rmined that her father’s age is four less than three times her age. If a represents Marcy’s age, which expression represents her fathers age?

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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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:

See explanation

Step-by-step explanation:

The question is incomplete, as the function is not given.

However, I will give a general rule.

From the question, we understand that the question requires the value of h(3)

Assume:

[tex]h(t) = 20 - 4t[/tex]

Then:

[tex]h(3) = 20 - 4*3[/tex]

[tex]h(3) = 20 - 12[/tex]

[tex]h(3) = 8[/tex]

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:

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

Consecutive terms in this sequence differ by p.

First term: p

Second term: p + p = 2p

Third term: 2p + p = 3p

and so on. It follows that the n-th term satisfies

np = 336

Presumably you meant to say the "sum of the first n terms" is 7224, which is to say

p + 2p + 3p + … + np = 7224

which can be rewritten as

p (1 + 2 + 3 + … + n) = 7224

p (n (n + 1)/2) = 7224

n (n + 1) p = 14,448

Substitute the first equation in the second one and solve for n :

336 (n + 1) = 14,448

n + 1 = 43

n = 42

Now solve for p :

42p = 336

p = 8

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

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:

a)125/291

b) 48/73

Step-by-step explanation:

a) total of yes/total asked

b) total above average yes/ total above average (yes and no)

Answer:

See explanation. You didn't specify on whether the problem asks for a fraction or decimal, so I put both decimal and fraction.

Step-by-step explanation:

First we answer a:

Total amount of people polled is 291. Number of people who wear glasses is: [tex]48 + 51 + 26 = 125[/tex]

Divide to get the proportion: [tex]\frac{125}{291}[/tex] which is also equal to: 0.4295532646

Then we answer b:

b asks for the proportion of all above average readers who wear glasses, so the total number would be: [tex]48 + 25 = 73[/tex]. The number of above average readers who wear glasses is then 48.

We then get the proportion: [tex]\frac{48}{73}[/tex], which is also equal to 0.6575342466.

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

(x, y) = (4,-3)

Step-by-step explanation:

...............

.

.

.

.

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]

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:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

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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Answer:

280

Step-by-step explanation:

7 x 5 x 8

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:

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:

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:

3.31 cups

Step-by-step explanation:

1/× =16/53

16x = 53

x = 53/16

x = 3.3125

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:

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:

I think that d is the answer

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:

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:

D

Step-by-step explanation:

3k +4k+2k+10+6

Collect like terms

9k +16

Answred Gauthmath

Answer:

D 3k + 4k + 2k + 10 +6

Step-by-step explanation:

A 4 + 5k + 10 +6 Combine like terms

5k+ 20  not equal

B 4 + 3k + 2k + 10 +6 Combine like terms

5k +20

C 2k +7 + 10 + 6  Combine like terms

2k + 23

D 3k + 4k + 2k + 10 +6  Combine like terms

9k+ 16