Solve the system of equations. \begin{aligned} & -10x+3y = 5 \\\\ & x=y-4 \end{aligned} ​ −10x+3y=5 x=y−4 ​

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?

Answer:

P( X' ∩ Y' ) = 0.205

Step-by-step explanation:

Let X is the event that the customer insures more than one car.

Let X' is the event that the customer insures exactly one car.

Let Y is the event that customer insures a sport car.

Let Y' is the event that customer insures not a sport car.

From the given information we have

70% of customers insure more than one car.

P(X) = 0.70

20% of customers insure a sports car.

P(Y) = 0.20

Of those customers who insure more than one car, 15% insure a sports car.

P(Y | X) = 0.15

We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

P( X' ∩ Y' ) = ?

Which can be found by

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

From the rules of probability we know that,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )    (Additive Law)

First, we have to find out P( X ∩ Y )

From the rules of probability we know that,

P( X ∩ Y ) = P(Y | X) × P(X)       (Multiplicative law)

P( X ∩ Y ) = 0.15 × 0.70

P( X ∩ Y ) = 0.105

So,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )

P( X ∪ Y ) = 0.70 + 0.20 - 0.105

P( X ∪ Y ) = 0.795

Finally,

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

P( X' ∩ Y' ) = 1 - 0.795

P( X' ∩ Y' ) = 0.205

Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

Answer:

This is because it contains the PAASCHE  and the LASPEYRES index, the index satisfies the time reversal test.

Step-by-step explanation:

Answer:

When you say that two numbers are relatively prime, it means that both numbers do not have a common factor except 1. Stephen is incorrect because 38 and 40 are both multiples of 2.

Answer:

Prime numbers are number that has its factors to be 1 and itself

38 and 40 are not prime because they have more than one factor

38 = { 1 , 2 , 19 , 38} and

40 = { 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 }

This make his statement incorrect.

Hope this helps.

Answer:

38 units

Step-by-step explanation:

We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.

Thus, see attachment below for the number of units of each length of the figure that we have counted.

The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38

Perimeter of the shaded figure = 38 units

Answer:

Negative Coterminal: -5π/4

Positive Coterminal: 11π/4

Step-by-step explanation:

The easiest way to find specific (not infinite) coterminal values is to ±2π. When you subtract 2π, you will get a negative coterminal. When you add 2π, you will get a positive coterminal. Keep in mind though that a tan∅ or cot∅ only needs ±π, not ±2π.

Answer:

a. x = 4

b. x = 17.5

Step-by-step explanation:

a. 5x/2 + 1 = 11

5x/2 = 10

5x = 20

x = 4

b. 2x/7 - 3 = 2

2x/7 = 5

2x = 35

x = 35/2

Answer:

a) x = 4

b) x = 17.5

Step-by-step explanation:

Isolate x variable to find the value.

5x/2 + 1 = 11

5x/2 = 10

5x = 20

x = 4

2x/7 - 3 =2

2x/7 = 5

2x = 35

x = 17.5

Answer:

There are 8 sections and 5 of them are less than 7 so the answer is 5/8 = 62.50%.

Answer:

62.5 percent

Step-by-step explanation:

there are a total of 8 options (2,3,4,5,6,7,8,9) the spinner could land on. 5 of these options are less than 7 (6,5,4,3,2)

5/8 is also 62.5 percent

Answer:

x^2 - 10x

Step-by-step explanation:

2x^2 - 4x - x^2 +6x

You subtract x^2 from 2x^2 and you get x^2

Then you add 6x and 4x together and get 10x

So then you have x^2 - 10x

(plus I took the test and this was the correct answer.)

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached.

From the diagram, it can be seen that point U is the midpoint of T and V. This means that TU = UV

Given TU=8x+11 and UV=12x−1

8x+11 = 12x -1

8x-12x = -1-11

-4x = -12

x = 3

Since TU = 8x+11

TU = 8(3)+11

TU = 24+11

TU = 35

Also UV = 12x-1

UV = 12(3)-1

UV = 36- 1

UV = 35

TV = TU+UV

TV = 35+35

TV = 70

Step-by-step explanation:

1. 35 + 65

2. y - 14

3. (6 x s) - 3

4. 10(x+8.5).. 6-p

Answer:

x = 3.6

Step-by-step explanation:

By the Postulate of intersecting chords inside a circle.

[tex]x \times 5 = 3 \times 6 \\ 5x = 18 \\ x = \frac{18}{5} \\ x = 3.6 \\ [/tex]

Answer:

9-x=3

x=9-3=6

x=6

9-6=3

Answer:

B,C,D,F

Step-by-step explanation:

i took the test and i got it right!!!!

Answer:

Option 3 or 4 is correct depending on the first term and common ratio

aₙ= a₁rⁿ⁻¹

Option 3 in case the first term is 1/2 and common ratio is 972

Option 4 in case the first term is 972 and common ratio is 1/2

Answer:

its D & the next is 7.594

Step-by-step explanation:

just got it on edge2020

Answer:

7.5 pounds

Step-by-step explanation:

30/4=7.5 :)

Answer:

A≈166.45 in^2

Step-by-step explanation:

A=a^2+2a√(a2/4+h^2)

a = base = 8 in

h = height = 5 in

A = 8^2+16√(8^2/4+5^2) = 166.449... in^2

224

Step-by-step explanation:

because my teacher said it was right

Answer:

The feature that makes the sample representative of the population is the choice of the contact mode (telephone landline or cellular phone line) with proportions representative of the ages of the subjects to be represented.

Step-by-step explanation:

The feature that makes the sample representative of the population is the choice of the contact mode (telephone landline or cellular phone line) with proportions representative of the ages of the subjects to be represented.

Older people tend to manage with landline phones, while younger people tend to have no landline phones but cell phone. Both groups must be proportionally represented to be representative of an adult population (18 years or older).

Answer:

It means in the middle of things, and Homer uses it in the Odyssey at the beginning of the epic because the story starts after the  Trojan War but before Ulysses gets back home.

Explanation:

Media res is a Latin phrase that means a situation where the narration starts in the middle of the story. In simple words, it means when a speaker talks about a story, starting with the middle of the plot but before the ending.

Likewise, Homer used this technique in his epic narrative story The Odyssey when he starts the story after the Trojan War and in the middle of the journey bur before the culmination of the story. Media res allows the middle of the plot to be the starting point and then gradually go back and forth in the narration between the past and the current/ situation.

Thus, the correct answer is the last or fourth option.

Answer:

1) A = 0.79

B = 0.4708

2) CI = (0.7728, 0.8072)

3) CI = (0.4481, 0.4935)

b. It appears that the proportion of adults who feel this way in country A is more than those in country B.

Step-by-step explanation:

1) Sample proportions for both Population A and B

For country A:

Sample size,n = 1500

Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]

For Country B:

Sample size,n = 1302

Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]

2) Confidence interval for country A:

Given:

Mean,x = 1185

Sample size = 1500

Sample proportion, p = 0.79

q = 1 - 0.79 = 0.21

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]

[tex] CI = (0.7728, 0.8072) [/tex]

3) Confidence interval for country A:

Given:

Mean,x = 613

Sample size = 1302

Sample proportion, p = 0.4708

q = 1 - 0.4708 = 0.5292

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]

[tex] CI = (0.4481, 0.4935) [/tex]

From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.

Option B is correct.

Answer: 34 beverages

Step-by-step explanation:

We can use system of equations to find the amount of adult beverages sold to women. Let's use x for women and y for men.

Equation 1

1.25x+2y=470.5

Equation 2

x+y=248

We can use elimination method to cancel out the y so we can find the about for women, since that is what the question is asking. To do so, we must multiply the entire second equation by 2 so both y equal.

1.25x+2y=470.5

2x+2y=496

Now, we can subtract both equations to cancel out 2y.

-0.75x=-25.5           [divide both sides by -0.75]

x=34

There were 34 adult beverages sold to women.

Answer:

0.989

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.

This means that [tex]p = 0.53[/tex]

6 randomly selected graduates

This means that [tex]n = 6[/tex]

Probability that at least one finds a job in his or her chosen field within a year of graduating:

Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]

Answer:

C =81.64 cm

Step-by-step explanation:

The circumference is given by

C = 2* pi *r

The radius is 13

C = 2 * 3.14 * 13

C =81.64 cm

Answer:

[tex]= 81.64cm \\ [/tex]

Step-by-step explanation:

[tex]c = 2\pi \: r \\ = 2 \times 3.14 \times 13 \\ = 81.64cm[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The 95% confidence interval for the difference between means is (-25.5, -14.7).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1 (Method 1), of size n1=63 has a mean of 52.2 and a standard deviation of 15.92.

The sample 2 (Method 2), of size n2=93 has a mean of 72.3 and a standard deviation of 17.96.

The difference between sample means is Md=-20.1.

[tex]M_d=M_1-M_2=52.2-72.3=-20.1[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{15.92^2}{63}+\dfrac{17.96^2}{93}}\\\\\\s_{M_d}=\sqrt{4.023+3.468}=\sqrt{7.491}=2.74[/tex]

The critical t-value for a 95% confidence interval is t=1.975.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=1.975 \cdot 2.74=5.41[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = -20.1-5.41=-25.5\\\\UL=M_d+t \cdot s_{M_d} = -20.1+5.41=-14.7[/tex]

The 95% confidence interval for the difference between means is (-25.5, -14.7).

Answer:

Step-by-step explanation:

Answer:

n³ + 4n² - 8n -9

Step-by-step explanation:

Just combine like terms while you add the 2 expressions together.

Answer:

(x+9)/(8x+4)

Step-by-step explanation:

Answer:

As Bill's sales is £25400, which is greater than £25000, he achieved his target.

Step-by-step explanation:

Cost of each laptop = £400

lets calculate for 40 laptops first

Given, he sold 40 of these at 30% profit

30% of cost price = 30% of  £400  = 30/100 * 400 = 120

Therefore, selling price of these laptops =  £400  +  £120 =  £520

Total sales generated from selling 40 of these laptop = 40*£520

= £520 =£20,800  

lets calculate for 10 laptops now

Given, he sold 10 of these at 15% profit

15% of cost price = 15% of  £400  = 15/100 * 400 = 60

Therefore, selling price of these laptops =  £400  +  £60 =  £460

Total sales generated from selling 10 of these laptop = 10*£460

= £4600

Total sales generated from selling all the 50 laptop =  

Total sales generated from selling 40 of these laptop + Total, sales generated from selling 10 of these laptop = £20,800  + £4600 = £25,400

Target for Bill = £25000

As his sales is £25400, which is greater than £25000, he achieved his target.

Answer:

1937.98

Step-by-step explanation:

In the given question, to find the value to be added per year we will use the formula

P= A. r/n/ (1 +r/n)ⁿ - 1

Here A = 50,000

r (rate of interest) = 5 % or 0.05.

n = 1

t = 17

P = value deposit per year

therefore, P = (50,000 X 0.05)/ (1 +0.05)¹⁷ - 1

P =   2500 / 2.29- 1

= 1937.98 $.

therefore, person has to deposit 1937.98 $ per month.

Answer:  a) base = 1 ft          b) height = 4 ft

Step-by-step explanation:

Set this up as a right triangle where base = x, height = 2x + 2, and hypotenuse (length of the ladder) = 13

Use Pythagorean Theorem to create a quadratic equation, factor, then apply the Zero Product Property to solve for x.

(x)² + (2x + 2)² = 13²

x² + 4x² + 8x + 4 = 169

        5x² + 8x - 165 = 0

       (5x + 13) (x - 1) = 0

       x = -13/5   x = 1

We know that distance cannot be negative so disregard x = -13/5.

The only valid answer is x = 1

base = x  --> x = 1

height = 2x + 2    --> 2(1) + 2 = 4

Answer:

446.153846154 per week

Step-by-step explanation:

Answer:

The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

The mean and standard deviation of the sampling distribution of sample proportion are:

[tex]\mu_{\hat p}=p=0.07\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.07(1-0.07)}{492}}=0.012[/tex]

Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:

[tex]P(|\hat p-p|>0.03)=P(|\frac{\hat p-p}{\sigma_{\hat p}}|>\frac{0.03}{0.012})[/tex]

                           [tex]=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090[/tex]

Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.