Select the correct locations on the graph.
The table lists data on the hair length and the age of nine girls. Select the points that represent this data.

Answer:

The answer is 36

Step-by-step explanation:

1) Add 30 + 2 and get 32

2) Then you just add 32+4 and get 36

Answer: We can factor the numerator and denominator of the expression as the difference of squares:

(x^2 - a^2) = (x - a)(x + a)

(x^4 - a^4) = (x^2 - a^2)(x^2 + a^2)

Substituting these into the limit expression, we get:

lim x→a [(x^2-a^2)/(x^4-a^4)]

= lim x→a [(x - a)(x + a) / (x^2 - a^2)(x^2 + a^2)]

We can simplify this expression by canceling out the common factor of (x - a) in the numerator and denominator:

lim x→a [(x + a) / (x^2 + a^2)]

Now, we can evaluate the limit by direct substitution, since the expression is continuous at x=a:

lim x→a [(x + a) / (x^2 + a^2)] = (a + a) / (a^2 + a^2) = 2a / 2a^2 = 1/a

Therefore, the limit of [(x^2-a^2)/(x^4-a^4)] as x approaches a (where a cannot equal 0) is 1/a.

Answer:

C: \(\lim_{x \to 0} y \to -\infty\)

Step-by-step explanation:

The y-axis is the asymptote, and G(x) approaches it as x is getting smaller and smaller.

Actually, even more accurate would be to write

\(\lim_{x \downarrow 0} y \to -\infty\)

The down arrow shows that x has to approach 0 from the positive side.

Answer: 38.31 km

Step-by-step explanation:

same concept: since circumference is \(\pi\)d, we want d. since d is r*2, d is 6.1*2 or 12.2.

multiply by 3.14 and we get 38.31

Answer:

click on A or fill it in

Step-by-step explanation:

Answer:

f(2)=3x²+2x-10

f(2)=3(2)² +2(2)-10

=12+4-10

=6

The measure of angles:

∠S = 72

∠Q = 72

∠R = 180

In the given trapezium

∠P  = 108 degree

We know that for a trapezium,

The sum of the angles of two adjacent sides = 180°.

Therefore,

∠S + 108 = 180

⇒       ∠S = 72 degree

And

∠Q + 108 = 180

⇒        ∠Q = 72 degree

Now.

  ∠S + ∠R = 108

⇒ 72 + ∠R = 180

⇒         ∠R = 108 degree

Hence,

∠S = 72

∠Q = 72

∠R = 180

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Answer:

The equation of the  perpendicular line is 2 x + y + 1 =0

Step-by-step explanation:

Step(i) :-

Given equation of the line  2y = x - 18

                                      x - 2y - 18 =0

The equation of the perpendicular line to the given line

                      b x - ay +k=0

                     -2 x - y + k =0  this line is passing through the point ( 0 , -1)

                ⇒  0 -(-1) + k=0

                ⇒ 1+k =0

               ⇒  k = -1

Step(ii):-

The equation of the line is perpendicular to the line

              -2x - y - 1 =0

              2 x + y + 1 =0

Conclusion:-

The equation of the  perpendicular line to the given  line  2 x + y + 1 =0

The required equation of the line \(l_1\)  is perpendicular line \(l_2\) is 2x + y +1 = 0

Given ,

The equation of the line \(l_1\) is Y = \(-\frac{1}{2} ( X- 18 )\)

We have to find ,

The equation of line which perpendicular to \(l_1\) and intersects the Y-axis at (0, -1).

According to the question,

\(Y = \frac{-1}{2} (X - 18)\)

2Y = -1 ( X - 18)

2Y = -X + 18

2Y + x - 18 = 0

Then , the given line is perpendicular to the line \(l_1\) to line \(l_2\)

b  = 2 , a = 1 ,

bx - ay + k = 0

2x - 1y + k = 0

The intersection point the Y- axis  ( 0 , -1 )  

2(0) - 1(-1) + k = 0

0 + 1 + k = 0

k = -1

Put the value of k in equation and write the equation at Y - axis

-2x -y -1 = 0

The required line is 2x+y+1 = 0

The required equation of the line \(l_2\) is perpendicular line \(l_1\) is 2x + y +1 = 0 .

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Using proportions, considering the ratio given in the double number line, it is found that there are 7.04 yards in 4 miles.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching the problem on the internet, it is found that there are 3.52 yards in 2 miles. Hence the following rule of three is used to find the number of yards in 4 miles.

2 miles - 3.52 yards

4 miles - n yards

Applying cross multiplication:

2n = 4 x 3.52

Simplifying by 2:

n = 2 x 3.52

n = 7.04 yards.

There are 7.04 yards in 4 miles.

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Answer:

can't see an image

Step-by-step explanation:

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

y = Asin(Bx-C) + D

D is midline.  A is amplitude.  Period is 2π/|B|  (More useful for graphing and shows the effect of B).  Strictly speaking, the frequency is the inverse of period:  f = |B|/(2π), but a lot of math texts say frequency when they mean angular frequency which is rad/s vs. cycles/sec.  The angular frequency ω = 2πf  (2π rads/cycle) or just |B|.  Finally the function is translated to the right  C/B (to the left if C/B is negative)

Step-by-step explanation:

The sine function has a midline of 3, an amplitude of 4, and a period of 2π will be y = 4 sin(2πx) + 3.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The sinusoidal function is given as,

y = A sin(2πx + ∅) + k

Where 'A' represents the amplitude, '∅' represents the phase difference, '2πx' represents the time period, and 'k' represents the midline.

The sine function has a midline of 3, an amplitude of 4, and a period of 2π will be given as,

y = 4 sin(2πx) + 3

The sine function has a midline of 3, an amplitude of 4, and a period of 2π will be y = 4 sin(2πx) + 3.

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In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Answer:

120

Step-by-step explanation:

480 total

1/2 = 240 are cows

1/8 = 60 are goats

remaining = 480-240-60 = 180 are chickens & ducks

33.3333% of 180 = chickens  =180/3 = 60 chickens

so ducks = 180-60 =120

Answer:

120

Step-by-step explanation:

given that out of 480 animals 0.5 of the animals are cows . So ,

no. of cows = 0.5*480 = 240

Again, we are given that 1/8 of the animals are goats , so the number of goats would be ,

no. of goats = 1/8*480 = 60

Total no. of goats and cows ,

= 240 + 60 = 300

No. of remaining animals= 480 -300 = 180

Now out of these 180 animals 33⅓ % animals are chickens and remaining are ducks.

Percentage of ducks = (100 - 33⅓ )% = 66.67%

So the number of ducks would be ,

180 * 66.67/100 = 120

And we are done!

Answer:

Step-by-step explanation:

The greater the angle the greater the opposite side

Sides in ascending order:

Angles in same order

As above, sides in ascending order:

Angles in same order

Exterior angle equals to sum of non-adjacent interior angles

Same subject and isosceles triangle:

Same subject

ΔPQS has two angles with the measure of x, hence their opposite sides are congruent and the triangle is isosceles

The difference between the medians is calculated as 0.75 times the interquartile range (IQR).

To compute this, we can refer to the box plot provided and obtain the necessary values for the medians and IQRs of the two groups being compared.

For Jolie, the median amount is 28 and the IQR is 16, while for Francesca, the median amount is 16 and the IQR is also 16.

Subtracting the two median values gives a difference of 12.

We can then express this as:

Difference = 12 * IQR/16

Simplifying this gives a difference in medians of:

Difference = 0.75IQR.

Therefore, we can conclude that the difference in median amounts is 0.75IQR.

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Using the Poisson distribution, the probability of observing exactly three accidents on this stretch of road next month is given by:

b) 0.052.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

Researching this problem on the internet, the mean is given by:

\(\mu = 7\).

The probability of observing exactly three accidents on this stretch of road next month is P(X = 3), hence:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 3) = \frac{e^{-7}7^{3}}{(3)!} = 0.052\)

Hence option B is correct.

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Step-by-step explanation:

I hope it helps.

.........

Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.

Step 1: factor the provided number into primes, or describe it as the product of primes.

Step 2: Write the prime factorization in exponent form in step three.

Step 3: Increase each exponent by one.

Step 4: Multiply each of the results.

There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.

In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.

b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.

The interpretation is yes

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Answer:

900,000

Step-by-step explanation:

you subtract smallest 7 digit number 1,000,000

by the smallest 6 digit number which is 100,000

1,000,000 minus 100,000 which is 900,000

cuemath

Maths Doubt

The bearing of R from P is found using trigonometry and the angle addition formula. The bearing is 210 degrees, with a distance of 3 from Q and 5 from P.

To find the bearing of R from P, we can use the bearings and distances given in the problem. Let P be a point, and line segment from P to Q with length 5. Then, from Q to R with length 3.

The angle of bearing of Q from P is 150 degrees, which means that the angle between the line segment PQ and the North direction is 150 degrees. We can say this angle as ∠PQ North. Similarly, the bearing of R from Q is 60 degrees, so we can say the angle ∠Q R North as 60 degrees.

Use trigonometry to find the angle between PR and the North direction. We can use the Law of Cosines to find the angle between PR and PQ:

cos(∠PQR) = (5^2 + 3^2 - PR^2) / (2 * 5 * 3)

cos(∠PQR) = (25 + 9 - PR^2) / 30

cos(∠PQR) = (34 - PR^2) / 30

Solving for cos(∠PQR), we get:

cos(∠PQR) ≈ 0.388

Taking the inverse cosine, we get:

∠PQR ≈ 67.6 degrees

Use the angle addition formula to find the bearing of R from P. Since we know the bearings of Q from P and R from Q, we can use the angle addition formula to find the bearing of R from P:

∠P R North = ∠PQ North + ∠Q R North

∠P R North = 150 degrees + 60 degrees

∠P R North = 210 degrees

Therefore, the bearing of R from P is 210 degrees (correct to the nearest degree).

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The system of equations is:

To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:

We have two equations to graph:

Comparing with the slope-intercept equation:

Where m is the slope and b is the y-intercept.

We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.

The graph of the two equations is shown in the following image:

Where the green line is the first equation, and the red line is the second equation.

There is no solution to this system of equations because the lines do not intersect each other.

To construct a 3x3 nonzero matrix A such that the vector [2 4 1 2 1 3 5] is a solution of the equation Ax = 0, we can choose the matrix A = [1 -1 2; -2 1 -3; 0 0 0].

Let's consider the equation Ax = d, where A is a 3x3 matrix, x is the vector [2 4 1], and d is the zero vector [0 0 0]. We want to find a matrix A that satisfies this equation.

We can write the equation as a system of linear equations:

2a + 4b + c = 0

2d + 1e + 3f = 0

5g = 0

To satisfy the equation, we need to choose values for the variables a, b, c, d, e, f, and g that make all the equations true.

For example, we can choose:

a = 1, b = -1, c = 2, d = -2, e = 1, f = -3, g = 0

Substituting these values into the equations, we get:

2(1) + 4(-1) + 2 = 0

2(-2) + 1(1) + 3(-3) = 0

5(0) = 0

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Using the combination formula, it is found that there are 220 ways to decide which countries to skip.

The order in which the countries are skipped is not important, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, 3 countries are skipped from a set of 12, hence the number of ways is given by:

\(C_{12,3} = \frac{12!}{3!9!} = 220\)

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Answer:

z=7

Step-by-step explanation:

3z+5=4z-2

5=4z-2-3z

5=z-2

5+2=z

7=z

z=7

The probability that the flower picked by the customer is not a rose is 0.75, or 75%. can be calculated by dividing the number of flowers that are not roses by the total number of flowers in the inventory.

In this case, the inventory has 2525 roses, and the total number of flowers in the inventory is the sum of the different types of flowers: 2525 + 1515 + 3030 + 2020 + 1010 = 10100.

To find the number of flowers that are not roses, we subtract the number of roses from the total number of flowers: 10100 - 2525 = 7575.

Therefore, the probability that the flower picked by the customer is not a rose is 7575/10100, which simplifies to 3/4 or 0.75.

So, the probability that the flower picked by the customer is not a rose is 0.75, or 75%.

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Answer:

18

Step-by-step explanation:

30-6=24

24-6= 18

    or

6x2=12

30-12= 18

Answer:

He has 18 whistles left.

-------WORK------

6x2=12 whistles he gave.

30-12=18 whistles he has left.

Step-by-step explanation:

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Answer:

1/6

Step-by-step explanation:

Side AB * scale factor = Side DE

72* scale factor = 12

Divide each side by 72

scale factor = 12/72

scale factor = 1/6

Option B is correct, 1/6 is the scale factor of triangle ABC to triangle DEF

A triangle is a three-sided polygon that consists of three edges and three vertices.

Dilation is a transformation, which is used to resize the object

The size by which the shape is enlarged or reduced is called as its scale factor.

DEF is dilated graph of ABC

Let us take any side of ABC and its corresponding side to find the scale factor

Side AB × scale factor = Side DE

72×scale factor = 12

Divide each side by 72

scale factor = 12/72

scale factor = 1/6

Hence, 1/6 is the scale factor of triangle ABC to triangle DEF

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The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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