What is the value of this expression?

Masja [62]

Answer: 80

Step-by-step explanation:

First you split the shape into simple parts, and think about the measurements when you do so. Although you can't see my work, the way I split it is a rectangle that measures 8 by 4, and a rectangle that measures 8 by 6. You find the answer to these separately (32 and 48) and add them together (80).

4 0

3 years ago

When visiting his parents, Tyler drives at an average speed of 42 km/h through urban areas and at an average speed of 105 km/h o

MaRussiya [10]

Answer:

168 km

Step-by-step explanation:

Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:

x/42 +y/105 = 2.5

x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours

Multiplying the first equation by 210, we have ...

5x +2y = 525

Multiplying the second equation by 420, we get ...

15x +7y = 1680

Subtracting 3 times the first of these equations from the second, we have ...

(15x +7y) -3(5x +2y) = (1680) -3(525)

y = 105

Putting this into the very first equation, we get ...

x/42 + 105/105 = 2.5

x/42 = 1.5 . . . . . . subtract 1

x = 63 . . . . . . . . .multiply by 42.

The total distance to Tyler's parents' house is ...

63 km + 105 km = 168 km

4 0

3 years ago

A random sample of 40 college students has a mean earnings of $3120 over the summer months. Assume the population standard devi

PSYCHO15rus [73]

Answer:

A normal distribution or z-test is used to construct a confidence interval.

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = $3120

Sample size, n = 40

Population standard deviation, σ = $677

The distribution of earnings of college is a normal distribution.

Conditions:

Since we are given the population standard deviation and the the sample size is also greater than 30.

Conclusion:

Thus, we use a normal distribution or z-test to construct a confidence interval.

4 0

4 years ago

6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP

adelina 88 [10]

Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = $360^{o}$ - $324^{o}$

= 0 $36^{o}$

Sum of angles in a triangle = $180^{o}$

<P + <Q + <S = $180^{o}$

048° + 0 $36^{o}$ + <S = $180^{o}$

$84^{o}$ + <S = $180^{o}$

<S = $180^{o}$ - $84^{o}$

= $96^{o}$

<S = $96^{o}$

Applying the Sine rule,

$\frac{y}{Sin P}$ = $\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin P}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin 48^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{y}{0.74314}$ = $\frac{17}{0.99452}$

⇒ y = $\frac{12.63338}{0.99452}$

= 12.703

y = 12.70 km

$\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{x}{Sin 36^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{x}{0.58779}$ = $\frac{17}{0.99452}$

⇒ x = $\frac{9.992430}{0.99452}$

= 10.0475

x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

6 0

3 years ago

What is the relation between the variables in the equation x^4/y=7?

makkiz [27]

Answer:

So, the relation between variables are

$y=\frac{x^4}{7}$

Step-by-step explanation:

We are given

$\frac{x^4}{y}=7$

Since, we have to find relation between variables

so, we can solve for y

$\frac{x^4}{y}=7$

Firstly, we will multiply both sides by y

$\frac{x^4}{y}\times y=7\times y$

we can simplify it

$x^4=7\times y$

we can isolate y

so, we can divide both sides by 7

so, we get

$y=\frac{x^4}{7}$

8 0

3 years ago