Write an equation to describe the situation. 3x=2 1/4

The probability that at least 4 of the 10 selected employees are women is approximately 0.671.

Let the probability that a randomly selected employee is a woman is "p",

The 120 employees are men and rest 80 are women,

We have,

⇒ p = (number of women)/(total number of employees),

⇒ p = (200 - 120)/200,

⇒ p = 0.4,

Let X = number of women among the 10 employees selected.

Then X follows a binomial distribution with parameters "n = 10" and "p = 0.4".

The probability of "at-least-4" selected employees are women is expressed as⇒ P(X ≥ 4) = 1 - P(X ≤ 3),

⇒ P(X ≤ 3) = [tex]\[ \sum_{k=0}^{3} \][/tex] C(10,k) × 0.4^k × 0.6^(10-k),

We can then subtract this value from 1 to obtain P(X ≥ 4),

⇒ P(X ≥ 4) = 1 - P(X ≤ 3),

⇒ P(X ≥ 4) ≈ 0.671

Therefore, the required probability is approximately 0.671.

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The value of "n" is 6.

"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:

7(n+4) = 5(n+8)

Expanding the brackets, we get:

7n + 28 = 5n + 40

Simplifying, we get:

2n = 12

n=6

A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.

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Answer:

Step-by-step explanation:

$1330.97 is the amount needed to repay the loan in full using the Rule of 78.

In finance and ecοnοmics, interest is payment frοm a bοrrοwer οr depοsit-taking financial institutiοn tο a lender οr depοsitοr οf an amοunt abοve repayment οf the principal sum, at a particular rate. It is distinct frοm a fee which the bοrrοwer may pay the lender οr sοme third party.

We wοuld subract interest  saved  frοm  the tοtal payment which Grant wοuld have tο pay if he cοntinued the lοan fοr 30 mοnths :

        7050-79.03= $6970.97

The Amοunt οf mοney Grant have already paid fοr 24 mοnths

= 24*235= $5640

The amοunt needed tο repay the lοan in full

= 6970.97 - 5640 = $ 1330.97

Thus, option a $ 1330.97 is correct.

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The function is defined by this set of rules and we got the cost of mailing a letter weighing 2.5 ounces from the United States to Mexico in 2018 using function P is $2.89.

Based on the rules, the function P is defined as follows:

P(w) = 1.15, if 0 < w ≤ 1

P(w) = 1.99, if 1 < w ≤ 2

P(w) = 2.89, if 2 < w ≤ 3

P(w) = 3.30 + 0.45(w-3), if 3 < w

This function gives the cost, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w.

To find the cost of mailing a letter weighing 2.5 ounces using function P, we need to evaluate P(2.5). Based on the rules defined above, we can see that 2 < 2.5 ≤ 3. Therefore, the cost of mailing a letter weighing 2.5 ounces would be:

P(2.5) = 2.89

So, it would cost $2.89 to mail a letter weighing 2.5 ounces from the United States to Mexico in 2018 using function P.

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Answer:

Step-by-step explanation:

You want the missing segment lengths in the kite shown, where half-diagonals are 3 and 6, and one side length is 5.

The diagonals of a kite cross at right angles, so each of the triangles shown is a right triangle. The figure has left-right symmetry about the vertical axis, so x=z.

We recognize the top triangles as being 3-4-5 right triangles, so the missing side length is y = 4.

These lengths are the hypotenuse of a right triangle with legs 3 and 6. The Pythagorean theorem tells us they are ...

  x² = 3² +6²

  x² = 9 +36 = 45

  x = √(45) = √(9·5) = 3√5

The lengths x and z are ...

  x = z = 3√5

__

Additional comment

In case you have never heard of a 3-4-5 right triangle, you can find y from the Pythagorean relation:

  5² = 3² +y²

  y² = 25 -9 = 16

  y = √16 = 4

The {3, 4, 5} Pythagorean triple is one of several in common use in algebra, trig, and geometry problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

Answer:

x = 6

Step-by-step explanation:

4x - 2x= 2x

15-3= 12

2x=12

12/2=6

6=x

Answer:

x<6<6

Step-by-step explanation:

4+3<2+15.

4x+3−3< 2x+15−3

4<2+12

4x−2x<2x+12−2x4−2<2+12−2

2x<122<12

2x2<12222<122

x<6

Answer: The inverse of the logarithmic function f(x) = log2x can be found by interchanging the roles of x and y in the function and solving for y. The steps are as follows:

Step 1: Replace f(x) with y.

y = log2x

Step 2: Interchange x and y.

x = log2y

Step 3: Solve for y.

We need to isolate y on one side of the equation. To do this, we can rewrite the equation in exponential form. Recall that the logarithmic function with base b is defined as follows:

logb(x) = y if and only if b^y = x.

Using this definition, we can rewrite the equation x = log2y as follows:

2^x = y

This means that the inverse of f(x) = log2x is given by:

f –1(x) = 2^x

Therefore, the correct answer is:

f –1(x) = 2^x.

Step-by-step explanation:

    ΔFIT ≅  ΔRIS triangle  are congruent.

How do triangles work?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point.

                       The triangle's three angles add up to a total of 180 degrees. A triangle is a closed, two-dimensional geometry with three sides, three angles, and three vertices. Polygons include triangles as well.

 In figure ,

              FI = IS

              RI = IT

            ∠FIT = ∠RIS

           ΔFIT ≅  ΔRIS

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The function table for the function y=−2x+1 if given below so that Output of  y  could be –2, –1, 0, 1.

[tex]\left[\begin{array}{ccc}X&Y\\1/2&0\\1&1\\0&-1\\-1/2&-2\end{array}\right][/tex]

Here, Y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x). The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), other abbreviated symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or unspecified.

The function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. German mathematician Peter Dirichlet first offered the modern definition of function in 1837.


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Two methods for proving that two triangles on a Cartesian coordinate plane are congruent are:

Two methods for proving that two triangles on a Cartesian coordinate plane are congruent are:

Side-Side-Side (SSS) congruence theorem: Two triangles are congruent if their corresponding sides are equal in length.

Side-Angle-Side (SAS) congruence theorem: Two triangles are congruent if two corresponding sides and the included angle are equal in both triangles.

To prove that two triangles on a Cartesian coordinate plane are congruent using coordinate geometry, we can follow these steps:

Identify the coordinates of the vertices of the two triangles.

Use the distance formula to find the lengths of the sides of each triangle.

Use the angle formula to find the measure of one angle in each triangle.

Check if the corresponding sides and angles of the two triangles are equal.

If the corresponding sides and angles are equal, the two triangles are congruent by SAS or SSS congruence theorem.

Here are the coordinates of the Triangles:

ΔABC = A(-3, 4) B (-4, 1) C (0,3)

ΔDEF = D(0, 2) E(3, 1) F(2, -2)


To prove whether the two triangles ΔABC and ΔDEF are congruent or not, we need to check if their corresponding sides and angles are equal.

Using the distance formula, we can find the lengths of the sides of each triangle:

AB = √[(4 - 1)² + (-4 - (-3))²] = 3.16

BC = √[(3 - 1)² + (0 - 4)²] = 4.47

AC = √[(3 - 4)² + (0 - (-3))²] = 3.16

DE = √[(2 - 1)² + (3 - 0)²] = 3.16

EF = √[(2-3)² + (-2- 1)²] = 3.16

DF = √[(0-2)² + (2 - - 2)²] = 4.47


Thus, on the basis of the side-side-side postulate, both triangles are congruent because the three sides have an equivalent on each triangle.

AB = DE
AC = EF
BC = DF

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If she receives $2 off the regular price, p. by using a coupon. her total cost, including 20% for tax and tip, is $9. then the regular price of the lunch special is $11.

Let's figure out why that is so. Romita gets a sushi lunch special at Yoshi's, with a coupon. Romita received a discount of $2 off the regular price, P.

         Let's assume that the price of lunch before the discount is $P.

 Therefore, after the discount, the cost of the lunch is (P - 2).

 Now, let's determine the total cost of the lunch. The price of the lunch is inclusive of 20% tax and tip. This implies that Romita's total cost is 120% of the final cost of the lunch.

    We can represent this information in the equation below:

             Total cost = 120% of (P - 2)

             Total cost = 1.2(P - 2)

    From the given information, we know that the total cost is $9.

    This means we can solve the equation for P.P = (9/1.2) + 2P = 7.5 + 2P = $11

         The regular price of the lunch special is $11.

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The steps that you should take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/20.

5. Reflect the intermediate image.

In Mathematics and Geometry, two geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image by the length of the pre-image or by multiplying the vertices by a specific scale factor.

This ultimately implies that, we would multiply the vertices of polygon ABCD by 1/20 and then apply a reflection of the intermediate image;

Vertices A' = (1 × 1/20, -6 × 1/20) = (1/20, -6/20)

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Step-by-step explanation:

Both of the expressions equal y....equate them

-6x + 8 = 5x-4

12 = 11x

x = 12/11 = 1  1/11

then y =  5x -4  = 5(12/11) - 4   = 1  5/11

( 1  1/11  ,  1  5/11 )

Answer:

2/5

Step-by-step explanation:

2/5 x 7/8 = 7/8 x 2/5

14/40 = 14/40

Helping in the name of Jesus.

Answer:

x = 5

Step-by-step explanation:

[tex]3x + 11 = 2(x + 8)[/tex]

[tex]3 x + 11 = 2x + 16[/tex]

[tex]x = 5[/tex]

The volume of the given prisms above is calculated as follows:

a.) = 432m³

b.) = 135m³

C.) = 1,332m³

For prism a:

Divide the prism to get two solid shapes and then add up the calculated volumes of each.

Vol of First shape = length× width× height

H = 12m

w = 4m

L = 7m

Vol = 12×4×7 = 336m³

Vol of second shape ;

=2( 4×4×3)

= 2 × 48

= 96m³

Therefore the volume of prism A = 336+96 =432

For prism b:

Volume= BH

B = area of the base

H = height of the prism

Volume = 1/2×5 × 6 × 9

= 5×3×9

= 135m³

For prism C:

Divide the prism to get two solid shapes and then add up the calculated volumes of each.

Vol of first shape = 5×15×12 = 900m³

Vol of second shape;

=2(6×12×3)

= 2(216)

= 432 m³

Volume of prism C = 900+432

= 1,332m³

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As we know consecutive angle of parallelogram are supplementary then the sum m∠JLM = 22°.

Let the m∠JLM be x.
Thus, x+56+27+75 = 189
x = 180 - 158
x = 22

Hence the angle m∠JLM would be 22°

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

The properties of a parallelogram are shared by the shapes of a square and a rectangle.

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The bacteria pοpulatiοn after 3 hοurs is 36864.

Expοnential grοwth:  

The cοncept used here is expοnential grοwth, which οccurs when the rate οf increase οf a quantity is prοpοrtiοnal tο its current value.

In this case, the bacteria pοpulatiοn dοubles every 15 minutes, which means that its rate οf increase is prοpοrtiοnal tο its current value.

This leads tο an expοnential grοwth curve, where the pοpulatiοn increases rapidly οver time.    

Here we have

An experiment begins with 9 bacteria that grοw at such a rate their pοpulatiοn dοubles every 15 minutes.

Since there are 4 sets οf 15 minutes in an hοur,

The pοpulatiοn will dοuble 4 times in οne hοur.

Therefοre, the bacteria pοpulatiοn after οne hοur will be:

=> 9 × 2⁴ = 9 × 16 = 144

After twο hοurs, the pοpulatiοn will dοuble 4 times again: Hence, the pοpulatiοn after 2 hοurs

=> 144 × 2⁴ = 144 × 16 = 2,304

Similarly, After three hοurs,

2,304 × 2⁴ = 2,304 × 16 = 36864

Therefοre,

The bacteria pοpulatiοn after 3 hοurs is 36864.

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Answer:

Step-by-step explanation: First, you need to convert the width of the mural from feet to meters.

1 meter = 3.28084 feet (approximately)

So, 1 foot is approximately 0.3048 meters.

13 feet x 0.3048 meters/foot = 3.9624 meters (rounded to four decimal places)

Therefore, the width of the mural on the scale drawing would be 3.9624 meters.

Next, you need to convert the height of the mural from feet to meters.

24 feet x 0.3048 meters/foot = 7.3152 meters (rounded to four decimal places)

Therefore, the height of the mural on the scale drawing would be 7.3152 meters.

So, the measurements of the mural on a scale drawing using the scale 3m: 2ft would be 3.9624 meters wide and 7.3152 meters tall.

Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Put the numbers in order and find the number in the middle

2,4,6,10,15  The number in the middle is 6.

Helping in the name of Jesus.

Answer: 6

Step-by-step explanation:

the median is the middle number to put it in an easy explanation. Since there are 5 numbers the 3rd one would be the middle one since there would be 2 numbers of the left and 2 number on the right!!!

sorry I forgot to put them in order so

2,4,6,10,15

out of those 6 is the one in the middle

Answer:

58.5

Step-by-step explanation:

[tex]A=\frac{h_bb}{2}[/tex]

[tex]\frac{6.5*18}{2}[/tex]

[tex]58.5[/tex]

Using diagonals from a common vertex of a decagon (a polygon with ten sides), a total of seven triangles can be formed.

To see why, we can apply the formula for the number of triangles formed by drawing all the diagonals from a single vertex of a polygon, which is (number of sides - 2). For a decagon, the formula gives us:

number of triangles = (10 - 2) = 8

However, we need to subtract one from the total because the vertex where the diagonals are drawn from is not included in any of the triangles. Therefore, the number of triangles formed by drawing diagonals from a common vertex of a decagon is:

number of triangles = 8 - 1 = 7

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Answer:

  x² -6x +22 = 0

Step-by-step explanation:

You want to write the quadratic equation that has roots x = 3±4i, starting from x -3 = ±4i.

The next step would be to square both sides of the equation:

  (x -3)² = (±4i)²

  (x -3)² = 16i² = -16

  (x -3)² +16 = 0 . . . . . . add 16

  x² -6x +22 = 0 . . . . .  expand the square