Four Ice Skaters participate in an ice skating competition. The table shows their scores. Who has the highest score?

Natasha 75.03

Taylor 75.39

Rowena 74.98

Suki 75.3

Sarah: 18

Brother: 24

The difference in ratio units is 4-3 =1. The difference in years is 6, so 1 ratio unit stands for 6 years.

Multiplying by 6, we have ...

... Sarah : Brother = 3·6 : 4·6 = 18 : 24

Sarah is 18; her brother is 24.

Answer:

It is rational

Step-by-step explanation:

2 * sqrt(3) * sqrt(12)

2 * sqrt(3) sqrt(4) * sqrt(3)

2 sqrt(3) 2 sqrt(3)

4 sqrt(3)^2

4 *3

12

The amount borrowed is $84,000. The annual interest rate is 6%. There are 12 payments per year for 21 years at a monthly payment amount of $587.

The question pertains to the fundamentals of loan calculation. Let us identify the components asked:

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In the loan scenario, the person borrowed $84,000 at an annual interest rate of 6%. They will make 12 payments of $587 each year for a term of 21 years.

In the provided loan scenario, the following key components can be identified:

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To find the area of a circle given its diameter's endpoints, determine the diameter length, radius, and then calculate the circle's area using the radius.

The area of a circle can be found using the distance formula between two points representing the diameter's endpoints. Given points P(3,2) and Q(7,10), the diameter length is calculated as sqrt((7-3)^2 + (10-2)^2) = sqrt(4^2 + 8^2) = sqrt(16+64) = sqrt(80).

Knowing that the radius is half the diameter, the radius, r = sqrt(80)/2 = 4*sqrt(5).

Finally, the area of the circle is A = pi*r^2 = pi*(4*sqrt(5))^2 = 80*pi square units.

Answer: No

Step-by-step explanation:

Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.

Answer:

The table A contains a set of non-linear ordered pairs.

Step-by-step explanation:

To answer this question we have to recall what is the meaning of a linear ordered pair. As you can see, in every table there are 4 values for x, and 4 values for y. In every case, the set of values for x are

[tex]x=\{0, 1, 2, 3\}[/tex]

but in every table, the values for y varies. Now, the key is to calculate the variation of these values, and in order to have a linear relation between x and y, the variation must be the same quantity for every y value that depend of each x value.

For example, in table B, the variation is +3, as from the first y value to the second, 3 is added... and this +3 variation must be the same for each new value of y (and as you can see, 4+3 is 7, 7+3 is 10, 10+3 is 13).

Keeping this in mind, the variation in table C is -2, and the variation in table D is +1, so tables B, C and D contains sets of linear ordered pairs.

To answer the question, we just have to realise that table A has differents variations in the values of y, and this means that it contains a set of non-linear ordered pairs, wich is the correct answer to the question.

x = 8.5

The other two sides are given in the diagram.

The Pythagorean theorem tells you ...

... 19² = 17² +x²

Subtracting 17², we have ...

... x² = 361 -289 = 72

Taking the square root gives x.

... x = √72 = 6√2

... x ≈ 8.5

Answer:

-16 sqrt(3) +16i

Step-by-step explanation:

z = 2 cis (pi/6)

z^5 = 2^5 cis (5*pi/6)

z^5 = 32 cis (5pi/6)

 z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)

        = 32 * (-sqrt(3)/2) + 32i (1/2)

        = -16 sqrt(3) +16i

Answer:

0.9885   (98.85%)

Step-by-step explanation:

Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.

So we want to calculate P( X < 20 ).

We can calculate the probability of complement event P( X = 20 ).

Use binomial formula b(x; n, p) = C( n, x ) p^(x) (1-p)^(n-x)

b( 20; 20, 0.8 )

= C( 20, 20 ) (0.8)^(20) (0.2)^0

= (0.8)^20 ≈ 0.0115

So since P( X < 20 ) = 1 - P( X = 20 ), we have

P( X < 20 ) ≈ 1 - 0.0115 = 0.9885

The required value of probability for the given sample is given as 0.9885.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Total number of students are given as 800.

The probability of students riding the school bus is 80% = 0.8.

Then,  probability of students not riding the school bus is 1 - 0.8 = 0.2.

The probability of finding at least one student out of 20 not riding the bus is given as,

1 - P(All of the students ride bus)

It can be solved using binomial distribution as follows,

⇒ 1 - ²⁰C₂₀(0.8)²⁰(0.2)⁰

⇒ 1 - 0.0115 = 0.9885

Hence, the probability that at least one of the students doesn't ride the bus is given as 0.9885.

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Answer:

Steplo-by-step explanation:loan is 1200.

The interest rate is 6.50

Pp 46.90

Cumulative payment $53.4

Total payments$1,282.93

Final answer:

Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.

Explanation:

Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:

I = PRT

where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.

First, we convert R to a decimal by dividing it by 100:

R = 6.5% / 100 = 0.065

Next, we substitute the values into the formula:

I = $1200 × 0.065 × 2

I = $1200 × 0.13

I = $156

Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.

Answer:

A. 36°

Step-by-step explanation:

Same-length chords subtend same-measure arcs. Arc YZ has the same measure as its central angle (∠YOZ) and the same measure as arc XY (36°).

the measure of angle YOZ is 36°, which corresponds to option A. Therefore, the correct answer is option b.

The measure of an angle formed by two chords in a circle is half the measure of the arc intercepted by the angle.

If chord XY is congruent to chord YZ, it means that the arcs intercepted by these chords are also congruent.

So, if the measure of arc XY is "x" degrees, then the measure of arc YZ is also "x" degrees.

Now, the angle YOZ is formed by these two congruent arcs. Therefore, the measure of angle YOZ is half the measure of the arcs XY and YZ.

Angle YOZ = 0.5 * (x + x) = 0.5 * 2x = x degrees.

Now, if you're given the measure of arc XY (or YZ), you can substitute that value into the formula to find the measure of angle YOZ.

The answer choices you provided are in degrees, so the correct answer is A. 36°, assuming you have the measure of the arc XY (or YZ) in the problem.

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Answer:

b

Step-by-step explanation:

Final answer:

Point P divides the distance from A to B into a ratio of 3:5, with P being 3/8 of the way from A to B. The correct option is c.

Explanation:

If point P is 3/8 of the distance from A to B, we can understand this situation by imagining the entire distance from A to B as being divided into 8 equal parts, and point P lies at the end of the third part when moving from A to B. Since P is 3 parts away from A, it leaves the remaining 5 parts to reach B. This sets up a partition of the segment into two parts: one from A to P and the other from P to B. The ratio of these distances is the number of parts from A to P to the number of parts from P to B. Therefore, the ratio of AP to PB is 3:5. Option c is accurate.

Answer:

it will grow 30 ft in 20 years

Step-by-step explanation:

the height will equal the growth rate times the time

height = 1.5 ft/year * 20 year

height = 30 ft

Answer:

x + y = 60

Step-by-step explanation:

In the given figure, we have two lines that intersect each other at one point.

Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:

2y - 5 = 95 --- (1)

3x + 55 = 85 --- (2)

Now solving each of the equations to find the value of x and y.

For y:

2y - 5 = 95

2y = 95 + 5

2y = 100

y = 50

For x:

3x + 55 = 85

3x = 85 -55

3x = 30

x = 10

Therefore, x + y = 10 + 50 = 60.

Answer:

[tex]h^{24}[/tex]

Step-by-step explanation:

[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]

When dividing two exponents (of the same bases) you subtract the exponents.  When there is an exponent to an exponent, you multiply the to exponents.

[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]

2

Solve the second equation for y.

... 8x -12 = 4y . . . . add 4y -12

... 2x -3 = y . . . . . . divide by the coefficient of y

The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...

... y = 2x -6 . . . . . . . . m = 2

will be parallel to the given line, so will not intersect it.

Answer:

D. 15 and 49

Step-by-step explanation:

Numbers are relatively prime if the only positive integer  that divides both of them is 1.

A. 12 and 54

both 12 and 54 can be divided by 3

12/3 =4   54/3 = 18

B. 9 and 21

both 9 and 21 can be divided by 3

9/3 =3  and 21/3 = 7

C. 21 and 39

both 21 and 39 can be divided by 3

21/3 =7 and 39/3 = 13

D. 15 and 49

13 is 3*5    and 49 is 7*7

This is relatively prime

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

_____

Of course, you know that 85% = 85/100 = 0.85.

Answer:

d. 13.5, 20.25

Step-by-step explanation:

An exponential function is monotonic and does not change sign. On this basis alone, the first three choices can be eliminated.

The common ratio is 6/4 = 3/2.

The term in the sequence after 9 is 9·(3/2) = 27/2 = 13.5.

The term in the sequence after 27/2 is (27/2)·(3/2) = 81/4 = 20.25.

Final answer:

The missing values for the exponential function table with an increasing common factor of 1.5 are 13.5 for x=1 and 20.25 for x=2, making the correct answer Option D.

Explanation:

The student's question pertains to finding the missing values for the exponential function represented by the table with given x and y values. Given the nature of an exponential function, we expect that as x increases by 1, the value of y is multiplied by the same factor each time. We can observe this behavior in the initial y-values: 4, 6, and 9. To find this constant multiplier, we can divide 6 by 4 and 9 by 6, which both give us 1.5. This constant factor, which we'll call base of the exponential function, indicates that for every increase of 1 in x, the value of y is multiplied by 1.5.

To find the missing y-values for x=1 and x=2, we just continue multiplying by the base 1.5. Thus, when x=1:

y = 9 × 1.5 = 13.5

When x=2:

y = 13.5 × 1.5 = 20.25

Hence, the completed table should read as follows:

x=-2, y=4

x=-1, y=6

x=0, y=9

x=1, y=13.5

x=2, y=20.25

The correct answer is therefore Option D: 13.5, 20.25.

Answer:

See the attached

Step-by-step explanation:

When in doubt, draw a diagram.

The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.

The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.

The perpendicular line to BC through A is ...

... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)

The intersection of that line and x=6 is ...

... y = -6/2 +7 = 4

Final answer:

After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).

Explanation:

Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.

First, let's convert them to decimal form:

2/3 is approximately 0.6667

7/12 is approximately 0.5833

Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.

Answer:

2^(8/9) in²

Step-by-step explanation:

Make use of the identity ...

... (a^b)^c = a^(bc)

Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity

... (ab)^c = a^c·b^c

In this case a = 2^(4/9), b = in, c = 2.

So, the working of your problem is ...

... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2

... = 2^(4/9·2) in^2 = 2^(8/9) in^2

Answer:

option 2

Step-by-step explanation:

in the given triangle,

tan45° = 8/x

=> 1 = 8/x

=>x = 8

for y,

cos45° = 8/y

=>1/√2 = 8/y

=>y = 8√2

Answer:

x=8, [tex]y=8 \sqrt2[/tex]

Step-by-step explanation:

Consider the given right triangle,

As, [tex]\tan \Theta = \frac{Perpendicular}{Base}[/tex]

Consider [tex]\tan 45^{\circ}=\frac{x}{8}[/tex]

[tex]1=\frac{x}{8}[/tex]

So, x=8

As, [tex]\sin \Theta = \frac{Perpendicular}{Hypotenuse}[/tex]

Consider [tex]\sin 45^{\circ}=\frac{8}{y}[/tex]

[tex]\frac{1}{\sqrt2}=\frac{8}{y}[/tex]

So, [tex]y=8 \sqrt2[/tex]

Therefore, x = 8 and [tex]y=8 \sqrt2[/tex]

Answer:

A = 10w

Step-by-step explanation:

In the area formula, the coefficient of width is length. Here, that is ...

... A = 7w

7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...

... A' = 10w

_____

Comment on the problem statement

The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.

Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.

Answer:

p = 1/12 = p(o1) = p(o3) = p(o5)

3p = 1/4 = p(o2) = p(o4) = p(o6)

Step-by-step explanation:

p(o1) +p(o2) +... +p(o6) = 1 . . . . the condition on the sum of probabilities

... p +3p +p +3p +p +3p = 1 . . . . substitute values

... 12p = 1 . . . . simplify

... p = 1/12 . . . . divide by 12

Then ...

... 3p = 3/12 = 1/4

Final answer:

The probabilities of rolling each face of a loaded six-sided die, where even numbers are three times more likely than odd numbers, are 1/9 for odd numbers (1, 3, 5) and 1/3 for even numbers (2, 4, 6), satisfying the condition that the total probability sums to 1.

Explanation:

The student is dealing with a probability question involving a "loaded" die. To find the probabilities for each face of the die, we assign a variable p to represent the probability of rolling an odd-numbered face and 3p for an even-numbered face. The sum of all probabilities must equal 1 because one of the outcomes must occur when the die is rolled. We can set up the following equation: p + 3p + p + 3p + p + 3p = 1.

Combining like terms gives us 9p = 1, so p = 1/9. Thus, the probabilities of rolling each face are as follows:

This system satisfies the condition that all probabilities sum to 1, making it the correct distribution for this loaded die.

Answer:

6 square root of 5 end root minus 4 square root of 7

Step-by-step explanation:

[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}=3\sqrt{5}-2\sqrt{7}+\sqrt{3^2\cdot 5}-\sqrt{2^2\cdot 7}\\\\=(3+3)\sqrt{5}+(-2-2)\sqrt{7}=6\sqrt{5}-4\sqrt{7}[/tex]

_____

Comment on the answer form

In symbols, parentheses are preferred for grouping:

... 6√(5) -4√7

or

... 6(√5)-4√7

As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.

Answer:

Answer:

6 square root of 5 end root minus 4 square root of 7

Step-by-step explanation:

_____

Comment on the answer form

In symbols, parentheses are preferred for grouping:

... 6√(5) -4√7

or

... 6(√5)-4√7

As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.

The angular velocity of the point is found this way:

w = v/r

w = 200/(8/2) <--the two is from 2 * Pi * r

w = 50 rad/sec.

Answer: 50 rad/sec.

fullness; live

Answer: the angle is 1°+n×120°

1°, 121°, 241°

Step-by-step explanation:

Angles are taken modulo 360°, so 363° = 3°.

Angle plus supplement gives 180°.

Let a be angle, s be supplement of a.

So s = 180-a. Given a = 3 + 2s

a = 3 + 2(180 - a)

a = 3 + 360 - 2a = 363 - 2a

3a = 363° or 3° or 723°

a = 121° or 1° or 241°

a = 1°

s = 179°

2s = 358°

2s+3 = 361° = 1° (modulo 360)

a = 121°

s = 180-121 = 59°

2s = 118°

2s + 3 = 121°, as required.

a = 241°

s = 360+180-241 = 540-241 = 299

2s = 598

2s + 3 = 601 = 241 (modulo 360)

Answer:

B

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

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

m = [tex]\frac{1+1}{1+1}[/tex] = 1 ← slope of graph

consider the slope of the given equations

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

(A)

y = 2x + 1 has slope = 2 → not parallel

(B)

x - y = - 3 ( subtract x from both sides )

- y = - x - 3 ( multiply through by - 1 )

y = x + 3 with slope = 1 → thus parallel to graph

(C)

x + y = 2 ( subtract x from both sides )

y = - x + 2 with slope = - 1 → not parallel

(D)

y = - x + 1 with slope = - 1 → not parallel

An equation of a line that is parallel to the line r shown in the graph include the following: B. x - y = -3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

First of all, we would determine the slope for this line by using these points (1, 1) and (0, 0);

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope (m) = (0 - 1)/(0 - 1)

Slope (m) = 1

For the line to be parallel to the line r, it must have the same slope as line r. At data point (0, 0) and a slope of 1, an equation for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

y - 0 = 1(x - 0)  

y = x

Based on the answer options, we have;

y = 2x + 1 ⇒ slope is 2 (not parallel).

x - y = -3

y = x + 3 ⇒ slope is 1 (parallel).

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The recursive formula

[tex] a_n = 2a_{n-1}+5 [/tex]

means that, to compute the next value, you have to double the previous one and then add 5.

So, we start with 5. To get the second term, we double it and add five, so we have

[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]

Next, we will double 15 and add 5:

[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]

So, the answer is B, because it's the only option starting with 5,15,35.

Just to check, let's compute the last step:

[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]

Which confirms option B