Solve the system, or show that it has no solution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)
20x − 80y = 100
−14x + 56y = −70
(x, y) =

Answer:

Notice that for 3 out of the 4 numbers, there is a relationship between the x and the y coordinate of the number; for 3+i, -2i, -2-4i we have that the real part is larger by 2 from the imaginary part. Thus, the points are on the same line in the imaginary plane; they satisfy x=y+2 or Re{z}=Im{z}+2. However, 2-4i does not satisfy this equation since 2 is not equal to -4+2. Hence, this point does not belong to the line that the other 3 points define.

Step-by-step explanation:

Answer:

£48

Step-by-step explanation:

£72 / 3 = £24

£24 x 2 = £48

Hope this helps c:

Answer:

3/10

Step-by-step explanation:

Total possibilities = 10

favourable possibilities = 3

Answer:

A

Step-by-step explanation:

There is a 1 out of 10 chance that it will land on 2.

There is a 1 out of 10 chance that it will land on 4.

There is a 1 out of 10 chance that it will land on 7.

[tex]\frac{1}{10}\cdot3=\frac{3}{10}[/tex] so the anwser is A.

Answer:

9.48

Step-by-step explanation:

Answer:

the probability that we hit the bullseye at least 100 times is 0.0113

Step-by-step explanation:

Given the data in the question;

Binomial distribution

We find the probability of hitting the dart on the disk

⇒ Area of small disk / Area of bigger disk

⇒ πR₁² / πR₂²

given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1

so we substitute

⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04

Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.

so

X ~ Bin( 2000, 0.04 )

n = 2000

p = 0.04

np = 2000 × 0.04 = 80

Using central limit theorem;

X ~ N( np, np( 1 - p ) )

we substitute

X ~ N( 80, 80( 1 - 0.04 ) )

X ~ N( 80, 80( 0.96 ) )

X ~ N( 80, 76.8 )

So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;

we covert to standard normal variable

⇒ P( X ≥  [tex]\frac{100-80}{\sqrt{76.8} }[/tex] )

⇒ P( X ≥ 2.28217 )

From standard normal distribution table

P( X ≥ 2.28217 ) = 0.0113

Therefore, the probability that we hit the bullseye at least 100 times is 0.0113

B is the answer.

The triangles doesnt creates a SSS,SAS,SAA, scenario.

This triangle isn't ASA because the triangles share the same side but it have different angles that include the side.

Volume of the 3d composite figure is,

(7×6×5)+(7×6×5)/3

= 210+70

= 280 cm³

Relationship between the two volumes,

Volume of the rectangular prism is 3 times the volume of the pyramid.

Answered by GAUTHMATH

Answer:

I was gonna anwer it but somone already did.

Step-by-step explanation:

Answer:

840 mm

Step-by-step explanation:

multiply by 10

Answer:

840 millimetres

Step-by-step explanation:

To convert cm to mm, multiply the value in cm by 10

84cm x 10 = 840 mm

Hope this helps! <3

Answer:

- [tex]\frac{26}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] = -  [tex]\frac{1}{2}[/tex]w - [tex]\frac{2}{3}[/tex]

multiply equation by a common denominator. Let's use 30.  

you get :

6 = -15w - 20

26 = -15w

w = -  [tex]\frac{26}{15}[/tex]

Answer:

y=103.13x - 183.98

Step-by-step explanation:

Given the data :

To obtain the linear equation which best fits the data ; we could perform a linear regression analysis using a technology to obtain a best fit line.

The linear regression Equation obtained by using technology is :

y=103.13x - 183.98

Where ;

Slope = 103.13

Intercept = - 183.98

y = response variable

x = predictor variable

Answer:

A

Step-by-step explanation:

the answer is A just completed it

Answer:

f(h(x)) = 2•(x²-1)² -4•(x²-1)

Step-by-step explanation:

A.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7

Answer:i think its 20

Step-by-step explanation: 20 x 2 is 40 plus 5 is 45

Answer:

✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20

Step-by-step explanation: Algebra.com

Answer:

Yes they ate Equivalent

Step-by-step explanation:

Given the expression

h(x) = - 3x – 1;j(x) = – 7x + 11 ; k(x) = 21.22 – 262 – 11

H(x)•j(x) = (-3x-1)(-7x+11)

H(x)•j(x) = (-3x)(-7x)-3x(11)-1(-7x)(-1)(11)

H(x)•j(x) = 21x²-33x+7x-11

H(x)•j(x) = 21x²-26x-11

This shows that H(x)•j(x) = k(x)

(not a or not b) implies c   <==>   not (not a or not b) or c

so negating gives

not [(not a or not b) implies c]   <==>   not[ not (not a or not b) or c]

which we can simplify somewhat to

not (not (not a or not b)) and not c

(not a or not b) and not c

(not a and not c) or (not b and not c)

not (a or c) or not (b or c)

not ((a or c) and (b or c))

not ((a and b) or c)

Answer:

Step-by-step explanation:

If the triangles given in the picture are similar,

ΔVUT ~ ΔVLM

By the property of similarity of two triangles, their corresponding sides will be proportional.

[tex]\frac{TV}{VM}= \frac{VL}{VU}[/tex]

[tex]\frac{49}{14}=\frac{28}{8}[/tex]

[tex]\frac{7}{2}=\frac{7}{2}[/tex]

True.

Therefore, ΔVUT and ΔVLM will be similar.

Answer:

71, 71, 75, 85, 98, 98, 104, 111, 114, 122, 164

The middle quartile is 98.

The lower quartile is 80

The upper quartile is 112.5

Answer:

Line 3

Step-by-step explanation:

→ Calculate gradient

[tex]\frac{6-3}{4-2} =1.5[/tex]

Answer:

Line 3

Step-by-step explanation:

(0,0) & ( 4 , 6)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

Answer:

1. +30

2. +64

3. 0

4. -3

5. +24

6. +18

7. -48

8. -64

9. +21

10. -30

11. +12

12. 0

13. -4

14. +56

15. +2

Step-by-step explanation:

When multiplying integers:

two negatives = positive

two positives = positive

one negative x one positive = negative

So, if the signs are the same, the answer is positive.

If you have two different signs, the answer is negative.

You multiply the integers like normal.

Anything multiplied by zero = 0.

Anything multiplied by one = itself (just be careful of the sign).

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

Answer:

Step-by-step explanation:

You could have a good credit score and good credit history.

Answer:

less

Step-by-step explanation:

An increase of 20% makes the price 120% of the original price.

A discount of 20% makes the discounted price 80% of the previous price.

Original price: x

20% increase in price: 1.2 * x

20% discount over the raised price: 0.8 * 1.2 * x

Now we multiply the numbers in the last expression and compare the result with x.

0.8 * 1.2 * x = 0.96x

0.96 is less than x, so the customer pays less than the original price.

Answer:

3, 6, 11, 18, 27

Step-by-step explanation:

hope it helps

Answer:

6

Step-by-step explanation:

You can apply the proportion of 9/6 to 4 to get 6:

6*(9/6)= 9

So

4*(9/6) = Length LA

6= Length LA

Answer:

Option C, or [tex]2\frac{2}{3}[/tex]

Explanation:

We can see that the Line FM in the smaller triangle dialates to Line LK in the bigger triangle by the scale factor of:

FM/LK

6/9 or 2/3

So we would know that to find out the value of LA in the bigger triangle we would have to dialate it’s corresponding side FI in the smaller triangle by the same scale factor:

4 * 2/3

=> [tex]2\frac{2}{3}[/tex] = LA

Hope this helps!

Answer:

2.5, 2.05, 0, -5, -15

Step-by-step explanation:

for negative numbers the bigger is worth less

Answer:

[tex]x^{2}[/tex] + 7x + 12

Step-by-step explanation:

The area of a parallelogram is A = bh, where the base is the length.

To solve this, you have to multiply 4 + x and x + 3.

(4 + x)(x + 3)

If you factor this more, it should be equal to:

[tex]x^{2}[/tex] + 3x + 4x + 12.

This simplified is equal to:

[tex]x^{2}[/tex] + 7x + 12.

Answer:

ab = 21

Step-by-step explanation:

[tex](a - b)^2 = (a^2 + b^2 ) - 2ab\\\\4^2 = 58 - 2ab\\\\16 - 58 = - 2ab\\\\- 42 = - 2ab\\\\ab = \frac{-42}{-2} = 21[/tex]

Step-by-step explanation:

Th value of ab is 21

Explanation is in the attachment

hope it is helpful to you ☺️

thank you for giving me a chance to answer your question

Answer:

a) -0.94

b) 0.3472

c) -2.327, 2.327

Step-by-step explanation:

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion is different from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]

A random sample of 551 children aged 6-10 showed that 48% of them play a sport.

This means that [tex]n = 551, X = 0.48[/tex]

(a) Calculate the value of the test statistic used in this test.

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{551}}}[/tex]

[tex]z = -0.94[/tex]

So the answer is -0.94.

(b) Use your calculator to find the P-value of this test.

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least 0.02, which is P(|z| > 0.94), which is 2 multiplied by the p-value of Z = -0.94.

Looking at the z-table, z = -0.94 has a p-value of 0.1736.

2*0.1736 = 0.3472, so 0.3472 is the answer to option b.

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level.

Two-tailed test(test if the mean differs from a value), Z with a p-value of 0.02/2 = 0.01 or 1 - 0.01 = 0.99.

Looking at the z-table, this is z = -2.327 or z = 2.327.