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

Answer:

1.5 meters

Step-by-step explanation:

The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:

3.75=h*(1.7+3.3)/2

3.75=h*2.5

h=3.75/2.5=1.5

Hope this helps!

Answer:

Step-by-step explanation:

use the formula and rearrange for h.

1/2 x h x  (a + b) = A

1/2 x (1.7 + 3.3) x h = 3.75

2.5 x h = 3.75

h = 1.5

hope this helps! :)

Answer:

[tex]x=15^\circ[/tex]

Step-by-step explanation:

Please refer to the attached figure for labeling of given diagram:

We are given the following angles:

[tex]\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ[/tex]

Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.

Using property of vertically opposite angles:

[tex]\angle EOF = \angle AOB = 7x^\circ[/tex]

Line CD is a straight line, so [tex]\angle COD = 180^\circ[/tex]

Also,

[tex]\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ[/tex]

Hence, answer is [tex]x = 15^\circ[/tex].

Answer:

250

Step-by-step explanation:

if x=50

5(x)=5*50=250

Hope it helps..Pls mark as Brainliest!!

By rounding of the following number to the nearest thousand is 2000.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

'

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

Round the following number to the nearest thousand

2385

= 2000

Thus, by rounding of the following number to the nearest thousand is 2000.

Learn more about rounding numbers here:

https://brainly.com/question/1285054

#SPJ2

Answer:

B.

Step-by-step explanation:

Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.

So

m<LYM = m<JYM

Also their arcs would be equal to their angles measures so,

Arc JK = 52°

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of guesses made for the sat questions.

Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2

Probability of failure, q = 1 - p = 1 - 0.2 = 0.8

the probability that the number x of correct answers is fewer than 4 is expressed as

P(x < 4)

From the binomial distribution calculator,

P(x < 4) = 0.97

Answer:

10,15.20.25

Step-by-step explanation:

+5 in each number

Answer:

n = 3 or n = 4

Step-by-step explanation:

Let the unknown number be n.  

Then:

n² = 7n - 12

In standard quadratic form, we have:

n² - 7n + 12 = 0

In factored form, we have:

(n - 3)(n - 4) = 0, and so

n = 3 and n = 4

Answer:

If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.

Step-by-step explanation:

The question is incomplete: no numerical values for the dimensions of the cone are given.

A right cone is defined by the radius r of the base and the height h.

The base area is the area of a circle with radius r:

[tex]A_b=\pi r^2[/tex]

The lateral area is calculated as:

[tex]A_l=\pi \cdot r\cdot l[/tex]

As the values for r and h are not given, we will use an example with r=2 and h=3.

Then, the amount of paper needed is:

[tex]A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2[/tex]

The amount of plastic needed is:

[tex]A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2[/tex]

Answer:

Top right option

Step-by-step explanation:

The answer is 1 7/20

2/5 x 4/4 + 7/10 x 2/2 + 1/4 x 5/5

=  8/20 + 14/20 + 5/20

= 27/20

= 1 7/20

Answer:

27/20 or 1 and 7/20

Step-by-step explanation:

All you do is find common factors.

Answer:

x <= 48

Step-by-step explanation:

Subtract 3 from both sides

x/12 <= 4

Multiply by 12

x <= 48

Answer:

Step-by-step explanation:

a)4a-6a                   d)2x+4y-10x

   =-2a.                     =-8-+4y

b)14-1-10

=3

c)2+8

=10

e)answer is 6 x raised to the power 3

f)7x raised to the power 2-5x-y

Answer:

The answer is y = -3x - 2.

Step-by-step explanation:

Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :

[tex]y = mx + c[/tex]

[tex]let \: m = - 3 \\ let \: c = - 2[/tex]

[tex]y = - 3x - 2[/tex]

Answer:

175

Step-by-step explanation:

+ × - = -

thus 199+(-24)

199-24

175

Answer: 199 + -24 = 175

Step-by-step explanation: 199 is a positive number and -24 is a negative number. If the positive number is bigger than the negative number you subtract. So forget that the - sign is there and subtract it.  

Answer:82

Step-by-step explanation:

a+b+c+d+e+f/6=72

a+b+c+d+e+f=6*72

a+b+c+d+e+f=432

a+b+c+d+e+f+g+h/8=74.25

a+b+c+d+e+f+g+h=594

g=80

h=?

432+80+h=594

512+h=594

h=82

hope it helps brainleast plz...

Answer: 5h/3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

5h 3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

Step-by-step explanation:

From the news story, we are told that:

The odds are 1 in 150 that a piece of Skylab will hit someone.

However, 4 billion people live in the zone in which pieces could fall.

Therefore, any one person’s chances of being struck are:

[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]

Therefore, the odds are one in approximately 27 million.

The inaccuracy presented in this reasoning was that the odds are one in 600 billion.

Answer:

Option D

Step-by-step explanation:

This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;

[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]

Hope that helps!

Answer:

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Step-by-step explanation:

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Answer:

Which earns more interest = Account B

How much more = $1,306.60

Step-by-step explanation:

Given;

Principal P = $2,000

Interest rate r = 5% = 0.05

Time t = 20 years

For account A;

Simple interest = P×r×t

Substituting the values;

Simple interest = 2,000 × 0.05 × 20 = $2000

Interest on account A = $2,000

For account B;

Compound interest

Final amount = P(1 + r)^t

Since it's compounded annually

Substituting the values;

Final amount = 2000(1+0.05)^20

Final amount = $5306.60

Interest = final amount - principal = $5306.60 -$2000

Interest = $3,306.60

Therefore, account B earns more interest.

Difference = account B interest - account A interest

Difference = $3,306.60 - $2,000

Difference = $1,306.60

Answer:

the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Step-by-step explanation:

The probability of the density function of the total claim amount for the health insurance policy  is given as :

[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]

Thus, the expected  total claim amount [tex]\mu[/tex] =  1000

The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]

However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100

To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :

P(X > 1100 n )

where n = numbers of premium sold

[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]

[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]

[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]

[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]

[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Answer:

The mass of the grains = 120 ± 1 g

Step-by-step explanation:

we are given the following:

Total mass of container + grains = 185 grams

Mass of container = 65 grams

Therefore, mass of grains is calculated as follows:

Mass of grains = ( Mass of container + grains) - mass of container

= 185 - 65 = 120 grams.

since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g

Answer:

a= -3/8

b= 1/8

Step-by-step explanation:

To remove i from the denominator, we need to multiply the numerator and denominator by -i

[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]

This simplifies to

[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]

This further simplifies to

[tex]\frac{i-3}{8}[/tex]

This can be rewritten as

[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]

a= -3/8

b= 1/8

Answer:

[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]

Step-by-step explanation:

[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]

Answer:

52300

Step-by-step explanation:

When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300

Answer:

b. external validity

Step-by-step explanation:

External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.

John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.

Answer:

x = 1/9

Step-by-step explanation:

3^ (x+1) = 9 ^ (5x)

Replace 9 with 3^2

3^ (x+1) = 3^2 ^ (5x)

We know that a^b^c = a ^(b*c)

3^ (x+1) = 3^(2 * (5x))

3^ (x+1) = 3^(10x)

The bases are the same so the exponents are the same

x+1 = 10x

Subtract x from each side

x+1-x = 10x-x

1 = 9x

Divide each side by 9

1/9 = 9x/9

1/9 =x

Answer:

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $91.78

Standard deviation r = $23.13

Number of samples n = 4

Confidence interval = 90%

Using the z table;

z(α=0.05) = 1.645

Critical value at 90% confidence = 1.645

Substituting the values we have;

$91.78+/-1.645($23.13/√4)

$91.78+/-1.645($11.565)

$91.78+/-$19.024425

$91.78+/-$19.024

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)