A sample of 50 high school and college students were surveyed to choose a favorite free-time activity: playing sports, dancing, or watching movies/TV. 40% of the sample is high school students. From the sample, it is found that 22% were high school students who chose playing sports, and 6% were high school students who chose dancing. 10% were college students who chose sports and 18% were college students who chose watching movies/TV. 38% of the students surveyed chose dancing.

Which of the following is a correct two-way relative frequency table for the data?


High School and College Student Leisure Time Activity Preferences
Sports Dancing Movies/TV Row Totals
High school students 0.22 0.06 0.12 0.40
College students 0.10 0.32 0.18 0.60
Column totals 0.32 0.38 0.30 1

High School and College Student Leisure Time Activity Preferences
Sports Dancing Movies/TV Row Totals
High school students 0.11 0.03 0.06 0.40
College students 0.05 0.16 0.09 0.60
Column totals 0.16 0.19 0.15 1

High School and College Student Leisure Time Activity Preferences
Sports Dancing Movies/TV Row Totals
High school students 11 3 6 20
College students 5 16 9 30
Column totals 16 38 30 50

High School and College Student Leisure Time Activity Preferences
Sports Dancing Movies/TV Row Totals
High school students 22 6 12 40
College students 10 32 18 60
Column totals 32 38 30 100

Using the fact that both triangles are similar, we will conclude that the measure of angle B is 59°.

First, two figures are similar if the figures have the same shape, then the interior angles are all the same in both figures.

Here we know that the two triangles are similar and thus, the internal correspondent angles of the two triangles are equal in measure.

First, there is a common vertex at C, so the angle there is the same for both triangles. We also can see that angles A and D have the same measure, then the angles B and b will also have the same measure.

And we know that the measure of angle b is 59°, then we can conclude that the measure of angle B will also be 59°, so the correct option is the first one.

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Using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).

A proportion refers to the fraction of the total amount, and the measures are related using a rule of three.

The midpoint of a segment refer to the mean of the coordinates of the endpoints, so we get that:

3.5 = (x + 8) / 2

x + 8 = 7

x = 7 - 8

x = - 1

-1 = (y + 5) / 2

y + 5 = -2

y = -2 - 5

y = - 7.

End point =- (-1, -7)

Therefore, using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).

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The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is [tex]x^{2} +7x+6=0[/tex].

Given that a Quadratic equation whose roots are -6 and -1 with leading coefficient is 1 and asked to find the equation of quadratic equation.

Quadratic equation:

The polynomial equations of degree two in one variable of form f(x) = a[tex]x^{2}[/tex] + bx + c = 0 and with a, b, c, ∈ R and a ≠0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x).

For a quadratic equation if (a,b) are roots then,

(x-a)(x-b) is the quadratic equation having roots "a" and "b"

The equation with roots -6 and -1 is
⇒(x+6)(x+1)

⇒[tex]x^{2}[/tex]+7x+6

Threfore,The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is [tex]x^{2} +7x+6=0[/tex].

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Answer:

1 < x < 7

Step-by-step explanation:

Hello!

There are two cases for this equation:

Solve for x in each case.

The solution set is 1 < x < 7.

Answer:

Option A on edge

Step-by-step explanation:

Its point W.

Answer:

18 cm Is the Answer To your Question

Answer:

-2

Step-by-step explanation:

3−11−(−6)=

3-11= -8

-8-(-6)

the two minus become plus so

-8+6= -2

Answer:

Interest = $63

Balance = $2,063

Step-by-step explanation:

Compound Interest Formula

[tex]\boxed{\sf I=P\left(1+\frac{r}{n}\right)^{nt} -P}[/tex]

where:

Given:

Substitute the given values into the formula and solve for I:

[tex]\implies \sf I=9000\left(1+\dfrac{0.014}{2}\right)^{2 \times 0.5}-9000[/tex]

[tex]\implies \sf I=9000\left(1+0.007\right)^{1}-9000[/tex]

[tex]\implies \sf I=9000\left(1.007\right)-9000[/tex]

[tex]\implies \sf I=9063-9000[/tex]

[tex]\implies \sf I=63[/tex]

Therefore, the account earns $63 interest in the first six months.

The balance after six months is $2,063.

The value of a based on the information is 4.

It should be noted that b = 5.5

It should be noted that e = 10

There are three alphabets in between them. This means the difference will be:

= (10 - 5.5)/3

= 4.5/3

= 1.5

Therefore, the value of a will be:

= 5.5 - 1.5

= 4

The value of a is 4.

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The value of a based on the information is 4.

How to calculate the value?

It should be noted that b = 5.5

It should be noted that e = 10

There are three alphabets in between them. This means the difference will be:

= (10 - 5.5)/3

= 4.5/3

= 1.5

Therefore, the value of a will be:

= 5.5 - 1.5

= 4

The value of a is 4.

Answer:

Hello,

Step-by-step explanation:

[tex]1) \ 4,7,10,13,16,....\\u_n=4+(n-1)*3=1+3n\\\\2)\ -10,-6,-2,2,6....\\u_n=-10+(n-1)*4=-14+4n\\\\3)\ \frac{6}{3} ,\frac{7}{3} ,\frac{8}{3} ,\frac{9}{3} ,\frac{10}{3} ...\\\\u_n=\frac{6}{3} +(n-1)*\frac{1}{3} =\frac{5}{3} +\frac{n}{3} \\[/tex]

The circumference is 150.72 millimeters and the area is 1808.64 square millimeters

The radius of the coin is given as

r = 12 millimeters

The diameter of the coin is calculated as

Diameter = 2 * r

So, we have

Diameter = 2 * 12 millimeters

Evaluate

Diameter = 24 millimeters

The circumference of the coin is calculated as

C = 2πr

So, we have

C = 2 * 3.14 * 24

Evaluate

C = 150.72 millimeters

The area of the coin is calculated as

A = πr²

So, we have

A = 3.14 * 24²

Evaluate

A = 1808.64 square millimeters

Hence, the circumference is 150.72 millimeters and the area is 1808.64 square millimeters

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Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

Answer:

Hello!

for 11 we can put in values

x = 0

y = 12 * 0^2

y=0

One point is (0,0)

x=1

y=12*1^2

y=12

Another point is (1,12)

x=-1

y = 12 * -1^2

y=12

A third point is (-1,12)

This tells us that this is not exponential since an exponential function as a steep curve on one side not two.

You can think of an exponential function as a half parabola if it helps.

13. We can plug in numbers again here.

x=0

y=7(0)+3

y=3

So the first point is (0,3)

x=1

y=7(1)+3

y=10

The second point is (1,10)

x=-1

y=7(-1)+3

y=-4

so the third point is (-1,-4)

This shows that the graph is not exponential it is linear since it goes in a straight line.

15. We just plug in -2 for t so

g(-2) = 2*0.4^-2

0.4^2 is 0.16 * 2 is 0.32 which is the answer

17. We can put 18 for w

h(18) = -0.5*4^18

This is where there is a issue because 4^18 is a extremely small number (6.9 * in scientific notation-

But we can multiply that by -0.5 to get

-3.4 *

which I believe is -0.000000034

Step-by-step explanation:

Answer: U'=(8, 5)

V'=(7, 5)

W'=(6, 10)

Step-by-step explanation:

When rotated around the origin by 180 degrees, the triangle will have all its coordinates' x and y values negated.

U=(-8, -5) ==> U'=(8, 5)

V=(-7, -5) ==> V'=(7, 5)

U=(-6, -10) ==> W'=(6, 10)

Answer:

angle 1 = 51

angle 2 = 39

Step-by-step explanation:

The sum of two angles is equal to 90° since they are complementary angles

angle 1 + angle 2 = 90° rewrite equation using given values

x + 38 + 3x = 90 add like terms

4x + 38 = 90 subtract 38 from both sides

4x = 52 divide both sides by 4

x = 13 now to find the measure of each angle replace x with 13

angle 1 = 51

angle 2 = 39

Answer:

3w - 4 1/2

Step-by-step explanation:

6(1/2w- 3/4)

distributing gives you

6/2w- 18/4

simplifying it gives you

3w-4 1/2

Answer:

1) [tex]|x-2| = 8[/tex]

2) [tex]|x+7.5|=2.5[/tex]

Step-by-step explanation:

Answer:

The tree is 30 feet

Step-by-step explanation:

Set up a proportion

[tex]\frac{height}{shadow}[/tex] = [tex]\frac{height}{shadow}[/tex]  Fill in what you know

[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{7}[/tex]  Cross multiply

7x = 210  Divide both sides by 7

x = 30

The way a flow proof shows logical steps in the proof of a conditional statement is; A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

A flow proof uses a diagram to show each statement leading to the conclusion. Arrows are drawn to represent the sequence of the proof. The layout of the diagram is not important, but the arrows should clearly show how one statement leads to the next. The explanation for each statement is written below the statement.

A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

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Answer: A conditional statement (also called an if-then statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.

Step-by-step explanation:

Answer: 97. -10<n<8

99. g>=7 or g<0

101. x<5 or x>=6

Step-by-step explanation:

97. -1<9+n<17

-1-9<9-9+n<17-9

-(1+9)<n<17-9

-10<n<8

99. g+5>=12

g+5-5>=12-5

g>=7

g/9 < 0

g<0

g>=7 or g<0

101.

2x<10

x<5

x/2 >=3

x>=6

x<5 or x>=6

Answer:

  a.  Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2

  b.  Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5

Step-by-step explanation:

Given two tables of values, you want to find the explicit and recursive formulas for those values.

When the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.

When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.

The constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).

The attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...

  f(x) = 2x² +3

The attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.

The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...

  an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term

Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...

  g(x) = 3x² +(-10 +(-2)(x -5))

 g(x) = 3x² -2x

A recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.

The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.

The applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...

  d(x) = -10 +4(x -(-2)) = 4x -2

Then the recursion relation is

  f(x) = f(x -1) +d(x) = f(x -1) +4x -2

And the recursive formula is ...

  f(-3) = 21; f(x) = f(x -1) +4x -2

The applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...

  d(x) = 31 +6(x -6) = 6x -5

Then the recursive formula is ...

  g(5) = 65; g(x) = g(x -1) +6x -5

Answer:

x = 18

Step-by-step explanation:

x/6  - 7 = -4

x/6 = -4 + 7

x/6 = 3

x = 6*3

x = 18

Check:

18/6  - 7 = -4

3 - 7 = -4

Answer:

20

Step-by-step explanation:

The common factors for 60,40,20,80 60 , 40 , 20 , 80 are 1,2,4,5,10,20 1 , 2 , 4 , 5 , 10 , 20 . The GCF for the numerical part is 20 .

Answer i dont get it

Step-by-step explanation:

The order of set of numbers {-415%, -√17, -4.1, -4.08} from least to greatest is {-415% < -√17 < -4.1 < -4.08}

Order of set of numbers:

Numerical order is a way of arranging a group of numbers into a sequence. This could be ascending or descending.

When we arrange numbers in ascending order, we arrange them from small to big, and when we arrange numbers from big to small, it is called descending order.

Given,

=> {-415%, -√17, -4.1, -4.08}

Here we need to convert the numbers into decimal for to arrange it,

First, we have to convert the value -415% into decimal,

=> -415%

=> -415/100

=> -4.15

Next, √17 is equal to,

=> -√17

=> -4.12

How we have to arrange them in order,

=> { -4.15< -4.12 < -4.1 < -4.08}

Which is equal to,

=> {-415% < -√17 < -4.1 < -4.08}

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The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)

The standard linear equation is expressed as y = mx + b where;

m is the slope

b is the y-intercept

Given the linear equation (y-1) = 3(x+3)

Expand

y-1 = 3x + 3

y-3x = 3 + 1

y-3x = 4

y = 3x + 4

The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)

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Answer:

ano yan ang tanong mo

Step-by-step explanation:

ano yan