Review the graph of complex number z.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1).

What is the modulus of z?

2
2StartRoot 2 EndRoot
3
StartRoot 10 EndRoot

The probability of having a height that is between 158 cm and 163 cm is 0.69011 and the value of x is 169 centimeters

The given parameters are:

Calculate the z-scores at x = 158 and x = 163 using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]z = \frac{158 - 161}{6} = -0.5[/tex]

[tex]z = \frac{163 - 161}{6} = 0.33[/tex]

The probability is then represented as:

P(158 ≤ x ≤ 161) = P(-0.5 ≤ z ≤ 0.33)

Using the z table, we have:

P(158 ≤ x ≤ 161) =  0.69011

Hence, the probability of having a height that is between 158 cm and 163 cm is 0.69011

The probability is represented as:

P(X ≥ x) = 1%

Express as decimal

P(X ≥ x) = 0.10

The z-score at p = 0.10 is:

z = 1.282

Substitute z = 1.282 in [tex]z = \frac{x - \mu}{\sigma}[/tex]

[tex]1.282 = \frac{x - \mu}{\sigma}[/tex]

Make x the subject

[tex]x = 1.282\sigma + \mu[/tex]

Substitute values for standard deviation and mean

x = 1.282 * 6 + 161

Evaluate

x = 168.692

Approximate

x = 169

Hence, the value of x is 169 centimeters

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Answer:

24

Step-by-step explanation:

Hello there!

To determine the amount (percentage) as from our question above, we have to divide the given percentage by 100% (original percentage) and then multiply by 120.

This is as shown below;

[tex] \frac{20\%}{100\%} \times 120 \\ \\ = 0.2 \times 12 \\ = 24[/tex]

. ° . = 24 <<<<<< Ans

I hope this helps.

Have a nice studies.

Omar ran farther than Paula by 950 meters. The total distance covered by Omar and Paula is 745000 centimeters.

The conversion of a unit from one dimension to another takes a standard approach. Here, we will be looking at conversion from kilometers and meters and meters to centimeters.

Given that:

Thus, It implies that Omar ran farther than Paula by 950 meters.

The total number of distance covered = (3250+ 4200) meters

= 7450 meters

= 745000 centimeters.

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The rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d

The number of days it would take the vine to grow to be 10.3 inches long is 45 days

From the question, we are to determine a linear function that describes the situation

From the given information,

Then vine is 1.3 inches long now

and it grows 0.2 inches a day

∴ After the days, the vine will increase by 0.2d in length

Then,

If L represents the length of the vine, d represent the number of days

The length of the vine after d number of days will be

L = 1.3 + 0.2d

Hence, the rule for the linear function that describes the length of the vine is L = 1.3 + 0.2d

Now, we are to determining the number of days it will take the vine to grow to be 10.3 inches long

Using the above linear function

L = 1.3 + 0.2d

10.3 = 1.3 + 0.2d  

0.2d = 10.3 - 1.3

0.2d = 9

d = 9 / 0.2

d = 45

Hence, the number of days it would take the vine to grow to be 10.3 inches long is 45 days

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Answer:

Constant term of an algebraic expression: A term of an algebraic expression which has a fixed numerical value in all situations and does not have any variable is called the constant term of an algebraic expression.

For examples, in the algebraic expression 5x + 2y + xy + 10, 10 is the constant term of the expression. therefore from the above algebraic expression 2x²+x-1, -1 will be the constant term

f(x) = | x + 61 | function is a translation of the parent absolute value function.Option B is correct.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

A single vertical parenthesis separating the equation on either side identifies an absolute value function. Option B is the only one with this indication.

B. f(x) = | x + 61 |

There are two ways to answer this equation;

1.f(x) = - (x + 61)

2.f(x) = x + 61

Hence,f(x) = | x + 61 | function is a translation of the parent absolute value function.

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Answer:

i can't send full page of it sorry

The equation y = 15000 - 950x best models the depreciation.

Option C is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The equation y = 15000 - 950x.

Here, y represents the value of the car after x years.

The initial value of the car is $15,000, which means the value of the car at x = 0 is $15,000.

The car depreciates by $950 each year, so after one year, the value of the car will be $15,000 - $950 = $14,050.

After two years, the value of the car will be $14,050 - $950 = $13,100, and so on.

This linear relationship between the value of the car and the number of years can be modeled by the equation y = 15000 - 950x,

where 15000 is the initial value and -950x represents the amount of depreciation each year.

Thus,

The equation y = 15000 - 950x best models the depreciation.

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Answer:

-4

Step-by-step explanation:

Consider (-4, -2) and (-2, -10).

Change in x: 2

Change in y: -8

Slope = (change in y)/(change in x) = -4

The slope of the function is -4.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us take two points from the table

(-4, -2) and (-2, -10)

Slope = -10+2/-2+4

=-8/2

=-4

Hence, the slope of the function is -4.

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Cassie need to make the model is 2250 cm²

A square pyramid has a square base and four lateral faces in geometry. A pyramid is a polyhedron with a base and three or more triangular faces that meet above it .

The complete question is attached below:

We know,

A= a(a+ √(a²+4h²))

and, a =25cm, h=30 cm

So,

A= 25(25+ √(25²+4*30²))

=25(25+65)

= 2250 cm²

Hence, Cassie need to make the model is 2250 cm²

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Answer:

[tex]x=\dfrac{42}{13}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{6}{(x^2-3x)}=\dfrac{12}{x}+\dfrac{1}{(x-3)}[/tex]

Factor the denominator on the left side:

[tex]\implies \dfrac{6}{x(x-3)}=\dfrac{12}{x}+\dfrac{1}{(x-3)}[/tex]

Combine the fractions on the right side by multiplying by the LCM:

[tex]\begin{aligned}\implies \dfrac{6}{x(x-3)} & =\dfrac{12}{x} \cdot \dfrac{(x-3)}{(x-3)}+\dfrac{1}{(x-3)} \cdot \dfrac{x}{x}\\\\& =\dfrac{12(x-3)}{x(x-3)}+\dfrac{x}{x(x-3)}\\\\& =\dfrac{12(x-3)+x}{x(x-3)} \end{aligned}[/tex]

As the denominators are now the same on both sides:

[tex]\begin{aligned}\implies \dfrac{6}{x(x-3)} & =\dfrac{12(x-3)+x}{x(x-3)}\\\\ \implies 6 & = 12(x-3)+x\end{aligned}[/tex]

Simplify and solve for x:

[tex]\begin{aligned}\implies 6 & = 12(x-3)+x\\\\6 & =12x-36+x\\\\6 & =13x-36\\\\13x & =42\\\\\implies x & =\dfrac{42}{13}\end{aligned}[/tex]

Answer:

900π

Step-by-step explanation:

Hello!

The radius is represented by the function [tex]r(t) = 15\sqrt{t +2}[/tex].

The radius of the ripple can be found when [tex]t=2[/tex]

Solve:

The radius of the ripple is 30 inches

The area of a circle is calculated by the formula [tex]A = \pi r ^2[/tex]

Given the radius is 30, we can find the area of the circle.

Solve:

Answer:

b)

Step-by-step explanation:

because there will be more

Answer:

[tex]x = 2\\ \\x= -\dfrac 78[/tex]

Step-by-step explanation:

[tex]~~~~~~~8x^2 -9x -14=0\\\\\implies 8x^2+7x-16x-14=0\\\\\implies x(8x+7)-2(8x+7)=0\\\\\implies (x-2)(8x+7) = 0\\\\\implies x = 2,~ x= -\dfrac 78[/tex]

Answer:

it's C just did the quiz and go it right

The number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of regular cones sold be x, and the number of Deluxe cones sold be y. Therefore, total number of cones sold can be written as,

x + y = 86

x = 86 - y

Now, the total money collected can be written as,

5x + 9y = 534

5(86 - y) + 9y = 534

430 - 5y + 9y = 534

4y = 104

y = 26

substitute the value of y in the first equation,

x = 86 - 26

x = 60

Hence, the number of regular cones sold on Wednesday is 60, while the number of deluxe ones sold is 26.

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The population mean (μ) is: 74

The standard deviation (σ) is: 30.6

There is an outlier, 15.

Population mean (μ) = sum of data points / number of data points

Standard deviation (σ) = √(sum of squares/number of data points) = √(SS/n)

Given the data, 15, 75, 88, 92, 100:

Population mean (μ) = (15 + 75 + 88 + 92 + 100)/5 = 74

Standard deviation (σ) = √(4678/5)

σ = √935.6

σ = 30.6

15 is more smaller compared to most of the data points in the data, so, it is an outlier.

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Answer:

4

Step-by-step explanation:

35-10=25

25÷5.75= 4.3

Hey there!

Unless the smaller object was rotated 360° (in which case the rotation wouldn't have to be mentioned), you can see that all of the lines are still in the same place and that it wasn't rotated at all. This eliminated any answer option that mentions a rotation, which is A and C.

Also, if you count the units of one of the straight lines – for example, line AB and A'B' – you can see that the smaller object is four times smaller than the larger object. In the case of line AB and A'B', line AB is 8 units long and A'B' is 2 units long. This means that the scale factor is [tex]1[/tex].

Lastly, the smaller object was moved from its initial location, which would be in the center of the larger object if it wasn't moved after being scaled down.

The answer will be, "a dilation with a scale factor of [tex]1[/tex] and then a translation."

Hope this helped you out! :-)

Answer:

10x^2+2x+13

Step-by-step explanation:

10x^2+3 - (-2x-10)

10x^2+3 +2x+10

10x^2+2x+13

Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,

The volume of the rectangular prism = 8in × 2in × 12.5in

                                                               = 200 in³

Hence, The volume of the rectangular prism is 200 in³.

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Answer:

6

Step-by-step explanation:

By the alternate exterior angles theorem,

120=15(x+2)

8=x+2

x=6

Answer:

y = -x - 1

Step-by-step explanation:

y = mx + b

slope (m): Since the line is going downhill, the slope will be negative

slope = rise / run

slope = 1 / 1

slope = 1

m = -1

y - intercept (b): this when x = 0, the line is crossing the vertical line (y-axis)

b = -1

so y = mx + b is

b = -1, m = -1

y = (-1)x + (-1)

Answer:

y = - x - 1

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 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-0}{0-(-1)}[/tex] = [tex]\frac{-1}{0+1}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - x - 1 ← equation of blue line

Using the tangent ratio, the height of the lighthouse from the top of the cliff ≈ 161.2 meters.

For solving a right triangle, the tangent ratio that can be applied is: tan ∅ = opposite length / adjacent length.

Find the height of the light house and the cliff using the tangent ratio:

tan 51.3 = height/980

Height of lighthouse + cliff = (tan 51.3)(980)

Find the height of the cliff only using the tangent ratio:

tan 47.3 = height/980

Height of cliff = (tan 47.3)(980)

Height of the lighthouse from the top of the cliff = (tan 51.3)(980) - (tan 47.3)(980)

Height of the lighthouse from the top of the cliff ≈ 161.2 meters.

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Answer:

9%

Step-by-step explanation:

(final - initial )/ initial * 100

3.87 / 43 * 100

= 9%

Answer:

y= -2/3x - 4

Step-by-step explanation:

the 2/3 comes from going up 2 spaces and over left 3 spaces. the b is negative 4 because of where it falls. the line is negative because of the direction it is in.

Answer:

1

Step-by-step explanation:

The points go rise:1 up:1 so the slope is 1.

Answer:

hey!! we can taIk here

Step-by-step explanation:

Answer:

The angle shows 90° so that means

90° - 42° = 48°

Therefore the angle of the depression is 48°

The angle of depression from C to point A 48°. The correct option is c. 48°

From the question, we are to determine the angle of depression from C to point A

The angle of depression is the angle formed between the horizontal line and the line of sight when an observer looks downwards at an object

Thus, in the given diagram

The angle of depression is 90° - 42°

Angle of depression = 48°

Hence, the angle of depression from C to point A 48°. The correct option is c. 48°

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Answer:

4 and 7/12

Step-by-step explanation:

This is addition with fractions.

We must convert to the same denominator.

1/3 and 1/4 becomes 4/12 and 3/12

This makes 7/12

1 add 3 add 7/12 is 4 and 7/12