All categories

2 years ago

A group of students are going on a trip and the trip costs $36.50 per student which

Mathematics

1 answer:

goblinko [34]2 years ago

7 0

Answer:

$18

Step-by-step explanation:

Let's subtract the lunch from the trip total to get the remainding cost!

36.50 - 9.50 = $27

Now let's set up an equation to figure out the amount of the entrance ticket and the gift coupon!

let's have x = the entrance ticket

27 = x + 1/2(x) -----------> 1/2 is next to x, because the gift coupon is 1/2, or 50% of the entrance ticket! Now solve for x!

27 = 3/2x

(2/3) 27 = 3/2x (2/3)

18 = x, so the entrance ticket is $18!

You might be interested in

Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^3

Paladinen [302]

Answer:

see explanation

Step-by-step explanation:

Given

V = $\frac{4}{3}$ πr³

Multiply both sides by 3 to clear the fraction

3V = 4πr³ ( divide both sides by 4π )

$\frac{3V}{4\pi }$ = r³ ( take the cube root of both sides )

r = $\sqrt[3]{\frac{3V}{4\pi } }$

6 0

3 years ago

A driver's education course compared 1,500 students who had not taken the course with 1,850 students who had. Of those students

aivan3 [116]

Answer:

P-value is less than 0.999995 .

Step-by-step explanation:

We are given that a driver's education course compared 1,500 students who had not taken the course with 1,850 students who had.

Null Hypothesis, $H_0$ : $p_1 = p_2$ {means students who took the driver's education course and those who didn't took have same chances to pass the written driver's exam the first time}

Alternate Hypothesis, $H_1$ : $p_1 > p_2$ {means students who took the driver's education course were more likely to pass the written driver's exam the first time}

The test statistics used here will be two sample Binomial statistics i.e.;

$\frac{(\hat p_1 - \hat p_2)-(p_1 - p_2)}{\sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } }$ ~ N(0,1)

Here, $\hat p_1$ = No. of students passed the exam ÷ No.of Students that had taken the course

$\hat p_1$ = $\frac{1150}{1850}$ Similarly, $\hat p_2$ = $\frac{1440}{1500}$ $n_1$ = 1,850 $n_2$ = 1,500

Test Statistics = $\frac{(\frac{1150}{1850} -\frac{1440}{1500})-0}{\sqrt{\frac{\frac{1150}{1850}(1- \frac{1150}{1850})}{1850} + \frac{\frac{1440}{1500}(1- \frac{1440}{1500})}{1500} } }$ = -27.38

P-value is given by, P(Z > -27.38) = 1 - P(Z > 27.38)

Now, in z table the highest critical value given is 4.4172 which corresponds to the probability value of 0.0005%. Since our test statistics is way higher than this so we can only say that the p-value for an appropriate hypothesis test is less than 0.999995 .

6 0

3 years ago

The mean of this data set is 9. What number is missing?<br><br> 11,20,_,3,1

kherson [118]

Let the missing number be x

Mean is the total sum of data over the number of data therefore,

(11+20+x+3+1) / 5 = 9
Then simplify
(35 + x) / 5 = 9
Then multiply 5 to both sides
35 + x = 45
Then subtract 35 to both sides to find x
X= 10

Hope this helps!

7 0

2 years ago

Calculate the marked price(original price)if after 20% discount, the price of an article.

Elina [12.6K]

Answer: An article was sold at a 20% discount, at Rs. 400. What was its marked price?

Let M denotes the required marked price of the given article.

Hence from above data we get following relation,

(1 - 20/100)*M = 400

or (4/5)*M = 400

or M = (5/4)*400 = 500 (Rs) [Ans]

Step-by-step explanation:

4 0

3 years ago

4x^2 y+8xy'+y=x, y(1)= 9, y'(1)=25

jarptica [38.1K]

Answer with explanation:

$\rightarrow 4x^2y+8x y'+y=x\\\\\rightarrow 8xy'+y(1+4x^2)=x\\\\\rightarrow y'+y\times\frac{1+4x^2}{8x}=\frac{1}{8}$

--------------------------------------------------------Dividing both sides by 8 x

This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.

Integrating Factor

$=e^{\int \frac{1+4x^2}{8x} dx}\\\\e^{\log x^{\frac{1}{8}+\frac{x^2}{2}}\\\\=x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}$

Multiplying both sides by Integrating Factor

$x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\times [y'+y\times\frac{1+4x^2}{8x}]=\frac{1}{8}\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\\\\ \text{Integrating both sides}\\\\y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\frac{1}{8}\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx \\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=-[x^{\frac{9}{8}}]\times\frac{ \Gamma(0.5625, -x^2)}{(-x^2)^{\frac{9}{16}}}\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=(-1)^{\frac{-1}{8}}[ \Gamma(0.5625, -x^2)]+C-----(1)$

When , x=1, gives , y=9.

Evaluate the value of C and substitute in the equation 1.

6 0

3 years ago