Weights of four-year-olds are Normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. At his four-year checkup, Marlon’s weight is measured to be greater than 30% of boys his age. How much does Marlon weigh?

Find the z-table here.

37.6 pounds
38.4 pounds
38.7 pounds
39.3 pounds

Picture posted below

Answer:

8

Step-by-step explanation:

You should have this in mind , one raise to the power of any number is one and also any number with the power zero is 1.

{(1)¹⁰⁰ + (−1)¹⁰¹+(2500)⁰} x2³

= 1 - 1 + 1 × 8

= 1 - 1 + 8

= 1 +7

= 8

The perimeter of the figure above is [tex]43\frac{22}{40} = 43\frac{11}{20}[/tex]

The perimeter of a shape is the sum of the whole sides.

Therefore, perimeter of the figure is the addition of the whole length.

Hence,

perimeter = [tex]14\frac{3}{4}+4\frac{1}{2}+8\frac{1}{2}+10\frac{2}{5}+10\frac{2}{5}+12\frac{4}{5}[/tex]

let's convert to improper fraction for easy calculation.

Hence,

perimeter = [tex]\frac{59}{4}+\frac{9}{2}+\frac{17}{2}+\frac{52}{5}+\frac{52}{5}+\frac{64}{5}[/tex]

perimeter = [tex]\frac{590+180+340+60+60+512}{40} =\frac{1742}{40} = 43\frac{22}{40}[/tex]

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Answer: 4/30

Step-by-step explanation:

it does

a)  Z-score for Patrisse test grade is 0.7288

b) z-score for Makayla test grade is -0.7441

c) Patrisse did better.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

Z-score for Patrisse test grade.

X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 81.4 - 72.8/ 11.8

Z= 0.7288

Now, z-score for Makayla test grade.

X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 60.6 - 67/ 8.6

Z= -0.7441

Hence, Patrisse did better as she had better z- score.

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Answer:

1st set of equations - parallel

2nd set - perpendicular

3rd set - neither

Step-by-step explanation:

First set:

simplify the equation for line 1  by dividing by -4: y = 0.5x + 1

simplify the equation for line 1  by dividing by -6: y = 0.5x - 1.5

Both have the same slope: 0.5 so the lines are parallel.

Second set:

simplify the equation for line 1  by dividing by 3: y = -2/3x + 4

simplify the equation for line 1  by dividing by -4: y = 3/2x - 7/4

-2/3 * 3/2 = -1, so the lines are perpendicular

Third set

simplify the equation for line 1  by dividing by 1/2: y = -2x+4

simplify the equation for line 1  by dividing by 2: y = -1/4x +2

-2x+4=-0.25x+2

-2x+0.25x=2-4

-1.75x=-2

x=1.14

y=-2(1.14)+4 = 1.7143. So there is an intersection point

The pair of lines 2x - 4y = -4 & 3x - 6y = 9, 2x + 3y = 12 & and 6x - 4y = 7, and x + (1/2)y = 2 & (1/2)x + 2y = 4 will be parallel lines, perpendicular lines, and neither parallel nor perpendicular, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The pair of lines is given as,

2x - 4y = -4     ⇒        y = (1/2)x + 1

3x - 6y = 9      ⇒        y = (1/2)x - 3/2

The pair of lines are parallel to each other because the slope is equal.

2x + 3y = 12     ⇒        y = -(2/3)x + 4

6x - 4y = 7       ⇒        y = (3/2) x - 7/4

The pair of lines are parallel to each other because the product of slopes is -1.

x + (1/2)y = 2        ⇒        2x + y = 4

(1/2)x + 2y = 4      ⇒        2x + 4y = 8

The pair of lines are neither parallel nor perpendicular to each other.

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Answer:

No

Step-by-step explanation:

If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.

The members of a possible set C are {6, 9, 12}

The universal set is the set that contains all other sets. Given the following sets

ξ = {x:x is an integer, 2 ≤ x ≤ 14}

B = {x:x is a prime number}

A = {x:x is a multiple of 3}

The sets B and A are:

B = {2, 3, 5, 7, 11}

A = {3, 6, 9, 12}

If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.

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Answer:

1-irrational 2-rational 3-rational 4-rational 5-irrational

Step-by-step explanation:

The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.

The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.

All parabolas can be obtained from the basic parabola by a combination of:

Thus, all parabolas are similar.

Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

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Answer:

G(-6) = -29

Step-by-step explanation:

plug -6 into the equation

G(-6) = 5(-6) +1

multiply

G(-6) = -30+1

add

G(-6) = -29

Answer:

X1 2/7

Step-by-step explanation:

Step-by-step explanation:

We can write it in radical form, and the denominator of the exponent became the power of the radical. That is

And

We can also write it as

And that's the simplified form of the given exponential form .

Answer:

D. 2

E. -2

Step-by-step explanation:

Answer:

-3(-4-4) would work giving you 24

Step-by-step explanation:

im sorry that qustion doesnt make sense, if you mean higher then 21, less than 30 than -3(-4-4) would work giving you 24

Answer:

value of car depreciate each year = $2000

y + 2000x = 16,500

slope of line = -2000

No, not proportional

Step-by-step explanation:

Value of depreciation of an object is given by :-

Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]

according to question ;

total cost = $16500

scrap value = $500

estimated life = 8 years

therefore,

depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000

now,

let the value of car after 'x' years be 'y'

therefore linear equation showing the relation of x and y is

y + 2000x = 16500

The graph of a linear equation is a line.

If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.

If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.

here equation is of type,

y = mx +c, thus it is not linear.

also in the equation y = mx +c,

'm' is the slope of line

therefore by comparing the equation,

y +2000x = 16500

y = -2000x + 16500

slope is - 2000

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Answer:

-38,994

Step-by-step explanation:

-291*134

=-38,994

Answer:

-38,994

Step-by-step explanation:

(-291) × 134

Apply PEMDAS.

Remember,

Solution:

Evaluating,we obtain

Answer:

d because the point satisfied both

Answer:

D

Step-by-step explanation:

9.7 to one significant figure is 10

We have:

9.7

To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.

When 9.7 is approximated, we have:

10

Hence, 9.7 to one significant figure is 10

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Answer:

h^24

Step-by-step explanation:

hope that helpssndbfbsb

Solving the given equations we get,

If the quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solutions of this are given by,

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here in the problem given that,

The first quadratic equation is [tex]9x^2-25=-12-10x[/tex]

Converting it into standard form of quadratic equation we get,

[tex]9x^2-25=-12-10x\\9x^2-25+12+10x=0\\9x^2+10x-13=0[/tex]

So here a=9,b=10,c=-13

The solutions of the equation is given by,

[tex]x=\frac{-10\pm\sqrt{10^2-4\times9\times(-13)}}{2\times9}=\frac{-10\pm\sqrt{100+468}}{18}\approx\frac{-10\pm23.83}{18}[/tex]

So either,

[tex]x=\frac{-10+23.83}{18}=\frac{13.83}{18}\approx0.77[/tex]

Or,

[tex]x=\frac{-10-23.83}{18}\approx-1.88[/tex]

So the solutions are given by x=0.77 and -1.88

Second quadratic equation is [tex]4n^2-1=12n+3n^2+11[/tex]

Converting the equation in its standard form we get,

[tex]4n^2-1=12n+3n^2+11\\4n^2-1-12n-3n^2-11=0\\n^2-12n-12=0[/tex]

so here a=1,b=-12,c=-12

Solutions are given by,

[tex]n=\frac{-(-12)\pm\sqrt{(-12)^2-4\times1\times(-12)}}{2\times1}=\frac{12\pm\sqrt{144+48}}{2}\approx\frac{12\pm13.86}{2}[/tex]

So either

[tex]n=\frac{12+13.86}{2}=12.93[/tex]

Or,

[tex]n=\frac{12-13.86}{2}=-0.93[/tex]

Solutions are given by n = 12.93 and -0.93

Hence the solutions are x=0.77 and -1.88 for first equation and n=12.93 and -0.93 for second equation.

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Using the cosine rule, BC = √(115² + 80² - 2(115)(80)(cos 72) ≈ 118.1 m (1 decimal place).

If we are given a triangle with two known sides and an included angle, the cosine rule that can be used to find the side opposite to the given angle is: a = √(b² + c² - 2bc(cos A)

We are given the following:

Plug in the values

BC = √(115² + 80² - 2(115)(80)(cos 72)

BC ≈ 118.1 m (1 decimal place)

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Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

Answer:

1. The data show that skipping breakfast is associated with earning lower exam grades.

2. There is an increase in B's for those who do eat breakfast before the exam.

A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. The various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.

A binomial expression is a two-term algebraic statement with variables, coefficients, exponents, and a constant. x² + 4x is an example of a binomial polynomial.

The variable terms that are possible in the expansion of (3a + 4b)⁸ are terms whose sum of powers is equal to 8.

Hence, the various terms that are possible are a⁷b, b⁸, a⁶b², and a⁸.

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The range of y = sin(x) is [-1,1]

The function is given as:

y = sin(x)

The above function is the parent function of a sine function.

A sine function has a minimum of -1 and a maximum of 1.

This is represented by the interval [-1,1]

Hence, the range of y = sin(x) is [-1,1]

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Answer:

Equation is 20 = 0.8 time x

x=25

Step-by-step explanation:

80% = 0.8

So to find x we 20/8

and we get 25 as the final answer

Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

While performing tasks during gymnastics she needs balance so that she can maintain and control a particular position.

Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

Balances are of two types dynamic and static. Balance used while moving and performing the task is dynamic balance while performing in a standing position is static balance.

Gymnasts require balancing as the main component cause they use poles and beams to perform their tasks.

Therefore, balance is the skill mainly required in gymnastics.

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The equation that models the data on pandas is FV = 25(1.066)^t.

The formula for calculating future value of the pandas is:

FV = P (1 + r) ^n

FV = 25(1.066)^t

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