negative number give positive output thus  (-1)⁶ = 1.

Thus, i¹² = 1

Hence "The value of the given imaginary number i¹² will be 1".

To learn more about complex numbers,

brainly.com/question/10251853

#SPJ2

To fully get the answer on the sample space and relative frequency, let's go directly to the analysis of the experiments as given.

(a) Sample space:

(b) Relative frequency of each outcome:

Relative frequency of an outcome is the number of times the outcome appears divided by the total number of trials. In a large number of repetitions of an experiment, the relative frequency of each outcome approaches the theoretical probability of that outcome.

Learn more on relative frequency here https://brainly.com/question/3857836

#SPJ1

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

for such more question on cost price

https://brainly.com/question/25799822

#SPJ11

Answer:

$638.4

Step-by-step explanation:

Randy's gross salary (salary without any deduction) = $760

taxed rate =16%

Amount tax paid =tax% of gross income

=16/100 * $760

=$16*760/100

=$12160/100

=$121.6

net salary = gross salary - tax paid

=$760 - $ 121.6

=$638.4

Randy's net salary is $638.40

Randy's gross salary = $760 per week.

Tax paid on his salary = 16%

Net salary is the difference between the salary earned and the amount paid as tax. This will be:

= Salary - Tax

= $760 - (16% × $760)

= $760 - (0.16 × $760)

= $760 - $121.60

= $638.40

Read related link on:

https://brainly.com/question/23421215

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

for such more question on values

https://brainly.com/question/27746495

#SPJ8

Answer:

Answer is 96%

Step-by-step explanation:

298-152/152 ×100

The percent increase in the number of people attending the exhibit will be 96%. Then the correct option is D.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

One weekend, 152 people attended an art exhibit.

The following weekend, 298 people attended.

Then the percent increase in the number of people attending the exhibit will be

P = [(298 - 152) / 152] x 100

P = (146 / 152 x 100)

P = 0.96 x 100

P = 96%

The percent increase in the number of people attending the exhibit will be 96.05%.

Then the correct option is D.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ2

Answer:

what?

Step-by-step explanation:

free points...thanks?

Step 1:

When by either

f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.

In general, a vertical stretch is given by the equation

y=bf(x). If b>1, the graph stretches with respect to the y-axis, or vertically. If b<1, the graph shrinks with respect to the y-axis. In general, a horizontal stretch is given by the equation y=f(cx) If c>1, the graph shrinks with respect to the x-axis, or horizontally. If c<1, the graph stretches with respect to the x-axis.

Step 2:

The function is vertically stretched by a factor of 2.

Step 3:

A horizontal translation is generally given by the equation

y=f(x−a). These translations shift the whole function side to side on the x-axis.

Hence, the function is translated 6 units to the right

Final answer

Answer:

a] 24.5; b] 2.8; c] 39.59.

Step-by-step explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

\(h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].\)

Answer:

1: 0.8461 = 84.61% probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

2: 0.9994 = 99.94% probability that the mean weight for a sample of size 10 1-year-old boys will be less than 25 lbs

3: In part 2, we use the sampling distribution of the sample means, which has more values closer to the mean due to the smaller standard error, so a higher probability of finding a mean less than 25 lbs.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 22.8 lbs and a standard deviation of about 2.15 lbs.

This means that \(\mu = 22.8, \sigma = 2.15\)

Part 1: Find the probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

This is the pvalue of Z when X = 25. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{25 - 22.8}{2.15}\)

\(Z = 1.02\)

\(Z = 1.02\) has a pvalue of 0.8461

0.8461 = 84.61% probability that a randomly selected 1-year old boy from the population will have a weight that is less than 25 lbs.

Part 2: Find the probability that the mean weight for a sample of size 10:

Now \(n = 10, s = \frac{2.15}{\sqrt{10}}\). So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{25 - 22.8}{\frac{2.15}{\sqrt{10}}}\)

\(Z = 3.24\)

\(Z = 3.24\) has a pvalue of 0.9994

0.9994 = 99.94% probability that the mean weight for a sample of size 10 1-year-old boys will be less than 25 lbs

Part 3: Explain the difference between Part 1 and Part 2.

In part 2, we use the sampling distribution of the sample means, which has more values closer to the mean due to the smaller standard error, so a higher probability of finding a mean less than 25 lbs.

Answer:

\(18x^{2} + 24x+8\)

Step-by-step explanation:

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

x = 1, y = -15

Step-by-step explanation:

7x + y = -8 ⇒ y = -7x-8

2x + 5y = -7

substitute -7x-8 for y:

2x + 5(-7x-8) = -7

2x - 35x - 40 = -7

-33x - 40  = -7

-33x = -33

x = 1

y = -7x-8 = -15

Answer:

\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

\(\boxed{f(x) = A \sin (B(x + C)) + D}\)

where:

Given values:

Calculate the value of B:

\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)

Substitute the values of A, B C and D into the standard formula:

\(f(x) = 5 \sin (16(x + 0)) + 7\)

\(f(x) = 5 \sin (16x) + 7\)

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)

3 and 2/4 converted as a percent is 3.50%.

Percent means 'out of 100'. Think of any measurement or object split into one hundred equal bits. Each bit is one percent of the whole thing.

Given the question above, we need to convert 3 and 2/4 as a percent.

So,

\(\sf \dfrac{2}{4} =0.50\)

\(3+0.50\)

\(=3.50\%\)

Hence 3 and 2/4 converted as a percent is 3.50%.

Learn more about percentage here:

https://brainly.com/question/12009252

Answer:

75cm²

Step-by-step explanation:

area of parallelogram= base*height

area=15*5=75cm²

Answer:

5pi/12

105 degrees

Step-by-step explanation:

I can help with the first 2 too many answers in one will get my answer deleted

7pi/12  x 180/pi

7x15=105

Hopes this helps please mark brainliest

The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

To know more about quadratic equation visit,

https://brainly.com/question/1214333

#SPJ1

Answer is 26/21

Or 1 5/21

Answer:

b=5

Step-by-step explanation:

2+b=7

Subtract 2 from each side

2+b-2=7-2

b= 5

Answer:

24'

Step-by-step explanation:

the slop aims for the angle in which the 78 can go in: hope this helps!!

Answer:

p < -15

Step-by-step explanation:

\(4 - \frac{1}{6} (p - 3) > 7\)

\( - \frac{1}{6} (p - 3) > 3\)

\(p - 3 < - 18\)

\(p < - 15\)

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

Learn more about null hypothesis at https://brainly.com/question/25263462

#SPJ1

The multiplication of the fraction 2/3 by 3 3/5 is 12/5 or 2 2/5

Given:

2/3 x 3 3/5

change 3 3/5

= {3(5) + 3} / 5

= (15+3) / 5

= 18/5

So,

2/3 x 3 3/5

= 2/3 × 18/5

= (2 × 18) / (3 × 5)

= 36 / 15

= 12/5

= 2 2/5

Therefore, 2/3 x 3 3/5 as a fraction equals 12/5 or 2 2/5

Read more:

https://brainly.com/question/2261275