help is needed for this one

Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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Answer:

The original price is $40.00.

Step-by-step explanation:

I am not sure what that given equation is.

But here is the correct answer and steps.

The marked down price is 75% of the original price.

The final price is 90% of the marked down price.

Lets say

\(T\) = Final Price

\(O\) = Original Price

We can write

\(T=(0.75*O)*(0.9)\)

Multiply \(0.9\) by \(0.75\).

\(T=0.675*O\)

We are given the final price. Lets substitute 27.00 for \(T\).

\(27.00=0.675*O\)

Divide both sides of the equation by \(0.675\).

\(40.00=O\)

Answer:

y=\(\sqrt[3]{x-1}\)

Step-by-step explanation:

y=x^3-1

Switch y and x

x=y^3-1

Solve for y

x-1=y^3

y=\(\sqrt[3]{x-1}\)

Answer:

The answer is 12

Hope it helps

Answer:

x = 12

Step-by-step explanation:

Since the 2 legs and base angles are congruent the triangle is isosceles.

The line from the vertex to the base is a perpendicular bisector dividing the triangle into  2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles with legs 3 and \(\frac{1}{2}\) x , hypotenuse \(\sqrt{45}\) , then

(\(\frac{1}{2}\) x )² + 3² = (\(\sqrt{45}\) )²

\(\frac{1}{4}\) x² + 9 = 45 ( subtract 9 from both sides ²)

\(\frac{1}{4}\) x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x = \(\sqrt{144}\) = 12

The simplified and rationalized expression is: (4√3)/x.

To simplify the expression and rationalize the denominator, we need to rewrite the expression with a rational denominator.

First, let's simplify the expression: √3 4/0.5x.

To simplify the square root term, we can write it as: √(3 * 4)/(0.5x).

Simplifying the numerator: √12/(0.5x).

Next, let's rationalize the denominator by multiplying both the numerator and the denominator by 2:

(√12 * 2)/((0.5x) * 2).

Simplifying further: (2√12)/(1x).

Finally, simplifying the square root term: (2√(4 * 3))/x.

Simplifying the square root: (2 * 2√3)/x.

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Answer:

CD = 48

Step-by-step explanation:

Find the value of x using the two equations

9x - 15 = 7x - 1

9(7) - 15 = 7(7) - 1

63 - 15 = 49 - 1

48 = 48

Answer: x = 7

Then get the result of both equations

CD = 48

The length of CD is 48 units.

Isosceles triangles are those triangles which has the length of two sides or angles are equal to each other.

Given triangle ABC is an isosceles triangle since the length of sides AB and BC are given to be equal.

BD is the altitude of the triangle from the vertex B.

We know that, altitude of an isosceles triangle from the non equal angle bisect the opposite side, which is base.

So, AC is bisected at D.

AD = CD

9x - 15 = 7x - 1

Solving,

9x - 7x = -1 + 15

2x = 14

x = 7

Length of CD = 7x - 1 = 49 - 1 = 48

Hence 48 units is the length of CD.

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Step-by-step explanation:

try to separate each shape and then multiply every number of that shape

Answer:

side = 14 cm

Step-by-step explanation:

Let 'x' be the side of the square.

Perimeter = 4 * side

                = 4*x

                = 4x

4x = 56

Solution:

4x = 56

Divide both sides by 4

x = 56/4

x = 14 cm

The percentage of calories that comes from saturated fat in each serving of these crackers is 0.4%

To calculate the percentage of calories that come from saturated fat, we need to first determine how many calories come from saturated fat in one serving of crackers.

We know that each serving of crackers provides 120 calories, and 0.5 grams of saturated fat. We can convert the amount of saturated fat from grams to calories by multiplying it by 9 (since 1 gram of fat provides 9 calories).

0.5 grams of saturated fat x 9 calories per gram = 4.5 calories from saturated fat

Therefore, out of the 120 total calories in one serving of crackers, 4.5 calories come from saturated fat.

To find the percentage of calories that come from saturated fat, we can divide the number of calories from saturated fat by the total number of calories in one serving of crackers, and then multiply by 100.

(4.5 calories from saturated fat / 120 total calories) x 100 = 0.0375 x 100 = 0.4%

Therefore, each serving of crackers provides 0.4% of calories from saturated fat.

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Answer:

73 x 4 + 13 is 305

Answer:

305

explaination:

73 x 4 = 292

292 + 13 = 305

The value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

To calculate the iterated integral ∬_S (y + y^2 cos x) dA over the given region S, where S is the rectangle defined by -5 ≤ x ≤ 5 and 0 ≤ y ≤ π/2, we will evaluate the integral in two steps: first integrating with respect to x and then integrating with respect to y.

Let's start by integrating with respect to x:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) ∫_(-5)^5 (y + y^2 cos x) dx dy

To integrate with respect to x, we treat y as a constant and integrate the expression (y + y^2 cos x) with respect to x over the range -5 to 5:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [(y * x + y^2 sin x)]|_(-5)^(5) dy

Now we have an expression in terms of y only. We substitute the limits of integration for x, which are -5 and 5, into the expression (y * x + y^2 sin x) and evaluate it:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [5y + y^2 sin 5 - (-5y - y^2 sin(-5))] dy

Simplifying further:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [10y + 2y^2 sin 5] dy

Now we integrate the expression [10y + 2y^2 sin 5] with respect to y over the range 0 to π/2:

∫_S (y + y^2 cos x) dA = [5y^2 + (2/3)y^3 sin 5] |_0^(π/2)

Evaluating the expression at the limits:

∫_S (y + y^2 cos x) dA = [5(π/2)^2 + (2/3)(π/2)^3 sin 5] - [5(0)^2 + (2/3)(0)^3 sin 5]

Simplifying:

∫_S (y + y^2 cos x) dA = [5(π^2/4) + (2/3)(π^3/8) sin 5] - [0]

Finally, we simplify the expression:

∫_S (y + y^2 cos x) dA = 5π^2/4 + (π^3/12) sin 5

Therefore, the value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

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The equality constraint A₂X₂ = b₂ becomes the second constraint in the dual problem, and X₂ > 0 corresponds to λ₂ ≥ 0 in the dual problem.

To write the dual problem equivalent to the given primal problem, we can follow these steps:

1. Define the variables:

  Let λ₁ and λ₂ be the dual variables corresponding to the constraints A₁X₁ > b₁ and A₂X₂ = b₂, respectively.

2. Define the objective function:

  The objective function of the primal problem, C₁T X₁ + C₂T X₂, will become the constraints of the dual problem with the coefficients as the variables.

3. Write the dual problem:

  Maximize Z = b₁λ₁ + b₂λ₂ subject to:

  - A₁T λ₁ + A₂T λ₂ ≤ C₁

  - λ₂ ≥ 0

The dual problem is written in its standard form, where Z represents the dual objective function to be maximized. The constraints of the primal problem become the objective function of the dual problem, and the coefficients of the primal variables become the constraints in the dual problem.

Note that the signs of the inequalities may change depending on the original problem's constraints (≤ or ≥). In this case, the original problem had A₁X₁ > b₁, so the corresponding constraint in the dual problem is A₁T λ₁ + A₂T λ₂ ≤ C₁.

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Answer:

641.29

Step-by-step explanation:

100% = 903.23

1% = 903.23 ÷ 100 = 9.0323

71% = 9.0323 x 71 = 641.2933

Rounded to 2 decimal places =

641.2933 = 641.29

Answer:

641.29 m

Step-by-step explanation:

Convert "71%" to the decimal fraction 0.71.  

Then multiply 903.23 m by this 0.71:

641.29 m

Answer:

X=6

Step-by-step explanation:

5(x+2)=6x+3x−1

Step 1: Simplify both sides of the equation.

5(x+2)=6x+3x−14

(5)(x)+(5)(2)=6x+3x+−14(Distribute)

5x+10=6x+3x+−14

5x+10=(6x+3x)+(−14)(Combine Like Terms)

5x+10=9x+−14

5x+10=9x−14

Step 2: Subtract 9x from both sides.

5x+10−9x=9x−14−9x

−4x+10=−14

Step 3: Subtract 10 from both sides.

−4x+10−10=−14−10

−4x=−24

Step 4: Divide both sides by -4.

−4x / -4= −24 / −4

x=6

Answer:

\(x=6\)

Step-by-step explanation:-

\(5\left(x+2\right)=6x+3x-14\)

First, we will Add smiler elements: \(6x+3x=9x\)

⇢ \(5\left(x+2\right)=9x-14\)

Expand \(5(x+2)\) by applying Distributive law: \(a(b+c)=ab+ac\)

⇢ \(5x+5\times \:2\)

⇢ \(5x+10\)

\(5x+10=9x-14\)

Now, Subtract 10 from both sides :

⇢ \(5x+10-10=9x-14-10\)

⇢ \(-4x=-24\)

Divide both sides by - 4:

⇢ \(\frac{-4x}{-4}=\frac{-24}{-4}\)

⇢ \(x=6\)

OAmalOHopeO

Answer:

16. a

17. b

18 19 20 don't know

y = 7 is the equation of the line passing through the coordinates (-2, 7) and having a slope of zero.

An algebraic equation is the equation of a line through a point. It is additionally known as the Slope-Intercept Equation.

Given,

The algebraic equation can be used to express the equation of the line through the point (x1, y1):

y = mx + c

where:

slope = m

c = y - intercept

Considering the query,

(x1, y1) = (-2, 7) (-2, 7)

Slope, m = 0

When these values are inserted into the algebraic equation,

7 = (0 x -2) + c

7 = 0

Thus, y = 7.

y = 7 is the equation of the line passing through the coordinates (-2, 7) and having a slope of zero.

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Answer:

4y + 14

Step-by-step explanation:

Hope this helps!

The correct statements about the equation are b, c, and e.

\(\rm 4.9x-(-3)=12.8\\\\ 3+4.9x=12.8\\\\12.8=4.9x+3\)

The highest power of the polynomial is called the degree of the polynomial.

We have to determine

Which equation accurately represents this statement?

Statement; Negative 3 less than 4.9 times a number, x, is the same as 12.8.

Then,

The equation accurately represents this statement is;

\(\rm 4.9x-(-3)=12.8\\\\4.9x+3=12.8\\\\4.9x=12.8-3\\\\4.9x=9.8\\\\x=\dfrac{9.8}{4.9}\\\\x=2\)

Hence, the correct statements about the equation are b, c, and e.

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Answer:

b,c,e

Step-by-step explanation:

Answer:

(2.5, 6.25)

Step-by-step explanation:

Given

A = (-2,4)

C = (4,7)

If B is located on AC such that AB to AC is 1:3

X coordinate of B;

X = ax1+bx2/a+b

X = 1(-2)+3(4)/1+3

X = -2+12/4

X = 10/4

X = 2.5

Y coordinate of B;

Y = ay1+by2/a+b

Y = 1(4)+3(7)/1+3

Y = 4+21/4

Y = 25/4

Y = 6.25

hence the coordinate of B is at (2.5, 6.25)

The equation of directrix is D. y=± 432/13.

Definition of hyperbola -

1. The vertex i at (0, 36) and a focus at (0, 39), then you have:

  a=36

a²=1296

2. The equation of directrix is:

y =  a² =c

c  =  39

y =  1296/39

y  =  432/13

Therefore, the answer is the option D, which is: D. y=± 432/13

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The complete question is -

A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)

Which are the equations of the directrices ?

A. x= ±12/13

B. y=±12/13

C. x=±432/13

D. y=± 432/13

Answer: Correct

Step-by-step explanation:

Answer:

B.18

Step-by-step explanation:

2+1+3

3+3=6

6+5=11

11+7=18

Answer:

work is shown and pictured

Steps to solve:

m - 2/6 < -1

~Add 2/6 to both sides

m < -4/6

Best of Luck!

Note that the volume   of the cuboid is approximately  1,974.08 cm³.

To find the volume of a cuboid,you need to multiply its length (L),   height (H), and width (W) together.

In this case, the length (L) is given as 19 cm, the height (H) is given as 4 cm, and the diagonal represents  the hypotenuse of a right-angled triangle formed by the length, height,and width of the cuboid.

Using the Pythagorean theorem, we can determine the width (W) of the cuboid  -

Width (W) = √(Diagonal² - Height²)

          = √(21² - 4²)

          = √(441 - 16)

          = √425

          ≈ 20.62 cm

Now that we have the values for L, H, and W, we can calculate the volume (V) of the cuboid  -

Volume (V) = Length (L) * Height (H) * Width (W)

            = 19 cm * 4 cm * 20.62 cm

            ≈ 1,974.08 cm³

Therefore, the volume of the cuboid is approximately 1,974.08 cm³.

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a) The explanatory variable in the study is the format of the stories presented to the four-year-olds: audio, illustrated, and animated. This variable is categorical because it involves distinct categories or formats.

b) The response variable in the study is the brain connectivity measured by the magnetic resonance imaging (MRI) machine. This variable is quantitative as it represents a numerical measurement of brain connectivity.

c) The study includes 27 four-year-olds as the observational units or individuals.

The study aimed to investigate the impact of different story formats on brain connectivity in four-year-olds. The explanatory variable, format, was categorized into three groups: audio, illustrated, and animated.

The response variable, brain connectivity, was measured using an MRI machine. The researchers found a "Goldilocks effect" in the brain connectivity, indicating that the audio format was associated with low brain connectivity, possibly due to the children straining to understand.

On the other hand, the animated format also resulted in low brain connectivity, suggesting that the animation did all the work for the children.

The highest brain connectivity, considered optimal, was observed with the illustrated format, which simulated the experience of reading a book to a child.

The study included 27 four-year-olds as the observational units, providing insights into the relationship between story format and brain connectivity in young children.

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