Suppose 40 cars start at a car race. In how many ways can the top 3 cars finish the​ race?

Answer:

Step-by-step explanation:

x2+3/x2-4x+3

Answer:

x^2+3/(x-1)(x-3)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If i understand the question correctly the plane will fly 6 trips of 500 miles each trip.

Number of minutes it takes the plane to fly 500 miles

= 500 / 11

= 45.45 minutes

For 6 trips this = 45.45 * 6 = 272.73 minutes

=  4.55 hours to nearest hundredth.

That would  be (40 + 110) / 2

= 150 / 2

= 75 degrees   answer

The definitions of the labels are:

Since RQU is the sum of RQS, SQT and TQU, it measures 19+71+18 degrees, i.e. 108 degrees, and thus it's obtuse

Similarly, SQU is the sum of SQT and TQU, so it measures 71+18 = 89 degrees, so it's acute.

Finally, RQT is the sum of RQS and SQT, so it measures 19+71=90 degrees, and it's a right angle.

obtuse, acute and right

∠RQU = 19° + 71° +18° = 108° ⇒ obtuse angle

∠SQU = 71° + 18° = 89° ⇒ acute

∠RQT = 19° + 71° = 90° ⇒ right

J(1 , 0); N(5, 0) ; M(5 , -3) and P(2 , -5)

Translation (x,y) -->(x-4, y+4)

J'(-3,4), N'(1, 4) ; M'(1 , 1) and F'(-2 , -1)

Answer is C)

J'(-3,4), N'(1, 4) ; M'(1 , 1) and P'(-2 , -1)

This question is about evaluating the solutions of two students, Alisha and Brianna, for a number puzzle involving sets and probabilities. Without specific puzzle instructions, it's hard to determine whose solution is correct. The correctness would depend on the puzzle's directions and the application of mathematical principles.

The question is a mathematical one, involving the solving of number puzzles by two students, Alisha and Brianna. The requirements are to evaluate their solutions for correctness based on given parameters or steps. However, without the specific steps or guidelines of the puzzles presented, it's difficult to provide a definitive assessment or explanation of whose solution would be correct.

From the provided resources, we can infer that we're dealing with a problem-solving scenario involving sets, probabilities, problem analysis, and solution refinement. An example scenario might be: Alisha and Brianna are solving a magic number puzzle where they need to calculate the probability of specific outcomes from a set of numbers. Alisha identifies sets S and A and calculates P(A) as the number of outcomes in A divided by outcomes in S, while Brianna might approach the puzzle differently. The correctness of their results will depend on the puzzle's instructions and the maths principles applied.

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A

the word 'of' means to multiply

0.45 × 80 = 36

Final answer:

To calculate the interest after 6 months with a principal of $750,000 and an annual interest rate of 5%, you need to convert the annual rate to a monthly rate and then use the formula Interest = Principal × Rate × Time. The interest after 6 months is $1,562.50.

Explanation:

To calculate the interest after 6 months, we can use the formula:

Interest = Principal × Rate × Time

Here, the principal is $750,000, the annual interest rate is 5%, and the time is 6 months.

First, we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 5% / 12 = 0.4167%

Now, we can calculate the interest:

Interest = $750,000 × 0.4167% × 6/12

Interest = $1,562.50

[tex]A.\ (-2,\ 0)\\\\substitute\ to\ y=x+2\\\\0=-2+2\\0=0\ CORRECT\\\\substitute \ to\ (x+1)^2+(y-4)^2=9\\\\(-2+1)^2+(0-4)^2=9\\(-1)^2+(-4)^2=9\\1+16=9\\17=9\ \ FALSE[/tex]

[tex]B.\ (1,\ -1)\\\\substitute\ to\ y=x+2\\\\-1=1+2\\-1=3\ \ \ FALSE[/tex]

[tex]C.\ (2,\ 4)\\\\substitute\ to\ y=x+2\\\\4=2+2\\4=4\ \ \ CORRECT\\\\substitute\ to\ (x+1)^2+(y-4)^2=9\\\\(2+1)^2+(4-4)^2=9\\3^2+0^2=9\\9+0=9\\9=9\ \ \ CORRECT[/tex]

[tex]D.\ (-1,\ 4)\\\\substitute\ to\ y=x+2\\\\4=-1+2\\4=1\ \ \ \ FALSE[/tex]

capacity of the stadium=23564

no.of seats occupied=3/4 of 23564

no.of people in the stadium=23564*3/4

=17673

Answer:

17673

Step-by-step explanation:

1/2 inch…………4.5 feet

x inches……….54 feet

x=(54•1/2)/4.5

x=27/4.5

x=6 inches

she has 40 nickels because: 80-40 = 40. this is equal to 40 nickels

It will take 120 minutes to fill up

The pump will take 120 minutes to fill the tank.

To answer the question of how many minutes it will take to fill an 800-unit tank that is already 1/4 full using a pump that can supply 5 units of water per minute, we must first determine the amount of water needed to fill the tank completely.

Since the tank is 1/4 full, it already contains 800 units * 1/4 = 200 units of water. Therefore, the remaining volume to fill is 800 units - 200 units = 600 units. Next, we divide this remaining volume by the rate at which the pump supplies water:

600 units / (5 units/minute) = 120 minutes.

It will take 120 minutes to fill the tank to its full capacity.

To find the general form of the equation of the quadratic function given a vertex and a point, we can proceed as follows:

The vertex form of the equation for a quadratic function can be expressed as:

\[ f(x) = a(x - h)^2 + k \]

where
- \( a \) is a coefficient that affects the width and direction of the parabola,
- \( (h, k) \) is the vertex of the parabola.

We've been given the vertex \( (h, k) = (-6, -1) \) and a point on the graph \( (x, y) = (-9, 8) \).

Let's use the vertex form and plug in the values of the vertex and the given point to solve for \( a \).

\[ 8 = a(-9 + 6)^2 - 1 \]
\[ 8 + 1 = a(-3)^2 \]
\[ 9 = a(9) \]
\[ a = 9 / 9 \]
\[ a = 1 \]

Now we know that \( a \) equals 1, and our vertex form equation becomes:

\[ f(x) = 1(x + 6)^2 - 1 \]

To write the equation in general form \( f(x) = ax^2 + bx + c \), we need to expand the equation:

\[ f(x) = 1(x + 6)^2 - 1 \]
\[ f(x) = (x^2 + 12x + 36) - 1 \]  (Expand the square)
\[ f(x) = x^2 + 12x + 36 - 1 \]

Finally, combine the constants:

\[ f(x) = x^2 + 12x + 35 \]

So the general form of the equation of the quadratic function given the vertex \( (-6, -1) \) and the point \( (-9, 8) \) is:

\[ y = x^2 + 12x + 35 \]

Here, \( a = 1 \), \( b = 12 \), and \( c = 35 \).

Answer:

 [tex]x^2-12x+36= -6+36[/tex]

Step-by-step explanation:

Equation : [tex]x^2-12x = -6[/tex]

General equation : [tex]ax^2+bx+c=0[/tex]

So,we need to add and subtract [tex](\frac{b}{2})^2[/tex] for completing square.

So, next step of completing square :

 [tex]x^2-12x+6^2-6^2= -6[/tex]

 [tex]x^2-12x+36= -6+36[/tex]

Hence Step 2 shows lamar's next step and the solution to the equation

The solution to the equation after completing the square is:

(x - 6)² = 30

Lamar starts with the equation x² - 12x = -6.

Step 2: To complete the square, Lamar takes the coefficient of the x term, which is -12, divides it by 2, and then squares it. In this case, (-12/2)² = 36.

Lamar adds 36 to both sides of the equation to maintain its balance. By doing so, he effectively creates a perfect square trinomial on the left side of the equation.

x² - 12x + 36 = -6 + 36

Simplifying the right side, -6 + 36 equals 30.

The equation now becomes:

x² - 12x + 36 = 30

Now, Lamar can rewrite the left side of the equation as a perfect square. The left side is (x - 6)² because (x - 6)(x - 6) equals x² - 12x + 36.

(x - 6)² = 30

Thus, the solution to the equation x² - 12x = -6, after completing the square, is (x - 6)² = 30.

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The amount of markup is $9.35 .The selling price of algebra1  books  after 55% increment is $26.35

If there is x% increment in y then the increment will be (x/100)*y and the  new amount after x% increment will be now  y + (x*y)/100

A  bookstore buys algebra 1 books at a wholesale price of $17 each.

Initial price of algebra 1 book was = $17

There is 55% increment in books price before selling

55% of initial price = (55/100)*17 = 935/100= $9.35

The selling price = wholesale price + 50% increment = 17 + 9.35 =26.35

Therefore, the amount of markup or increment is $9.35 the selling price of the algebra 1 books after 55% markup is $ 26.35.

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GIVEN: y = -5/6x + 6

slope of given line = -5/6

--> Because the line you are trying to find is perpendicular to the given line, you must find the opposite reciprocal of the slope

opposite reciprocal of the slope = 6/5

You need to find what "b" is for your equation

Plug "b" back into the slope-intercept form along with your equation's slope

y = mx + b

(if your teacher doesn't want any decimals, then write: y = 6/5x + 89/5)

The equation of the line that is perpendicular to y=-5/6x+6 and cross through the point (-9,7) is y = 6/5x + 29.8, found by using the slope-intercept form and the concept of negative reciprocal slopes.

To find the equation of the line that is perpendicular to y=-5/6x+6 and crossing through the point (-9,7), we first need to find the slope of that line. We can determine that by knowing that the slopes of perpendicular lines are negative reciprocals of each other. So, if the slope of given line is -5/6, the slope of the line perpendicular to it will be the negative reciprocal, which is 6/5.

Now we have a point (-9,7) and a slope (6/5) and can use the slope-intercept form of a line to write the equation of a line.

We use the formula y = mx + b:

 Where 'y' and 'x' are coordinates of a point on the line, 'm' is the slope, and 'b' is the y-intercept. We know 'm', 'y' and 'x', so we can solve for 'b'. Substituting, we get: 7 = (6/5)(-9) + b, which simplifies to b = 29.8.

The equation of the line in slope-intercept form is: y = 6/5x + 29.8

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460 cm

note that 1m = 100 cm, thus

4.6m = 4.6 × 100 = 460 cm

Answer:

45%

Step-by-step explanation:

To find the percent, we write the information as part/whole:

99/220

Now we convert to a decimal by dividing:

99/220 = 99÷220 = 0.45

Lastly, multiply by 100:

0.45(100) = 45

Answer:

Option C, 18/24 = 75%

Step-by-step explanation:

Patients who were addicted to cocaine were divided into 3 groups of 24.

Each group was treated with three different drugs. One group of 24 patients were put on Lithium for treatment out of 24 patients who relapsed were 18.

So conditional relative frequency for relapse among patients who took Lithium would be :

Relative frequency of patients = (patients relapsed) / (total number of patients)

Relative frequency = [tex]\frac{18}{24}[/tex] = 75%

Option C, 18/24 = 75% would be the answer.

Solution

Step 1: Isolate the variable x and plug in the values of x in the second and third equations.

Step 2: Isolate variable y and solve for y.

We get the value of y = 5/26

When we substitute the value of y , 1 = 0 which is not true.

Therefore, this system has No Solution.

Answer: No solution

Final answer:

The equation that demonstrates the additive inverse property is B. 6 + (-6) = 0, where 6 and -6 are additive inverses of each other.

Explanation:

The equation that illustrates the additive inverse property is B. 6 + (-6) = 0. The additive inverse property states that for any number 'a', there is a number '-a' such that 'a' plus '-a' equals zero. This is because adding a number to its additive inverse (which is the negative of the number) will result in zero.

Examples demonstrating the additive inverse include subtracting a positive number and changing its sign before operating the addition, for instance, 5-(+3) results in 5-3, which equals 2. Conversely, if you subtract a negative number, like subtracting -6 from 2, you would perform 2-(-6) which equals 2+6, resulting in 8.

[tex]7x > -35\qquad|\text{divide both sides by 7}\\\\x > -5\\------------------------------------\\\\3x\leq30\qquad|\text{divide both sides by 3}\\\\x\leq10\\\\Answer:\ b)\ -5 < x\leq10[/tex]

answer : D

A. (6 × 7) + 6 = 48

Associative property of multiplication . Here we have +6 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

B. 6 × (4 + 2) = 36

Here we have 4 +2 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

C. (6 + 4) × 2 = 20

Here we have 6 + 4 . there is a + sign inbetween.  so it does not comes under Associative property of multiplication

D. (6 × 4) × 2 = 48

Here we have 6 times 4 times 2.  so it comes under Associative property of multiplication

(-3j²k³)²(2j²k)³ = When a power is raised to a power the exponents have to be multiplied.​

​= (-3²j⁽²*²⁾k⁽³*²⁾)(2³j⁽²*³⁾k³) = We can take out the constants

​= (9)(8)(j⁴k⁶)(j⁶k³) = We can group the same variables

= 72(j⁴j⁶)(k⁶k³) = When multiplying two powers that have the same base, you have to add the exponents.​

= 72 j⁽⁴⁺⁶⁾k⁽⁶⁺³⁾ = 72j¹⁰k⁹​

​Answer = 72j¹⁰k⁹

​Hope this helps!​​​​

​​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Hey there!!

Let's take the first number an the smallest number as ' x '

Then, the second consecutive even integer would become ' x + 2 '

Third integer ' x + 4 '

Hence, adding them up, we get,

x + x + 2 + x + 4

... 3x + 6

This is equal to 4 times the smallest number.

We got the smallest number as ' x '

Hence, the final equation :

... 3x + 6 = 4x

Hope my answer helps!!