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3 years ago

C D

Mathematics

1 answer:

denis23 [38]3 years ago

4 0

Answer:

Option (4)

Step-by-step explanation:

Given system of equations is,

y = -x²- 4x - 3

y = 2x + 5

To get the solution of the system of equations algebraically,

2x + 5 = -x²- 4x - 3

Now combine like terms onto one side of the equation.

-x² - (4x + 2x) - (3 + 5) = 0

x² + 6x + 8 = 0

Then factorize the equation,

x² + 4x + 2x + 8 = 0

x(x + 4) + 2(x + 4) =0

(x + 2) (x + 4) = 0

x = -2, 4

Option (4) is the answer.

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The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must

Natalka [10]

Answer: 12 students

Step-by-step explanation:

Let X and Y stand for the number of students in each respective class.

We know:

X/Y = 2/5, and

Y = X+24

We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:

(Y-x)/(X+x) = 1

---

We can rearrange X/Y = 2/5 to:

X = 2Y/5

The use this value of X in the second equation:

Y = X+24

Y =2Y/5+24

5Y = 2Y + 120

3Y = 120

Y = 40

Since Y = X+24

40 = X + 24

X = 16

Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:

(Y-x)=(X+x)

(40-x)=(16+x)

24 = 2x

x = 12

12 students must transfer to the more difficult, very early morning, class.

7 0

3 years ago

last year the cost of a season ticket for a rugby club £370. This year the cost of a season ticket for the club has been increas

Elden [556K]

Answer:

$\frac{80}{370}$ OR $\frac{8}{37}$

Step-by-step explanation:

So first you find the difference between the new cost and the old cost:

450 - 370 = 80

So the increase was 80.

When you write it as a fraction you write the increase ( 80 ) over the starting cost ( 370 ).

Thus the answer becomes $\frac{80}{370}$

But you can always reduce it to its lowest terms thus:

$\frac{8}{37}$

HOPE THIS HELPED

4 0

3 years ago

0.234 is bigger or less than 0.76

Katarina [22]

Answer: 0.234 is less than 0.76

Step-by-step explanation:

0.234 can be rounded out to 0

0.76 can be rounded out to 1

8 0

3 years ago

Read 2 more answers

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard

avanturin [10]

Answer:

There is a 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean \mu and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard deviation of 2503 miles.

This means that $\mu = 33208, \sigma = 2503$ .

What is the probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct?

This is the pvalue of Z when $X = 33208+633 = 33841$ subtracted by the pvalue of Z when $X = 33208 - 633 = 32575$

By the Central Limit Theorem, we have t find the standard deviation of the sample, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{2503}{\sqrt{49}} = 357.57$

X = 33841

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33841 - 33208}{357.57}$

$Z = 1.77$

$Z = 1.77$ has a pvalue of 0.9616

X = 32575

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{32575- 33208}{357.57}$

$Z = -1.77$

$Z = -1.77$ has a pvalue of 0.0384.

This means that there is a 0.9616 - 0.0384 = 0.9232 = 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.

4 0

3 years ago

I need help with both of these someone please help me . you’ll get 20 brainly points !!

Orlov [11]

Answer:

First question: 42cm^2

Second question:

whole figure: 150 cm^2

blue part: 96cm^2

white part:54cm^2

Step-by-step explanation:

Lets do math:

look you gave me alot to do but lets go:

Question 1:

lets find the area of the whole rectangle without the parts taken away.

6*10-60

lets put that away for a little bit and move onto the empty space that we have to take away from the rectangle to get this shape.

im now going to subtract 2 from 10 to get 8. I did this to find out the a length

8*3=24

18 is the area of the shape that we have to subtract from the big rectangle

lets now take out the area we put away for a little while.

60-18=42

so 42 is the area of the first shape.

Question #2:

This problem needs multiple answers so lets get started.

first we need to find the area of the big rectangle.

10*15=150

lets put that away for a little bit.

now lets find the area of the little rectangle

6*9=54

to find the blue we have to subtract 54 from 150 which is 96

so now we have this:

area of the whole figure:150

area of the shaded rectangle inside (white): 54

area of the shaded rectangle (blue): 96

phew that was a lot of typing

the end

8 0

4 years ago