7. Solve -4(6x + 3) = -12(x + 10).

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

x = -2

Step-by-step explanation:

Divide both sides by 3

3 (2x + 5)/3 = 3/3

Simplify

2x + 5 = 1

Subtract 5 from both sides

2x + 5 - 5 = 1 - 5

Simplify

2x = -4

Divide both sides by 2

2x/2 = -4/2

Simplify: 2x/2

Divide the numbers: 2/2 = 1

= x

Simplify: -4/2

Apply the fraction rule: -1/b = -a/b

= - 4/2

Divide the numbers: 4/2 = 2

= -2

x = -2

Answer:

D

Step-by-step explanation:

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).

The coordinate of the new rectangle after the reflection across is given as,

Q' = (-3, -2)

R' = (-1, -4)

S' = (2, -1)

T' = (0, 1)

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

More about the transformation of a point link is given below.

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9514 1404 393

Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

Answer:

11,232,000 license plates are possible.

Step-by-step explanation:

The order in which the symbols are chosen is important(ABC is a different plate than BAC), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

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

In this question:

3 letters from a set of 26.

3 digits from a set of 10. So

[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!} \times \frac{10!}{7!} = 11232000[/tex]

11,232,000 license plates are possible.

Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Answer:

Step-by-step explanation:

Use the change-of-base rule.

Answer:

f(0) = 6

Step-by-step explanation:

Complete question:

The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y

From the pair of coordinates given, hence;

f(1) = 0

f(-10) = 2

f(0) = 6

f(3) = 17

f(-2) = -1

From the following options, this shows that f(0) = 6 is correct

Answer:

f(0) = 6

Step-by-step explanation:

EDGE

Answer:

36 people

Step-by-step explanation:

The expected value E(X) = mean of sample = np

Where, p = population proportion, p = 9% = 0.09

n = sample size, = 400

The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36

36 people

Answer:

I think that d is the answer

Answer:a.3/6

Step-by-step explanation:

Because there’s a total of 12 files in each bag which is 6 in each

Answer:

Step-by-step explanation:

r is the common ratio.

Third term minus first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

Fourth term minus second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

:::::

r²-1 = 48/a₁

a₁ = 6

:::::

a₆ = a₁r⁵ = 1458

(i) The common ratio for the given condition is 3.

ii) The first term of the sequence is 6.

iii) The 6th term of the sequence​ is 1458.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,

It is given that a  is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.

Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.

As the third term minus the first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

The fourth term minus the second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

r²-1 = 48/a₁

a₁ = 6

a₆ = a₁r⁵ = 1458

Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence​ is 1458.

Learn more about the sequence here:

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Answer:

9

Step-by-step explanation:

8 5/6

5/6 is close to 1 so it will round up

8+1 = 9

8 5/6 rounds to 9

Answer:

[tex]9[/tex]

Step-by-step explanation:

Step 1:  Round [tex]8\frac{5}{6}[/tex] to the nearest whole number

In order to round up, the fraction needs to be either 1/2 or greater than 1/2.  In our case, it is greater than half therefore we will round up to 9.

Answer:  [tex]9[/tex]

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

Answer:

76 students scored above 80%.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.

This means that [tex]\mu = 67, \sigma = 8.1[/tex]

Proportion above 80:

1 subtracted by the p-value of Z when X = 80, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 67}{8.1}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

Out of 1390 students:

0.0548*1390 =  76

76 students scored above 80%.

Answer:

D. Rotation reflection is the right answer

Answer:

Rotation, reflection

Step-by-step explanation:

R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.

(It's kind of weird to explain) Sorry if that was confusing.

Answer:

2.7°C.

Step-by-step explanation:

If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.

Proof:

-7.4

-4.7

--------

2.7

Answer: attached below is the missing p chart

a)  0.07133

b)  2

c)  0.098

d) 0.045

Step-by-step explanation:

sample size = 150 castings

number of periods = 10

a) Determine the center Line of the control chart

( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10

mean = 0.07133

standard deviation = 0.01335

b) Determine the value of Z to be used

Given that we are using 2sigma limits .

the value of Z to be used = 2

c) Upper limit control

= mean value +  z-value * std

= 0.0713 + 2*0.01335 =  0.098

d) Lower Control Limit

= mean value - z-value * std

= 0.0713 - 2*0.01335 = 0.045

Answer:

13.9 (if x is the Hypotenuse)

Step-by-step explanation:

which one is the Hypotenuse (the side opposite of the 90 degree angle) ?

because that determines the calculation.

if x is the Hypotenuse then Pythagoras looks like this

x² = 7² + 12² = 49 + 144 = 193

x = sqrt(193) = 13.9

if 12 is the Hypotenuse, then it looks like this

12² = 7² + x²

144 = 49 + x²

95 = x²

x = sqrt(95) = 9.75

Answer:

15.072

Step-by-step explanation:

Pls Mark Brainiest okay

Answer:

2.88 pi or approximately 9.0432 cm^2

Step-by-step explanation:

The area of a semicircle is 1/2 the area of a circle

A = 1/2 pi r^2

A = 1/2 pi ( 2.4)^2

A = 2.88 pi cm^2

If we use 3.14 as an approximation for pi

A = 2.88 * 3.14

A =9.0432 cm^2

(A)

Step-by-step explanation:

This system of equations will no solution if they have the same slope and only differ in the y-intercept values. So let's rewrite the two equations into their slope-intercept forms:

[tex]y = \frac{3}{h-2}x + 5[/tex]

[tex]y = \frac{8}{h}x + \frac{5}{h}[/tex]

For them to have no solution, their slopes must equal each other:

[tex]\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16[/tex]

or

[tex]h = \dfrac{16}{5}[/tex]

Putting this value into our system of equations, we get

[tex]y = \frac{5}{2}x + 5[/tex]

[tex]y = \frac{5}{2}x + \frac{25}{16}[/tex]

This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.

Answer:

Step-by-step explanation:

The formula to find arc length is

[tex]AL=\frac{\theta}{360}*\pi d[/tex] where theta is the measure of the central angle and d is the diameter. If we are dealing with a semicircle, the measure of the central angle is 180 degrees. Filling in:

[tex]AL=\frac{180}{360}*\pi (18)[/tex] which simplifies a bit to

[tex]AL=\frac{1}{2}*\pi (18)[/tex] and a bit more to

AL = 9π. That answer is obviously in terms of π; if you need it in terms of whatever your measurement is (feet, inches, cm, etc.) the answer would be, rounded to the nearest tenth, 28.3 units

Step-by-step explanation:

Actually, it tells you exactly what to do.

First, translate, i.e., move over, the coordinates up by 3:

[tex](1, 4)\rightarrow (1+3, 4+3) = (4, 7)[/tex]

Then reflect this point about the x-axis and to do this,

[tex](x, y) \rightarrow (x, -y)[/tex]

[tex](4, 7) \rightarrow (4, -7)[/tex]

Answer:

The answer is 1/9 and 1/2

Answer:

it's true

Step-by-step explanation:

To factorise you need to work out a number that add up to the number with a letter and multiply to the last number

Answer:

(r/s)(6) = r(6)/s(6) = 3(6)-1 / 2(6)+1 = 18-1 / 12+1 = 17/3

So basically the first one is the correct answer.

Step-by-step explanation:

I hope this helped and please kindly mark Brainliest. Thank You <3

Answer:

x = 11 * sqrt(2)

y = 11

Step-by-step explanation:

Use the ratios of the lengths of the sides of a 45-45-90 triangle.

y = 11

x = 11 * sqrt(2)