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3 years ago

At a concert

Mathematics

1 answer:

Paladinen [302]3 years ago

7 0

Answer:

Each child ticket costs £2

Each adult ticket costs £5

Step-by-step explanation:

Let's define:

C = cost of a child ticket

A = cost of an adult ticket.

We know that:

"3 adult and 4 child tickets cost £23"

This can be written as:

3*A + 4*C = £23

"1 adult and 5 child tickets cost £15"

This can be written as:

1*A + 5*C = £15

Then we have the system of equations:

3*A + 4*C = £23

1*A + 5*C = £15

To solve it, we start by isolating one of the variables in one of the equations:

Let's isolate A in the second equation:

A = £15 - 5*C

Now let's replace this in the first equation:

3*( £15 - 5*C) + 4*C = £23

Let's solve this for C

£45 - 15*C + 4*C = £23

£45 - 11*C = £23

£45 - £23 = 11*C

£22 = 11*C

£22/11 = £2 = C

Each child ticket costs £2

And with the equation:

A = £15 - 5*C we can find the price of an adult ticket if we replace the value of C by £2

A = £15 - 5*£2 = £5

Each adult ticket costs £5

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Triangle Q M N is shown. The length of Q M is 18, the length of M N is 17, and the length of Q N is 20. Law of cosines: a2 = b2

kvasek [131]

Answer:

53°

Step-by-step explanation:

17² = 18² + 20² - 2(18)(20) cos Q

289 = 324 + 400 - 720 cos Q

289 = 724 - 720 cos Q

-435 = -720 cos Q

0.6042 = cos Q

$cos^{-1} (0.6042) = Q$

Q = 52.83

3 0

3 years ago

Use the quadratic formula to solve the equation x^2-7x-6=0

olganol [36]

Answer:

$\frac{7\pm\sqrt{73}} {2}$

Explanation:

We have been given with the quadratic equation $x^2-7x-6=0$

We have general formula to find the roots of a quadratic equation first we find the discriminant with formula

$D=b^{2}-4ac$

and after that to find the variable suppose x we have the formula

$x=\frac{-b\pm\sqrt{D}} {2a}$

And general quadratic equation is

$ax^2+bx+c=0$

On comparing the given quadratic equation with genral quadratic equation we will have values

a=1, b=-7 and c=-6

After substituting these values in the formula we will get

$D=(-7)^2-4(1)(-6)={73}$

After substituting in the formula to find x we will get

$\frac{-(-7)\pm\sqrt{73}} {2}= \frac{7\pm\sqrt{73}} {2}$

4 0

3 years ago

Read 2 more answers

This was useless because a selected the exact answers and they where all wrong :(

ivanzaharov [21]

Answer:

srry

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $35 c

MrRissso [65]

Answer:

There is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 35,000 dollars per year

Sample mean, $\bar{x}$ = 34,700 dollars per year

Sample size, n = 100

Alpha, α = 0.10

Population standard deviation, σ = 3,500 dollars per year

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}$

We use one-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571$

Now, $z_{critical} \text{ at 0.10 level of significance } = -1.28$

Since,

$z_{stat} > z_{critical}$

We fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.

3 0

3 years ago

A psychologist obtains a random sample of 2020 mothers in the first trimester of their pregnancy. The mothers are asked to play

leva [86]

Answer:

First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.

In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.

According to the problem, the null hypothesis must be: $H_{o} : u = 100$ ; because it says that 100 is the normal mean that is used.

The alternative hypothesis must be: $H_{a} : u > 100$ ; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.

Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: $Z=\frac{x-u}{\frac{o}{\sqrt{n} } }$ ; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.

Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.

Applying all values to the formula: $Z=\frac{104.3 - 100}{\frac{14}{\sqrt{20} } } = \frac{4.3}{\frac{14}{ 4.5} }=\frac{4.3}{3.1}=1.4$

Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.

<em>In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.</em>

Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).

5 0

3 years ago