r²-6 r+9 can be factorized to give an expression of the form (r+a)²,
where a is an integer.
Work out the value of a.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The filling in of the formula for the n-th term is pretty straightforward. The attachment shows how simple it is.

The 7th term is found by evaluating the expression for n=7.

  a₇ = 192

Answer:

10 16

Step-by-step explanation:

when x= 0 h(x)=2x²-3x+10

⇒ h(0)=2*0²-3*0+10=10

when x= 4 h(x)=[tex]2^{x}[/tex]

⇒ h(4)=[tex]2^{4}[/tex]=16

The value of the given piecewise function at [tex]x=0[/tex] is [tex]h(0)=10[/tex] and the value of the function at [tex]x=4[/tex] is [tex]h(4)=16[/tex].

Important information:

         [tex]h(x)=\begin{cases}3x-4, &x < 0 \\ 2x^2-3x+10, &0\leq x < 4 \\ 2^x, & x\geq 4\end{cases}[/tex]

The function for [tex]x=0[/tex] is [tex]h(x)=2x^2-3x+10[/tex].

[tex]h(0)=2(0)^2-3(0)+10[/tex]

[tex]h(0)=10[/tex]

The function for [tex]x=4[/tex] is [tex]h(x)=2^x[/tex].

[tex]h(4)=2^4[/tex]

[tex]h(4)=16[/tex]

Therefore, the required values of the piecewise function are [tex]h(0)=10[/tex] and [tex]h(4)=16[/tex].

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Answer:

y = 4x - 1

Step-by-step explanation:

y = mx + b

Here m is slope and b is y-intercept

m = 4;  b = -1  

y = 4x - 1

x=6 is the answer to 8-6/x=5+12/x

Answer:

0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

3.5% of the people in the area where a large wedding is to be held are pollotarian.

This means that [tex]p = 0.035[/tex]

300 guests

This means that [tex]n = 300[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.035[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.035*0.965}{300}} = 0.0106[/tex]

What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals?

This is 1 subtracted by the pvalue of Z when X = 0.05. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.05 - 0.035}{0.0106}[/tex]

[tex]Z = 1.41[/tex]

[tex]Z = 1.41[/tex] has a pvalue of 0.9207

1 - 0.9207 = 0.0793

0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals

Answer:7.93%

Step-by-step explanation:

Answer:The person is 5feet, 6inches Note: 12 inches= 1 foot, so 6 inches= 1/2 a feet and 6 inches= .5 feet

Step-by-step explanation:

Answer:

78.5

Step-by-step explanation:

.....ur welcome.........

3.14×5²

Answer:

C. 31.4

Step-by-step explanation:

To find circumference, you need to use πd. Or just pi times whatever the circumference is. Hope this helped you!!!

Answer:

50°

Step-by-step explanation:

Subtract 360° from 410°

50° is positive, less than 360°, and is a coterminal of 410°

Answer:

90 degree angle i think

Step-by-step explanation:

Hope this helps you

9514 1404 393

Answer:

  b = 90°

Step-by-step explanation:

Angles a, b, c total 180°, and angles a and c are complementary, meaning they total 90°. The measure of angle b is ...

  b = 180° -90°

  b = 90°

__

All of the angle measures are ...

  a = 90° -c = 90° -56° = 34°

  b = 180° -90° = 90°

  c = given = 56°

  d = given = 124°

  e = c = 56°

Answer:

Step-by-step explanation:

Step-by-step explanation:

X1 + X2 = 73.80

Assumption : X1 = 44.25

X2 = unknown angle = 29.55

Answer:

87 m²

Step-by-step explanation:

The picnic area is the white inner rectangle, while the courtyard is the outer pink rectangle.

The area of the courtyard available for use = area of the pink rectangle - area of the white rectangle

✔️Area of the courtyard (pink rectangle) = L*W

L = 13 m

W = 7 m

Area of pink rectangle = 13*7 = 91 m²

✔️Area of the picnic (white rectangle) = L*W

L = 4 m

W = 1 m

Area = 4*1 = 4 m²

✅Area available in the courtyard for use = 91 m² - 4 m² = 87 m²

I’ll answer, but wait, do I send a picture of my work? or not? It says I have to make a table of values, so

Answer:

B 125.6

Step-by-step explanation:

We can use the formula for the circumference to solve.

C=2[tex]\pi[/tex]r

C=2[tex]\pi[/tex](20)

C=(6.28)(20)

C=125.6

The Area of triangle represented using inequality is A ≤  48.67 [tex]ft^{2}[/tex].

The area of a triangle is half the product of its base and height.

i.e., Area of triangle= [tex]\frac{1}{2} * b* h[/tex]

Given, b= 6.2 feet and h= 15.7 feet

Area of triangle= [tex]\frac{1}{2} * b* h[/tex]

                          = 0.5 x 6.2 x 15.7

                          = 48.67 [tex]ft^{2}[/tex]

The inequality will be: Area of triangle, A≤  48.67 [tex]ft^{2}[/tex]

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Answer:

We say that a function is increasing on an interval if the function values increase as the input values increase ...

Step-by-step explanation:

Answer:

I don't understand but I believe the answer is 16y^8

Step-by-step explanation:

Answer: (4 x a x a x a x a) x (4 x a x a x a x a)

HOPE THIS HELPS

Answer:

Step-by-step explanation:

81 = m/9

Divide both sides by 9

9 = m

h ÷ 3 = 12

h = 12/3 = 4

In this way you have to solve the other questions

Answer:

x ≥ -2

Step-by-step explanation:

my teacher went over this with us

Answer:

1/23

Step-by-step explanation:

This honestly super easy, but here it is!

12/23+(-11/23)

With no negatives, it would be 12/23+11/23 and the answer would be 23/23 AKA 1, because 12+11=23.

With negatives though, you always have to subtract the number itself from the positive number if the number is negative. Here we will subtract 11 from 12, which brings us to 1/23.

Hope this helped!

I wouldn't mind a 5-star rating, a thanks, or even a Brainliest :D

-ChocoChocoCho

Answer:

Hello your question has some missing information attached below is the missing information

answer :

i) ( 0.158 , - 1.018 )

ii)  the difference in expected earnings can be computed as

( [tex]X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}[/tex]

Step-by-step explanation:

i) Construct a 95% confidence interval ( between Juanita and Molly )

Expected difference in earnings = ( X[tex]_{6}[/tex][tex]_{,A}[/tex] - X[tex]_{6.B}[/tex]) = [tex]\beta _{0}[/tex]= ( [tex]\beta + \beta _{6}[/tex] )

∴ 95% confidence interval

-0.43 ± 1.96 * 0.30 = [ -0.43 ± 0.588 ] =  ( 0.158 , - 1.018 )  ( hence confidence interval at 95% = 1.96 )

ii) Construct a 95% confidence interval ( between Juanita and Jennifer )

Juanita is a student from the south and Jennifer is a student from Midwest

therefore the difference in expected earnings can be computed as

( [tex]X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}[/tex]

therefore a 95% confidence interval can be calculated with the above regression model.

Answer: The answer would be 3/7.

Step-by-step explanation:

Answer

m =18.4 minutes

Step-by-step explanation:

220 = 700 x  (0.939)^m

220/700 = (0.939)^m

m = Log(220/700) / Log(0.939)

m =18.4 minutes

Answer: the answer would be 18.4 minutes

Step-by-step explanation:

The experimental probability that Jason will roll a 2 is 3/14.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, Jason rolls the die 14 times.

From the given table,

Number of favorable outcomes = 3

Total number of outcomes = 14

So, the probability = 3/14

Therefore, the experimental probability that Jason will roll a 2 is 3/14.

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Answer:

24

Step-by-step explanation:

30% of the pie chart is pizza. 30% of 80 = 0.3 * 80 = 24

Answer:

The answer is 24 students

Step-by-step explanation:

The pizza section of the pie chart is 30% and the total amount of students is 80 so you just have to find 30% of 80. You find this by multiplying 80 times .3 . Then you will get 24.

9514 1404 393

Answer:

  (c)  - It is contained in the set of natural numbers, whole numbers, integers, and rational numbers, but it is not contained in the set of irrational numbers.

Step-by-step explanation:

The improper fraction (a rational number) reduces to 15, a whole number, natural number, and integer. A ratio of integers is never an irrational number.

The best description is the third one:

- It is contained in the set of natural numbers, whole numbers, integers, and rational numbers, but it is not contained in the set of irrational numbers.