The two conditional relative frequency tables below show the results of a survey asking students whether they are taking a foreign language or not.

A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.34, 0.66, 1.0. The third column is labeled not taking a foreign language with entries 0.64, 0.36, 1.0. The fourth column is labeled total with entries 0.4, 0.6, 1.0.

Table B: Frequency of Foreign-Language Studies by Row

A 4-column table with 3 rows. The first column has no label with entries middle school, high school, total. The second column is labeled taking a foreign language with entries 0.68, 0.88, 0.8. The third column is labeled not taking a foreign language with entries 0.32, 0.12, 0.2. The fourth column is labeled total with entries 1.0, 1.0, 1.0.

Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?”

Table A, because the given condition is that the student is in high school.
Table A, because the given condition is that the student is taking a foreign language.
Table B, because the given condition is that the student is in high school.
Table B, because the given condition is that the student is taking a foreign language.

Answer:

C

Step-by-step explanation:

7 × ln(x) = 2.4

ln(x) = 2.4/7 = 0.342857143...

x = e^0.342857143... = 1.408967466... ≈ 1.41

Answer:

B.

Step-by-step explanation:

Since all bulbs are connected in series, by opening switch A, you break the series connection, and all bulbs go out.

Answer:

48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

edge 2023

The correct expression is : [tex]\frac{4 cm }{1 year}[/tex] x [tex]\frac{10 mm}{1 cm}[/tex] x [tex]\frac{ 1 year }{365 days}[/tex]

What is the correct expression?

The first step is to convert year to days.

1 year = 365 days

The next step is to convert cm to mm.

1cm = 10 mm

4 x 10 = 40mm

Now, divide 40 mm by 365 days

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Answer:

The range is all real numbers.

Step-by-step explanation:

The function shown is a line (and not a horizontal line).

The range is all the y's on the graph or all the y's that can be generated by the equation of the function.

f(x) = 3x + 9

You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.

The range is All Real Numbers.

Answer:

f(8) = 9

Step-by-step explanation:

f(x)=(x-5)^2

Let x = 8

f(8)=(8-5)^2

     = 3^2

     = 9

Answer: -8

Step-by-step explanation:

Answer:

7(w+13)=35

7w + 91 =35

7w=35-91

7w= -56

7w/7 = -56/7

w=-8

The value of z is 119° and the value of y is 28°.

When two parallel lines meet any other line, comparable angles are generated in matching corners or corresponding corners with the transversal, these angles are called corresponding angles.

If the given diagram is modified a bit it will look as shown below, the two angles will be 61° because the two angles are corresponding angles.

Now, since 61° and x lie on the same side of the line, therefore, the sum of the two angles will be,

61° + x = 180°

x = 119°

Also, the angles measured at 61° and (3y-23)° lie on the same side of the transversal, therefore, these two angles are corresponding angles. Thus,

61° = (3y-23)°

61 = 3y - 23

y = 28

Hence, the value of z is 119° and the value of y is 28°.

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Answer:5.5

Step-by-step explanation:first we have to plus 4 and 7 and then we to divide the answer we get by 2 because there are only 2 digits and then the mean is 5.5

hope it helps

Answer:

x • (2xt + 7y)

Step-by-step explanation:

1. ((5xy-((x2)•t))+2xy)+(3x2•t)

2. Pull out like factors :

  2x2t + 7xy  =   x • (2xt + 7y)

Final result

x • (2xt + 7y)

Answer:

[tex]7xy + {x}^{2} t[/tex]

Step-by-step explanation:

[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]

Answer:

b(n) = -11 + (n-1)*8

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

b(1)   -11         + 8 =   -3

b(2)   -3          + 8 =    5

b(3)   5         + 8 =   13

b(4) 13

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

b(n) = -11 + (n-1)*8

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   YES

The value of x would be 5 for the model 2x+4.

Rearrange unknown terms to the left side of the equation,
[tex]= > 2x-3x = -1 - 4[/tex]

Combine like terms[tex]= -x = -1-4[/tex]

By calculating the sum or difference : -x = -5

Lets divide both sides of the equation by the resulting coefficient 5
So x = 5

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All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.

Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

Answer:

$5.88

Step-by-step explanation:

3 erasers ⇒ $4,41

4 erasers ⇒ $A

A = 4 erasers * $4.41 / 3 erasers

A = $ 5.88

Answer:

see below

Step-by-step explanation:

Proportion:

4.41 is to 3 erasers as   'x' is to 4 erasers:

4.41 /3     =  x / 4       <======this is your proportion

 or rearrange

      4 *  4.41/3   = x  

(this results in x = $ 5.88  for 4 erasers )

Answer:

B. -2

Step-by-step explanation:

-12x -2(x+9) = 5(x+4)

*ALWAYS REMEMBER YOUR BODMAS*

-12x -2x - 18 = 5x + 20

*group the like terms*

-14x - 5x = 20 + 18

-19x = 38

x = -2

The value of x that makes the equation true is: x = -2.

B. -2.

Here, we have to find the value of x that makes the equation true, we need to solve for x.

Let's solve the equation step by step:

-12x - 2(x + 9) = 5(x + 4)

Distribute the -2 and 5 on the right side of the equation:

-12x - 2x - 18 = 5x + 20

Combine like terms on both sides:

-14x - 18 = 5x + 20

Move the variable terms (5x) to one side of the equation and the constant terms to the other side.

Let's subtract 5x from both sides:

-14x - 5x - 18 = 5x - 5x + 20

-19x - 18 = 20

Move the constant term (-18) to the other side of the equation.

Let's add 18 to both sides:

-19x - 18 + 18 = 20 + 18

-19x = 38

Finally, divide both sides by -19 to isolate x:

x = 38 / -19

x = -2

So, the value of x that makes the equation true is: x = -2.

B. -2.

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jAlright, let's take this problem step-by-step:

What is the perimeter:

 ⇒ all the side-lengths added up

    ⇒ need to find side-length using distance formula

                [tex]Distance_._. Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                         - (x₁,y₁): first point

                         - (x₂,y₂): second point

Let's solve:

           ⇒ first point: (5,7)

           ⇒ second point: (3,3)

           [tex]Distance =\sqrt{(3-5)^2+(3-7)^2} =\sqrt{4+16} =\sqrt{20} =4.472[/tex]

          ⇒ first point: (5,7)

          ⇒ second point:(8,6)

           [tex]Distance=\sqrt{(8-5)^2+(6-7)^2} =\sqrt{9+1} =\sqrt{10}=3.162[/tex]

          ⇒ first point: (8,6)

          ⇒ second point: (3,3)

           [tex]Distance = \sqrt{(3-8)^2+(3-6)^2} =\sqrt{25+9} =\sqrt{34}=5.831[/tex]

Now let's solve for the perimeter:

  [tex]Perimeter = 4.472+ 3.126+ 5.831=13.429[/tex]

Answer: 13.43 (rounded to the nearest hundredth)

Hope that helps!

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Using translation concepts, the method that Howard could have used to determine the coordinates of the vertices of the image is:

(x,y) -> (-x,y).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection over the y-axis can be described according to the following rule:

(x,y) -> (-x,y).

Hence this rule can be applied to find the vertices.

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Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.

[∵ TP=TQ = Tangents from T upon the circle]

⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ

⠀⠀⠀

___________________________________________

[tex]\longmapsto{}[/tex]By Applying Pythagoras Theorem in ∆OPR :

OR = √OP² - PR²

OR = √5² - 4²

OR = 3cm

__________________________________________

Now,

[tex]\leadsto[/tex]∠TPR + ∠RPO = 90° (∵TPO=90°)

[tex]\leadsto[/tex]∠TPR + ∠PTR (∵TRP=90°)

[tex]\leadsto[/tex]∴ ∠RPO = ∠PTR

⠀⠀

∴ Right triangle TRP is similar to the right triangle PRO. [By A-A Rule of similar triangles]

⟼[tex]\frac{TP}{PO} = \frac{RP}{RO} [/tex]

⟼[tex]\frac{TP}{5} = \frac{4}{3} [/tex]

⟼[tex]TP= \frac{20}{3} [/tex]

⠀⠀⠀⠀⠀

Answer:

Which one does not belong to the group

The equation given is matched with the respective vertex forms.

The standard equation for a circle is given by

(x-h)² + (y-k)² = r²

The equation given in the question are

x² + y²  − 4x + 12y − 20 = 0

(x − 6)²  + (y − 4)²  = 56

x²  + y²  + 6x − 8y − 10 = 0

(x − 2)²  + (y + 6)²  = 60

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

5x²  + 5y²  − 10x + 20y − 30 = 0

(x+3)²  + (y-4)²  = 35

2x²  + 2y²  − 24x − 16y − 8 = 0

(x-1)²  + (y+2)²   = 11

The first equation is

x² + y²  − 4x + 12y − 20 = 0

It can be written ad

x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0

(x-2)² +(y+6)²= 60

The second equation is

x²  + y²  + 6x − 8y − 10 = 0

x² +6x +9-9 +y²  -8y +16-16 -10 = 0

(x+3)²  + (y-4)²  = 35

The third equation is

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

The fourth equation is

5x²  + 5y²  − 10x + 20y − 30 = 0

(x-1)²  + (y+2)²   = 11

The fifth equation is

2x²  + 2y²  − 24x − 16y − 8 = 0

(x − 6)²  + (y − 4)²  = 56

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[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.

An absolute value inequality is an expression with absolute functions as well as inequality signs.

According to the question:

Mathematically absolute value inequality is represented as :

|X -20|≤ 5

Solving the equation using

|z| ≤ a→ -a ≤ z  ≤ a :

here, z = X- 20 and a = 5:

[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]

By Solving X adding 20 on the three sides of the inequality

[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]

By simplifying it:

[tex]15 \leq X \leq 25[/tex]

Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]

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The zeroes of the function f(x) = x (x – 8) will be 0 and 8.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The function is given below.

f(x) = x (x – 8)

The zeroes of the function f(x) is given by the factor equals to zero.

Then we have

      f(x) = 0

x(x – 8) = 0

          x = 0, 8

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[tex]\textsf {Finding y :}[/tex]

[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]

[tex]\implies \mathsf {y^{2} = 8}[/tex]

[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]

[tex]\textsf {Finding z :}[/tex]

[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]

[tex]\implies \mathsf {z^{2} = 72}[/tex]

[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]

Answer:

z =8.49 or 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]

Length of hypotenuse = 8+1=9

length of one side = 3

so, a²+3²=9²

     a²+3²=9²

     a²=81-9

     a²=72

     a=√72=8.49 or 6[tex]\sqrt{2}[/tex]

Answer:

3.256*10³2

Step-by-step explanation:3.256 * 1000 = 3256 1000 =10³

Answer:

Option 1

Step-by-step explanation:

See attached image

The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

The given sequence ;

–3.2, 4.8, –7.2, 10.8, …

The common ratio

= -4.8/ 3.2

= - 1.5

The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.

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Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ABD and △ACB,

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, △ABD ∼ △ACB (by AA similarity criterion)

Similarly, we can prove △BCD ∼ △ACB.

Thus △ABD ∼ △ACB,

Therefore, AD/AB = AB/AC.

We can say that AD × AC = AB².

Similarly, △BCD ∼ △ACB.

Therefore,

CD/BC = BC/AC.

We can also say that

CD × AC = BC².

Adding these 2 equations, we get

AB² + BC² = (AD × AC) + (CD × AC)

AB² + BC² =AC(AD +DC)

AB² + BC² = AC²

Hence proved

Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

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At least 1 right angle = A, C and E

At least 2 sides of equal length = B and E

At least 1 pair of parallel sides= B and E

Parallel lines are those lines that are apart and they never meet till infinity.

Example of shapes that have sides with parallel line are the rectangle and parallelograms.

The shape B and E are rectangles and parallelograms respectively.

The shape that has angle 90° are right angle triangles and trapezium.

Therefore, the shapes that has right angles are A which is a trapezoid and E which is a rectangle.

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