11. If using the method of completing the square to solve
the quadratic equation x² + 13x - 32 = 0, which
number would have to be added to "complete the square"?

Answer:

see below

Step-by-step explanation:

7,12,16,20,27,40,56,64

The square numbers are 16 = 4^2   and 64 = 8^2

The difference is 64 - 16 =48

The cube numbers are 27 = 3^3 and 64 = 4^3

64 - 27 =37

Answer:

a. 48

b. 37

Step-by-step explanation:

7,12,16,20,27,40,56,64

Square numbers= 16=4², 64=8²

Cube numbers= 27=3³, 64=4³

Answer:

bro speak english

SPEAK ENGLISH

The region that contains the most dispersed data is between the upper quartile and the median.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.  

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Answers:

A, B, D, E

Nearly everything except choice C is true.

====================================================

Explanation:

11%

Hope this helps! :)

______________

Answer:

\( \frac{195.80}{220} \times 100 \% \\ = 0.89\%\)

Answer:

0.2

Steps:

To convert to a decimal, divide the percent number by 100.

So, 20 divided by 100 = 0.2

Answer:

B. 10C6(5y)^4(3)^6

Step-by-step explanation:

The general binomial expansion formula is expressed using the formula:

(x+y)ⁿ = nCr x^{n-r}y^r

Given the equation (5y+3)^10

To get the sixth term of the expansion, we will compare the general formula given with the question

On comparison, x = 5y y = 3 and n = 10. Since we need the sixth term of the sequence, r will be equal to 6 i.e r = 6

Substitute the variables into the binomial formula above to get the sixth term.

(5y+3)^10 = 10C6 (5y)^10-6 (3)6

(5y+3)^10 = 10C6(5y)^4(3)^6

Hence the sixth term in the binomial expansion is 10C6(5y)^4(3)^6

Answer:

A on edge

Step-by-step explanation:

The given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\)as we have multiplied 8 in both numerator and denominator.

The given expression is \(g^2/3h\).

Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:

\((g^2/3h) * (8/8)\)

Simplifying further, we get:

\((8g^2)/(24h)\)

Therefore, the expression equivalent to \(g^2/3h\) is \((8g^2)/(24h)\).

Thus, the given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\) as we have multiplied 8 in both numerator and denominator.

The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.

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The complete question is :

Which expression is equivalent to \(g^2/3h\)?

Click on the correct answer.

(A) \(g^2+5/3h+5\)

(B) \(6g^2/15h\)

(C) \(8g^2/24h\)

Answer: C

Step-by-step explanation:

Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

Answer:

2286

Step-by-step explanation:

If you take 14 percent of a number and get 320, then what is that number? In other words, you know that 14 percent of a number is 320 and you want to know what that initial number is.

To solve this problem you multiply 320 by 100 and then divide the total by 14 as follows: (320 x 100) / 14

When we put that into our calculator, we get the following answer:

2285.71

can't have a portion of someone to you round it to the nearest whole number.

Answer:

The town’s population is 2286 (approximately)

Step-by-step explanation:

Let x be the number of the town’s residents :

We can translate the statement “14% of the town’s population is over the age of 65 and there are 320 residents over the age of 65” mathematically like this :

\(\frac{14}{100} x=320\)

\(\Longrightarrow 14x=320\times 100\\\\\Longrightarrow 14x=32000\)

\(\Longrightarrow x=\frac{32000}{14}\)

\(\Longrightarrow x=2285.71428571429\)

Therefore , the solution of the given problem of congruent comes out to be in this case we have two side equal and one side common so it is sss

Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

SSS definitions. an autonomous government organization responsible for overseeing military conscription. Selective Service and Selective Service System are synonyms. independent agency kind. a federal agency that was established by a congressional act and is unrelated to the executive departments.

In this case we have two side equal and one side common so it is sss

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Answer: 250

Step-by-step explanation: because i got it right

Answer:

Step-by-step explanation:

110

Answer: 0.204

Step-by-step explanation:

The formula to use to solve this is the combination formula.

Combination formula =

C(n, r) = nCr = n!/r! (n - r)!

Total number of kittens = 8 boy kittens + 9 girl kittens

= 17 kittens

Step 1

We find the probability of choosing 4 boy kittens out of 8 boy kittens

= 8C4 = 8!/4! × (8 - 4)!

= 8C4 = 8! / 4! × 4!

= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)

8C4 = 70

Step 2

We find the probability of choosing 7 girl kittens out of 9 girl kittens

9C7 = 9!/7! × (9 - 7)!

= 9C7 = 9! / 7! × 2!

= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)

9C7 = 36

Step 3

Find the probability of Picking 11 kittens out of 17 kittens

17C11 = 17!/11! × (17 - 11)!

= 17C11 = 17! / 11! × 6!

= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)

17C11 = 12,376

Step 4

The final step

The probability that the director chooses 4 boy kittens and 7 girl kittens

= 8C4 × 9C7/ 17C11

= 70 × 36/12376

= 2520/12376

= 0.2036199095

Approximately to 3 decimal places = 0.204

Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204

Answer:

false

Step-by-step explanation:

a line is infinite but a line segment has starting and end point. line segment is a small segment taken out from that infinite line

Answer:

Other side, the opposite function, on both sides of the equation, in the numerator, not the denominator

Step-by-step explanation:

To isolate a single variable when rearranging equations, move all other variables to the other side of the equation by using the opposite function on them and remembering to perform that operation on both sides of the equation. Make sure the rearrangement has the target variable in the numerator, not the denominator.

other side

the opposite function

on both sides of the equation

in the numerator, not the denominator

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Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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27 "

Explanation

Step 1

graph

to find the total height of teh staircase we need to add all teh rises, ( in other words we can multiply the length of a rise by the number of steps)

then ; let

number of steps=4

rise=.75

therefore, the answer is

27 "

I hope this helps you

x

The value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

A quadratic relation has the equation y= a(x - s )(x – t).

y = a(x - 2)(x + 6) and (3,5) is a point on the graph

Plug x = 3 and y = 5

5 = a(3 - 2)(3 + 6)

a = 5/9

The parabola has zeros of 4 and -2 and a y-intercept of 1

y= a(x - s )(x – t)

0= a(4 - s )(4 – t)

0= a(-2 - s )(-2 – t)

1= a(0 - s )(0 – t)

No solution.

Similarly, it can find the equation of the parabola in the remaining part,

Thus, the value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

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Answer:

The null and alternative hypothesis for this study are:

\(H_0: \mu=18500\\\\H_a:\mu< 18500\)

The null hypothesis is rejected (P-value=0.004).

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Then, the null and alternative hypothesis are:

\(H_0: \mu=18500\\\\H_a:\mu< 18500\)

The significance level is 0.05.

The sample has a size n=150.

The sample mean is M=18200.

The standard deviation of the population is known and has a value of σ=1400.

We can calculate the standard error as:

\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624\)

This test is a left-tailed test, so the P-value for this test is calculated as:

\(P-value=P(z<-2.624)=0.004\)

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Answer: Choice B

Each time we're adding 122 to each term to get the next term

This goes on forever because of the three dots, hence the set is infinitely large.

We say that the common difference is 122. Subtracting any two adjacent terms gets us this value. Eg: 354-232 = 122.

IfIf Ryan claims that the cost of Plan A and Plan B differ a lot. The statement that best explains why Ryan was misled by the graph is: b.) The scale of intervals on the horizontal axis of both graphs is inconsistent.

Based on the graph we can see that the graph is inconsistent based on the fact that the scale of intervals on the horizontal axis of Plan A  graph and Plan B graph are inconsistent.

The reasons why the both graphs are inconsistent was  because the lines did not intersect or are not on the same line which means that they are parallel lines.

Therefore the correct option is B.

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Answer:

Step-by-step explanation:

The two graphs use different vertical scales.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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Answer:

0.551

Step-by-step explanation:

Let no. of people who take discount = x

Using binomial distribution, N c X. p^x. q^(n-x)

p : customer getting discount = 0.3, q : customer not getting discount = 0.7   n : no. of customers = 8

Probability that x < 3 : Prob (x=0) + Prob (x=1) + Prob (x=2)

= 8 c 0. (0.3)^0 . (0.7)^8 + 8 c 1. (0.3)^1 . (0.7)^7 + 8 c 2. (0.3)^2 . (0.7)^6

0.05764801 +  0.19765032 + 0.29647548

0.551