Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The solution is,  15 is the value of x in the equation 3 x - y = 30,

when y = 15.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

the equation 3x - y = 30,

now, we have, to find the value of x in the equation 3 x - y = 30,

when y = 15

so, we get,

3x - y = 30

putting y = 15, we get,

3x - 15 = 30

or, 3x = 30 + 15

or, 3x = 45

or, x = 45/3

or, x = 15

Hence, 15 is the value of x in the equation 3 x - y = 30, when y = 15.

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The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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Answer:

x-7

Step-by-step explanation:

We can see here that the statement that best describes the zeros of the function h(x) = (x – 6)(x² + 8x + 16) is: C. The function has one real zero and two complex zeros.

In mathematics, a function is a special type of relation. A relation is a set of ordered pairs, where each ordered pair consists of two elements.

To determine the zeros of the function h(x) = (x - 6)(x^2 + 8x + 16),

we can set the function equal to zero and solve for x.

Setting h(x) = 0, we have:

(x - 6)(x^2 + 8x + 16) = 0

Setting x - 6 = 0, we find:

x = 6

Setting x^2 + 8x + 16 = 0,

we can attempt to factor or use the quadratic formula.

Therefore, the function:

h(x) = (x - 6)(x^2 + 8x + 16) has one real zero (x = 6) and two complex zeros.

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Answer:

cucurbitacin

Step-by-step explanation:

It makes it tastes bitter

Why does cucumber taste like shampoo ?

It doesn't . Maybe just your taste is weird . Why do you taste shampoo in the first place !

Answer:

8

Step-by-step explanation:

Since the sides are congruent, the angles are as well. So if you draw point W along line RT, then the angle W and S are the same, so the length is also the same, which is 8.

please hit the heart button :)

Answer:

6

Step-by-step explanation:

The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

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Answer:

1728

Step-by-step explanation:

He climbed 3/4 of a mile in 2/3 of an hour.

Now we're getting somewhere.

Speed = (distance) / (time)

Speed = (3/4 mile) / (2/3 hour)

Speed = (3/4) / (2/3)    mile/hour

Speed = (3/4) x (3/2)   mile/hour

Speed = 9/8   mile/hour

Speed = 1 and 1/8   mile/hour

That's Choice-C.

Answer:

Step-by-step explanation:

formula

rate = distance / time

r = d/t

Givens

distance = 3/4 of a mile

time = 2/3 of an hour

Solution

Put the fractions in for d/t

\(\frac{\frac{3}{4} }{\frac{2}{3} }\)

Turn the denominator upside down and multiply the result by 3/4

r  =  3/4 * 3/2 = 9 / 8 miles / hour

Answer  r = 1 1/8 or C

Step-by-step explanation:

j. seems to be challenging

The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

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Answer:

ummm what is the area?

Step-by-step explanation:

you need to factors to complete this question

The value of the y is 18 when x = 5.

Given,

In the question:

If y varies inversely as x

and, y=9 when x =10

To find the value of y when x = 5

Now, According to the question:

Based on the given conditions:

Formulate:

y = k/x

Calculate and substitute y = 9 , x = 10 into y = k/x

9 = k/10

k = 90

To find the equation of the function:

y = 90/x

Calculate and substitution x = 5 into y = 90/x

y = 18

Hence, The value of the y is 18 when x = 5.

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Answer:

The vertex of the graph is:

As this parabola opens upwards, the vertex is the minimum point.

From inspection of the graph, vertex = (-3, -1)

Equation of the graph

From inspection we can see that the x-intercepts are when
x = -4 and x = -2

\(\sf x = -4 \implies x+4=0\)

\(\sf x = -2 \implies x+2=0\)

Therefore:

\(\sf y=(x+4)(x+2)\)

Expand:

\(\sf \implies y=x^2+6x+8\)

Answer:

\(B)f(x) = {x}^{2} + 6x + 8\)

Step-by-step explanation:

Let \( f(x)=x^2\) be the parent function. With transformation of function, firstly,we know that,

algebraically

Clearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to

secondly, we know that,

algebraically,

in case,

Since the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes

simplifying it yields:

\(\implies \boxed{f(x) = {x}^{2} + 6x + 8}\)

Hence,B is our required answer

Answer:

Graphing Polynomial Functions

Find the intercepts, if possible.

Check for symmetry. ...

Use the multiplicities of the zeros to determine the behavior of the polynomial at the x-intercepts.

Determine the end behavior by examining the leading term.

Use the end behavior and the behavior at the intercepts to sketch a graph.

The standard form of this expression is equal to 10 + 20i.

Complex numbers are those numbers that contain the imaginary and the real part.

Complex value z is written in a rectangular form as; z = x+iy where (x, y) is the rectangular coordinates.

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

We are given that the expression as (1+7i)(3-i)

Solving it;

(1+7i)(3-i)

3 - i + 21i - 7i^2

3 - i + 21i + 7

10 + 20i

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Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

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The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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Answer:

Invest today: $8895.36

Interest earned: $3104.64

Explanation:

The amount after t years can be calculated as:

Where P is the initial amount invested, r is the interest rate and t is the number of years and n is the number of times the interest rate is compound. Solving the equation for P, we get:

Now, we can replace A by $12,000, r by 5% = 0.05, n by 12 because it is compounded monthly and t by 6

Therefore, he should invest $8895.36 today to have enough money in 6 years.

Finally, the interest earned is calculated as

$12000 - $8895.36 = $3104.64

So, the answers are:

Invest today: $8895.36

Interest earned: $3104.64

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The rational functions is graphed below is f(x)=1/x-4.

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers excluding the zeros in the denominator. First example: f(x) = x/ (x - 3). There is just one zero in the denominator, x = 3. Usually, the numerator and denominator degrees of rational functions serve as indicators. A quadratic/cubic rational function, for instance, is one that has a cubic denominator and a quadratic numerator. A generalization of the polynomial model is the rational function model. A function that compares the two polynomials. Due to the fact that one is divided by the other, it is a "rational" ratio.

From the graph, we can get the function is f(x)=1/x the k=4.

So, f(x)=1/x-4

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Point in original figure: (-1,5)

Point in final figure: (7,2)

Take the bold point on the figure and drag it 8 to the right.

Once you arrive at this point, drag it 7 up.

Hope this helps.

Answer:

The formula determine the distance from C to D is the attached image.

So, here we have:

(a,b)=(a,b) and (c,d)=(0,b)

The formula used to determine the distance from point C to point D is

Distance formula ,CD = √(0-a)² + (b - b)².

There are two points in the Cartesian plane as P(a, b) and Q(c, d) then the distance between two points

PQ = √ (c - a)² + (d -b)²

We have,

A is (0, 0), Bis (a, 0), Cis (a, b), and Dis (0, b).

Using Distance Formula

CD = √(0-a)² + (b - b)²

CD = √ (-a)²+  (0)²

CD = √a² + 0

CD = √a²

CD = a unit

Thus, the distance between point C and D is a unit.

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Step-by-step explanation:

B is wrong -21/7 leaves us with -7.

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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