Multiply and simply: (4 - 3i) (2 + i)

Answer: C

Step-by-step explanation:

g(5)=1

By using the rate of change formula for linear equations, we will see that the statement is true.

Here we have the following statement:

"The student reads at a rate of 48 pages per hour."

Which relates to the linear equation represented on the table.

A general linear equation is written as:

y = a*x + b

Where a is the rate and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the rate is:

rate = (y2 - y1)/(x2 - x1)

Using the first two points (1,644) and (4, 500) we can get the rate:

R = (500 - 644)/(4 - 1) = -48

So the number of pages remaining decreases by 48 each hour of reading, then yes, the student reads at a rate of 48 pages per hour.

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Answer:

2

Step-by-step explanation:

If the doors for the small cabinets are 17.5 in long, and the doors for the large cabinets are 3.5 times longer, find the length of the large cabinet doors by multiplying the length of the small cabinet doors by 3.5:

⇒ Length of large cabinet doors = 17.5 × 3.5 = 61.25 in

1 foot = 12 inches

⇒ 12 foot = 12 × 12 = 144 inches

To find how many large doors can be cut from a board that is 12 feet long, divide 144 inches by the found length of the large door:

⇒ 144 ÷ 61.25 = 2 r 21.5

Therefore, 2 large doors can be cut from a board that is 12 feet long.

(There will be 21.5 inches of board left over).

Answer:

The measure of its supplementary angle is 18.6 degrees

Step-by-step explanation:

A Supplementary angle is any two angles that sum up to 180 degrees

With this in mind we can subtract 180 - 161.4 to get the measure of the other angle.

Since 161.4 + 18.6 = 180 this is correct

Answer: The supplementary angle to 161.4 degrees is 18.6 degrees.

Step-by-step explanation: the sum of two supplementary angles is always 180 degrees.

180-161.4 is equal to 18.6 degrees.

The distance traveled with 3 gallons is 96 miles.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

The distance traveled with 11 gallons = 352 miles

This means,

1 gallon = 352/11 miles

1 gallon =  32 miles

Now,

1 gallon =  32 miles

Multiply 3 on both sides.

3 gallons = 3 x 32 miles

3 gallons = 96 miles

Thus,

The distance traveled with 3 gallons is 96 miles.

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The rectangle's area is growing at a rate of 170 cm per second.

Given that,

Area of Rectangle given by.

A = length x width

A = LW

L =length of Rectangle

W =width of Rectangle

Now, dA/dt = W dl/dt + l dw/dt

dA/dt is the rate of change of area of the rectangle

dl/dt is the rate of change of length of the rectangle

dw/dt is the rate of change of width of the rectangle

at  L = 40cm, W= 15 cm

dw = 2 cm/s,

dl = 6 cm/s,

dA = ?

dA/dt = W dl/dt + l dw/dt

         = 15x6 + 40x2

         = 90 +80

          =170 cm /sec

Thus, the area of the rectangle increasing at 170 cm /sec

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Answer:

I believe the answer is Yes because there is a constant arithmetic sequence and I believe the common difference is 4.

From the given statements regarding angle the point b) DE is parallel to AC with its reason - AB is a transversal cutting DE and AC will be the correct statement.

DE and AC are parallel for this to work angle 1 is at A, angle 2 is at B and angle 3 is at C. In addition, angle 4 is the alternate interior angle to angle 1 once DE is constructed, as is angle 5 to angle 3. Then the missing reasons are alternate interior angles theorem and definition of congruent angles.

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Answer:

  (9, 7)

Step-by-step explanation:

You want the coordinates of the image of point (9, -7) after it has been reflected across the x-axis.

The image point will be as far above the x-axis as the original point is below the x-axis. The y-coordinate of -7 tells you the point is 7 units below the x-axis. The reflected point will be 7 units above the x-axis, so will have a y-coordinate of +7.

The image coordinates are (9, 7).

__

Additional comment

Reflection across the x-axis changes the sign of the y-coordinate.

Reflection across the y-axis changes the sign of the x-coordinate.

False, As the sample size is increased, the standard deviation of a sampling distribution of the sample's mean drops.

The term "standard error" also refers to the sample mean's standard deviation. The high dimensionality theorem establishes that as sample size increases, the sample mean's sampling distribution becomes more or less normal.

Using the formula below, the sample mean's standard deviation is determined.

σ ÷ √n

where n is the sample size and would be the population standard deviation.

As the denominator, or n, increases, the standard variance of the sample average would also decrease, as shown by the aforementioned calculation.

It follows that the standard deviation of a sample's average decreases as the sample size grows.

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The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.

In this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.

The equations of the line are defined by functions of the form:

y = m · x + b

Where:

And the slope relationship between two perpendicular line:

m · m' = - 1

Where:

First, derive the equation of the line in slope-intercept form:

x + 2 · y = - 4

2 · y = - x - 4

y = - (1 / 2) · x - 2

Second, calculate the slope of the perpendicular line by the slope relationship:

m' = - 1 / (- 1 / 2)

m' = 2

Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:

b = y - m · x

b = - 5 - 2 · (- 3)

b = - 5 + 6

b = 1

Then, obtain the equation of the line in slope-intercept form:

y = 2 · x + 1

The equation of the line is y = 2 · x + 1.

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The probability of each event will be

a. 0.122

b. 0.1

c. 0.64

d. 0.63

Probability of a $2 winner is 1 in 10

Probability of a $5 winner is 1 in 50

Probability of a $10 winner is 1 in 500

The formula to find probability is

1. no. of favorable outcomes / total no. of favorable outcomes

                                                  OR

2. P(A) = n(A)/n(S)

where

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space

Now we will use formula to find probability of different events happening

a. To find the probability of getting either a $2, or $5, or $10 winner we

will find probability of $2 , $5 and $10 and add them together.

1/10 + 1/50 + 1/500 = 0.122

b. The probability of getting a $2 winner will be

1/10 = 0.1

c. The probability of getting no $5 winner is (49/50)^50 = 0.36

So the probability of getting $5 winner will be 1 - 0.37 = 0.64

d. The probability of getting no $10 winner is (499/500)^500 = 0.37

And we can take probability of total no. of outcomes as 1.

So the probability of getting $10 winner will be 1 - 0.37 = 0.63

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In the garden club there are 18 ladies and 2 gentlemen.

Given, In a garden club, 90% is ladies.

The number of ladies is 12 more than 3 times the number of gentlemen.

Let the total members be, x

the number of ladies be, l and the number of gentlemen be, g

according to the question,

l = 90x/100

l = 9x/10

also, l = 12 + 3g

g = (l - 12)/3

as, l + g = x

9x/10 + (9x/10 - 12)/3 = x

9x/10 + 9x/30 - 4 = x

36x/30 - 4 = x

6x/30 = 4

x = 20

so, ladies be, l = 9x/10 = 18

and gentlemen be, g = 20 - 18 = 2

Hence, in the garden club there are 18 ladies and 2 gentlemen.

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Solving for g in the equation g =  (c - p)/0.325

An equation is a mathematical expression that show the relationship between two variables.

Since we are given the equation c = 0.325g + p, we desire to make g subject of the formula.

To do this, we perform some mathematical operations on it.

So, c = 0.325g + p

Now, to isolate 0.325g on the right hand side, we subtract p from both sides of then equation.

So, c = 0.325g + p

c - p = 0.325g + p - p

c - p = 0.325g

Now to isolate g, we divide both sides of the equation by 0.325. So, we have

c - p = 0.325g

(c - p)/0.325 = 0.325g/0.325

g = (c - p)/0.325

So, we have g =  (c - p)/0.325

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In longhand notation, the electron configuration is

1s² 2s² 2p6 3s¹

Noble gas configuration

[ Ne ] 3s¹

Complete question:

Choose the electron configuration for sodium (Na) in both longhand notation and noble-gas notation.

What is electron configuration?

The arrangement of electrons in atomic or molecular orbitals of an atom, molecule, or other physical structure is referred to as the electron configuration in atomic physics and quantum chemistry.

In longhand notation, the electron configuration is

1s² 2s² 2p^6 3s¹

Noble gas configuration

[ Ne ] 3s¹

Here, the configuration 1s² 2s² 2p^6 is replaced by [ Ne ].

[ Ne ] represents the electron configuration of [ Ne ].

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Answer:

D) [Ne]3s1

☆
EDGE2023; Good Luck :D!!!

Answer:

138° (nearest degree)

Step-by-step explanation:

Bearing:  The angle (in degrees) measured clockwise from north.

The given scenario can be modelled as a right triangle (see attachment).

Therefore, the bearing is 90° + θ (shown in green on the attached diagram).

To find angle θ, use the cosine trigonometric ratio:

[tex]\implies \cos{\theta}=\dfrac{A}{H}[/tex]

[tex]\implies \cos{\theta}=\dfrac{624}{927}[/tex]

[tex]\implies \theta=\cos^{-1}\left(\dfrac{624}{927}\right)[/tex]

[tex]\implies \theta=47.69018863...[/tex]

[tex]\implies \theta=48^{\circ}\; \; \sf (nearest\;degree)[/tex]

Therefore, the bearing of the drawbridge from the tower is:

[tex]\begin{aligned}\implies \sf Bearing&=90^{\circ}+\theta\\&=90^{\circ}+48^{\circ}\\&=138^{\circ} \end{aligned}[/tex]

Answer:

-----------------------------

Add 90° to the angle measure we just found, since bearing is counted from the north direction:

After one hour (60 minutes, the value of the temperature is 550 degrees.

Temperature is the degree of hotness and coldness that a body contains.

In this case, after graph, after 12 minutes the coffee is about 110 degrees. The temperature per minute will be:

= 110 / 12

= 9.167° per minute.

Therefore, the temperature after 1 hour which is 60 minutes will be:

= Time × Rate

= 60 × 9.167°

= 550°

The temperature is 550°.

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Answer:

3

Step-by-step explanation:

45*64=2880

48*60=2880

3 is the amplitude, -4 is the minimum value, and 2 is the highest value.

acc to our question-

Hence,3 is the amplitude, -4 is the minimum value, and 2 is the highest value

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Answer:

x = 20

Step-by-step explanation:

We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.

We subtract 180 - 110 which will come out to 70 which is the value of angle B

We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.

Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x

the company uses 37 screws to make each table and 14 screws to make each chair. The company needs to order screws for 12 tables and 48

The length of XN is 6

Calculation

By angle bisector theorem

[tex]\frac{AX}{NX} =\frac{AY}{NY}[/tex]

[tex]\frac{18}{NX} =\frac{12}{4}[/tex]

[tex]NX=\frac{18*4}{12} =6[/tex]

Therefore, the length of side NX in the given triangle is 6.

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The length of side NX in the given triangle is 6.

By angle bisector theorem

According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures

Therefore, the length of side NX in the given triangle is 6.

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The probability distribution is a) discrete, with b) a mean of 1.23, the standard deviation is c) 0.6458, d) the probability that an American will take 3 or more trips is 0.04, e) the probability that an American will take 2 or less trips is 0.96 and, f) the probability to take at least one trip is 0.94

It is given that the probability distribution of the no. of trips an American adult takes that lasts 5 nights or more

x              probability

0                  0.06

1                   0.70

2                  0.20

3                  0.03

4                  0.01

a)

Here we can see that all the values are isolated and there is no continuity between them. The distribution clearly has breaks between them.

Hence, we can say that the distribution is discrete.

b)

The expected value of any probability

E(X) = ∑xp(x)

where,

x is the random variable

p(x) is the probability of the corresponding random variable hence we get

E(X) = 0 × 0.06  +  1 × 0.70  +  2 × 0.20  +  3 × 0.03  +  4 × 0.01

= 0  +  0.7  +  0.4  +  0.09  +  0.04

= 1.23

Hence the expected value is 1.23

c)

The standard deviation is √σ²

Where σ² = variance of the distribution

σ² = E(X²) - {E(X)}²

{E(X)}² = 1.23²

= 1.5129

E(X²) = ∑x²p(x)

= 0 × 0.06  +  1 × 0.70  +  4 × 0.20  +  9 × 0.03  +  16 × 0.01

= 0.7  +  0.8  +  0.27  +  0.16

= 1.93

Therefore,

σ² = 1.93  -  1.5129

= 0.4171

Therefore

σ = 0.6458

d)

The probability to take 3 or more trips is

P(X≥3)

= P(X = 3)  +  P(X = 4)

= 0.03 + 0.01

= 0.04

e)

The probability of an American taking 2 or less trips is

1 - P(X≥3)

= 1 - 0.04

= 0.96

f)

The probability that an American will take at least one trip is

P(X≥1)

= 1 - P(X = 0)

= 1 - 0.06

= 0.94

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The absolute value function y = |x - 3| + 5 generates the representation set on Cartesian plane.

In this question we need to determine the equation behind a representation set on a Cartesian plane. After a quick inspection, we find that the representation shows an absolute value function of the form:

y = |x - a| + b

Where:

Based on all the given facts, the primitive absolute value function (f'(x) = |x|) is translated horizontally 3 units in the +x direction and vertically 5 units in the +y direction. If we know that a = 3 and b = 5, then we find the absolute value function y = |x - 3| + 5, whose representation is shown below.

In a nutshell, the representation comes from the absolute value function y = |x - 3| + 5.

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