Write the product in standard form. (2 + 3i)(2 - i)

Answer:

Ac CA is your answer

Step-by-step explanation:

MARK ME AS BRAINLIEST

AC and CA

Step-by-step explanation:

[tex]line \: which \: has \: endpoint \: \\ \\ A \: and \: C \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ it \: shows \: that \: line \: starts \: from \: \\ \\ A \: \: and \: ends \: with \: C \\ \\ so \: \: its \: name \: is \: \: \: \: AC \\ \\ hope \: it \: is \: helpful \: to \: you....[/tex]

Answer:

Approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.43cm, standard deviation of 0.35cm.

What percentage of the apples have diameters that are between 7.08cm and 7.78cm?

7.43 - 0.35 = 7.08 cm.

7.43 + 0.35 = 7.778 cm.

Within 1 standard deviation of the mean, so approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

Answer:

A’(-5,5)

Step-by-step explanation:

x’ = 2.5 * -2 = -5

y‘ = 2.5  * 2 = 5

Answer:

18

Step-by-step explanation:

when there is a - in front of an expression in parentheses, change the sign of each term in the expression

6+14+(-2)

then calculate the sum or difference

6+14-2= 18

Answer:

3

Step-by-step explanation:  6  11 10  48

spent $504

hair dryers cost $8 each

6 floors with the same number of rooms on each floor.

Money spent / hair dry cost  =  number of hair dryers bought

number of hair dryers   = number of floors  =  hair dryers per floor Plus any remainder

    504 /  8  =  63 hair dryers  

    63 / 6   =    10.5     so 10 rooms per floor = 60 hairs dryers with 3 left over

Answer:

well IMA just copy the other guy and say 3

Step-by-step explanation:

just cause it is.

Answer:

[tex](a)\ 200 \to 249 =3[/tex]

[tex](b)\ 150 \to 199 = 0[/tex]

[tex](c)\ Total = 20[/tex]

Step-by-step explanation:

Given

See attachment for cumulative frequency histogram

Solving (a): Swimmers between 200yd and 249yd

To do this, we simply read the data from the 0 mark

From the histogram, we have:

[tex]0 \to 249 = 15[/tex]

and

[tex]0 \to 199 = 12[/tex]

So:

[tex]200 \to 249 = 0 \to 249 - 0 \to 199[/tex]

This gives:

[tex]200 \to 249 = 15-12[/tex]

[tex]200 \to 249 =3[/tex]

Solving (b): Swimmers between 150yd and 199yd

To do this, we simply read the data from the 0 mark

From the histogram, we have:

[tex]0 \to 149 = 12[/tex]

and

[tex]0 \to 199 = 12[/tex]

So:

[tex]150 \to 199 = 0 \to 199 - 0 \to 149[/tex]

This gives:

[tex]150 \to 199 = 12-12[/tex]

[tex]150 \to 199 = 0[/tex]

Solving (c): Total swimmers

To do this, we simply read the longest bar of the histogram

[tex]Longest = 20[/tex]

Hence:

[tex]Total = 20[/tex]

Answer:

(-3,-6)

Step-by-step explanation:

You need to solve for the system of equations.

Step-by-step explanation:

-4x+y=6

-5x-y=21

y=6+4x

-5x-(6+4x)=21

-5x-6-4x=21

-5x-4x=21+6

-9x=27

-9x÷9=27÷9

x=3

y=6+4x

=6+4(3)

=18

Answer:

Undefined

Step-by-step explanation:

The square root of a negative number does not exist in the set of real numbers so it would be Undefined

Answer:

Let x = quarts of water to be added

so then

12* 10% + x * 0% = (12+x) * 6% (this says 12 quarts of 10% solution + x quarts of 0%(water) equals the new total (12+x) of a 6% solution

1.2 = .72 + .06x

.48 = .06x

x = 8 (quarts of water to be added)

Step-by-step explanation:

Hope this helps

Answer:

The top choice

Step-by-step explanation:

1/2 x -2 > 0

Add 2 to each side

1/2 x -2+2 > 0+2

1/2 x > 2

Multiply each side by 2

1/2 x *2 > 2*2

x > 4

There is an open circle at 4 and the line goes to the right

Answer:

It is the first option everything to the right of 4.

Step-by-step explanation:

Answer:

I think its b but im not sure

Step-by-step explanation:

Answer:

The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

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 establishes 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.

Central Limit Theorem for the sample mean:

Sample of size n, and thus:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

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

Probability of the sample mean exceeding a value:

The probability is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which X is the value we want to find the probability of the sample mean exceeding, [tex]\mu[/tex] is the population mean, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Answer:

-1, 2, 4

Step-by-step explanation:

As one can see in the given values,

(-1, 0), (2, 0), (4, 0)

When one substitutes these values for (x), the outputs, also known as the results or what (f(x)) equals or the (y) values are equal to (0). Therefore, (f(x)) equals zero at these given values.

9514 1404 393

Answer:

  II only

Step-by-step explanation:

You can simplify the inequality like this:

  3 -8 > 8 -8 + 5x . . . . . . . . subtract 8 from both sides

  -5 > 5x . . . . . . . . . . . . . simplify

  -5/5 > (5x)/5 . . . . . . . divide both sides by 5

  -1 > x . . . . . . . . . . . . simplify

I find this easier to compare to a numbers on a number line if the inequality symbol points to the left. (This is a personal preference. YMMV)

  x < -1

Now, we can see that only numbers to the left of -1 on the number line will be suitable values for x. Of those listed, only -9 is a solution.

  II only

Answer:

The margin of error of u is of 3.8.

The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 28 - 1 = 27

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7707

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.7707\frac{7.3}{\sqrt{28}} = 3.8[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error of u is of 3.8.

The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes

The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes

The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.

Answer:

The actual distance is of 21.76 kilometers.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

The scale on a map is given as 1 : 320,000

This means that each unit on the map represents 320,000 units of distance.

Distance between the top of the two mountains on the map is 6.8cm

Then

1 cm - 320,000 cm

6.8 cm - x

Applying cross multiplication:

[tex]x = 6.8*320000 = 2176000[/tex]

Distance in kilometers

To convert from centimeters to kilometers, we divide by 100000. So

2176000/100000 = 21.76

The actual distance is of 21.76 kilometers.

Answer:

Angle A = [tex]77^{o}[/tex]

Step-by-step explanation:

cos A = adjacent / hypotenuse

cos A = 18/82

cos A = 0.22

A = [tex]cos ^{-1}[/tex]0.22

A = [tex]77^{o}[/tex]

Answer:

20

Step-by-step explanation:

diameter=√(12²+16²)=√[4²(3²+4²)]=4√(9+16)=4√25=4×5=20

Answer:

y = 33/5

Step-by-step explanation:

Distribute

3(2y-8)-y = 9

6y - 24 - y

5y - 24 = 9

Add 24 to both sides

5y = 9 + 24

5y = 33

y = 33/5

Answer:

y = - 4.5x + 120

75 = - 4.5x + 120

x = 10 minutes

Step-by-step explanation:

To model the scenario described above, we use the linear equation model ;

Where ;

y = bx + c ; c = intercept ; b = slope ; y = altitude at time x

The initial altitude of the hot air Ballon here is the intercept = 120 meters

The descent rate = 4.5 m per minute is the slope ; since it is descent, then the slope will be negative as the altitude will reduce.

Hence, we have ;

y = - 4.5x + 120

Hence, the time altitude will be 75 cabnbe modeled as :

y = 75

75 = - 4.5x + 120

75 - 120 = - 4.5x

- 45 = - 4.5x

x = 10 minutes

Answer:

It results to two triangles

Step-by-step explanation:

There are two angle b

Answer:

The missing value is 5/2

Step-by-step explanation:

Answer:

It would be Linear

Step-by-step explanation:

Answer:

i think its quadratic because the graph isnt straight and has different slopes between the x,y.

Step-by-step explanation:

9514 1404 393

Answer:

  D(1, 2)

Step-by-step explanation:

The ordered pair is always (x-coordinate, y-coordinate).

The x-coordinate is the distance to the right of the y-axis. (It is negative for points left of the y-axis.) Here, point D lies 1 unit right of the y-axis, so its x-coordinate is 1.

The y-coordinate is the distance above the x-axis. (It is negative for points below the x-axis). Here, point D lies 2 units above the x-axis, so its y-coordinate is 2.

The ordered pair describing the location of D is ...

  (x-coordinate, y-coordinate) = (1, 2)