The data given below consists of the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12. Find the z-score corresponding to the median of school allergies. You may use your calculator to find the mean and standard deviation.

Answers

Answer 1

Answer:

z -score = 0.0459

Step-by-step explanation:

Given that:

the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.

The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.

Mean = sum of the sample/ total number of the sample

Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25

Mean = 219/25

Mean = 8.76

Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]

Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)

Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]

Standard deviation = 5.2174

The standard z score formula is:

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

where X = median (13th observation ) = 9

[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]

[tex]z = \dfrac{0.24}{5.2174}[/tex]

z -score = 0.0459


Related Questions

Is math a feature of the universe or a feature of human creation?

Answers

Answer:

a feature of the universe

Step-by-step explanation:

Math is a feature of the universe because what we call math is just a way of explaining how things work.

Maria operates a taco truck in her neighborhood. She has created a graph based on her business performance in the previous year. The price she currently sells tacos for is $2.30. Which two statements correctly interpret this graph? Revenue and Cost Functions 1)Maria’s business is incurring losses. 2)Maria’s costs are rising over time. 3)Maria is running a profitable business. 4)Maria’s total revenue exceeds her total profit. 5)Maria’s total profit exceeds her total revenue.

Answers

Answer:

3)Maria is running a profitable business.

4)Maria’s total revenue exceeds her total profit.

Step-by-step explanation:

The graph shows variation of revenue and cost with respect to price of product and not with respect to time .

The price of the product is 2.30 . From this graph , we see  that at this price revenue exceeds total cost . So maria is running a profitable business .

Total profit can not exceed total revenue as

Total revenue - total cost = total profit .

So total profit will always be less than total revenue .

If m2 DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc in circle 0.
Find measure of arc DC.

Answers

Answer:

44°

Step-by-step explanation:

Given:

m<DOC = 44°

m<COB = 80°

Required:

Angle measure of arc DC

SOLUTION:

A central angle is said to be equal to the angle measure of the arc it intercepts or corresponds with. Therefore, angle measure of arc DC = m<DOC.

measure of arc DC = 44°

there was a total of 400 oranges and mangoes at a fruit stall.3/8 of these fruits were mangoes.each orange was priced at 40 cents,and each mango was priced at 60 cents.how much would mr.mead make if he sold 2/3 of the mangoes and 4/5 of the oranges?

Answers

Answer:

First find the number of Mango and oranges. 400 divided by 8 = 50. We use 8 because it is the whole part of the percentage. Since, there is 3/8 mangoes, multiply 50* 3= 150 mangoes and 50*5= 250 oranges.

2/3 of 150=100 mangoes. You would find this by dividing 150/3=50 then multiply by 2.

4/5 of 250= 200 oranges. You would find this by dividing 250/5=50 then multiply by 4.

$.40*100= $40.00 mangoes

$.60*200= $120.00 oranges

Mr. Mead would make $160.00

Step-by-step explanation:

Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente

Answers

De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL

O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.

Fazendo a classica regra de 3, podemos chegar no volume desejado:

(atentar que 500mg = 0,5g)

     g               mL

     1    ---------   2

    0,5  ---------  X    

1 . X = 0,5 . 2

X = 1mL

If you want to turn a ball into a giant water balloon, how many cubic feet of lake water can you fill it with if the radius of this balloon is 1.5 feet?

Answers

Answer:

14.13 cubic feet of lake water can fill the given balloon.

Step-by-step explanation:

concept used:

volume of sphere = 4/3 [tex]\pi r^3[/tex]

where r is the radius of sphere

we take [tex]\pi[/tex] = 3.14

_____________________________________

shape of balloon can be taken as spherical.

Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.

Given radius of balloon = 1.5 feet

Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3

volume of balloon = 42.39/3 = 14.13 cubic feet

Thus, 14.13 cubic feet of lake water can fill the given balloon.

If cot Theta = Two-thirds, what is the value of csc Theta? StartFraction StartRoot 13 EndRoot Over 3 EndFraction Three-halves StartFraction StartRoot 13 EndRoot Over 2 EndFraction Eleven-thirds

Answers

Answer:

csctheta= [tex]\frac{\sqrt{13} }{3}[/tex]

Step-by-step explanation:

answer is provided on top

The value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]. Cosec is found as the ratio of the hypotenuse and the perpendicular.

What is trigonometry?

The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle

The given data in the problem is;

[tex]\rm cot \theta = \frac{2}{3}[/tex]

The [tex]cot \theta[/tex] is found as;

[tex]\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\[/tex]

From the phythogorous theorem;

[tex]\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\[/tex]

The value of the cosec is found as;

[tex]\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]

Hence the value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex].

To learn more about the trigonometry refer to the link;

https://brainly.com/question/26719838

X2 + (y - 1) 2 = 4 .............................

Answers

Answer:

Step-by-step explanation:

x²+(y-1)²=4

x²+y²+1-2y=4

x²+y²-2y=3

Answer:

[tex]x=\pm \sqrt{6-2y}[/tex]

[tex]$y=\frac{1}{2} (6-x^2)$[/tex]

Step-by-step explanation:

[tex]x^2+(y-1)\cdot 2 =4[/tex]

[tex]x^2+2y-2 =4[/tex]

[tex]x^2+2y =6[/tex]

I will solve it for [tex]x[/tex]

[tex]x^2 =6-2y[/tex]

[tex]x=\pm \sqrt{6-2y}[/tex]

Solving for [tex]y[/tex]

[tex]$y=3-\frac{x^2}{2} $[/tex]

[tex]$y=\frac{1}{2} (6-x^2)$[/tex]

Given that a is a multiple of 456, find the greatest common divisor of 3a^3+a^2+4a+57 and a.

Answers

Answer: 57

Step-by-step explanation:

Given: a is a multiple of 456

Let [tex]a = 456 x[/tex]

Then, expression [tex]3a^3+a^2+4a+57 =3(456x)^3+(456x)^2+4(456x)+57[/tex]

Since 456 = 57 x 8

Then, [tex]3(456x)^3+(456x)^2+4(456x)+57=3(57\times 8x)^3+(57\times 8x)^2+4(57\times 8x)+57[/tex]

[tex]=3(57)^3\times (8x)^3+(57)^2\times (8x)^2+4(57)\times (8x)+57[/tex]

Taking 57 out as common

[tex]=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex]

Now, the greatest common divisor of [tex]a = 456 x[/tex] and [tex]3a^3+a^2+4a+57=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex] is 57.

Hence, the greatest common divisor of 3a^3+a^2+4a+57 and a is 57.

Tia uses 3/4 cup of pumpkin to make 1 1/4 pounds of dog treats. How much pumpkin does Tia use to make 1 pound of treats?

Answers

Answer:

4/5 cups  to make 1 pound of dog treats

Step-by-step explanation:

3/4 cups : 1 1/4 pounds

x cups : 1 pound

Cross multiply

3/4 * 1  = 1 1/4  * x

x = 3/4 / 1 1/4

= 3/4  /  5/4

= 3/4 * 4/5

= 3/5 cups

A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a medium that imparts a viscous force of 2 N
when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass.
A)Find the solution of the initial value problem in the above problem.
B)Plot the graph of the steady state solution
C)If the given external force is replaced by a force of 2 cos(ωt) of frequency ω , find the value of ω for which the amplitude of the forced response is maximum.

Answers

Answer:

A) C1 = 0.00187 m = 0.187 cm,  C2 = 0.0062 m = 0.62 cm

B)  A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

i will rate you branliest

Answers

Answer:

a₃ = 9

Step-by-step explanation:

The numbers in the set are referred to as { a₁, a₂, a₃, ... }

Answer:

a3 = 9 is the answer to this question

PLEASE ANSWER!!! Brainliest to whoever answers at first!Order the following expressions by their values from least to greatest.

Answers

Answer:

  -j, 0, j-k

Step-by-step explanation:

j is a positive number, so -j will be less than 0.

j is a number greater than k, so j - k will be greater than 0.

From least to greatest, the order is ...

  -j, 0, j-k

Answer:

Step-by-step explanation:

help please I need help :(

Answers

A = 1 and 8

B = 2 and 4

C = 2 and 7

I’m pretty sure this is right? I’m still learning too :p

Answers:Angle 1 and angle 8 are alternate exterior angles (so are angle 5 and angle 4; but you only need to pick one pair)Angle 1 and angle 3 are corresponding angles (there are 3 other possible answers. See the second section below)Angle 2 and angle 7 are alternate interior angles (so are angle 3 and angle 6; but you only need to pick one pair)

=======================================================

Explanations:

For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.

When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are

angle 1, angle 5, angle 4, angle 8

The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.

---------------------------------

Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.

Angle 1 and angle 3 are corresponding angles because they

a) are to the left of each parallel line (m and n)b) both below the transversal line

So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs

angle 1 and angle 3angle 2 and angle 4angle 5 and angle 7angle 6 and angle 8

---------------------------------

As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.

So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.

1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
Rolling a single die 53 times, keeping track of the "fives" rolled.
A) Not binomial: there are too many trials.
B) Not binomial: there are more than two outcomes for each trial.
C) Not binomial: the trials are not independent.
D) Procedure results in a binomial distribution.
2. Determine whether the given procedure results in a binomial distribution. If​ not, state the reason why.
Spinning a roulette wheel 7​ times, keeping track of the winning numbers.
A) Not binomial: there are more than two outcomes for each trial.
B) Procedure results in a binomial distribution.
C) Not binomial: there are too many trials.
D) Not binomial: the trials are not independent.

Answers

1. Not binomial: there are more than two outcomes for each trial.

Thus, option (B) is correct.

2. Procedure results in a binomial distribution.

Thus, option (B) is correct.

1. Not binomial: there are more than two outcomes for each trial.

In a binomial distribution, each trial can have only two outcomes (usually referred to as success and failure).

In this case, the procedure involves rolling a single die 53 times and keeping track of the "fives" rolled.

Since the outcome can be any number from 1 to 6 on each trial, it does not meet the criteria for a binomial distribution.

Thus, option (B) is correct.

2. Procedure results in a binomial distribution.

In this case, the procedure involves spinning a roulette wheel 7 times and keeping track of the winning numbers. The outcome of each trial is either a win or a loss, which satisfies the requirement for a binomial distribution.

Thus, option (B) is correct.

Learn more about Binomial Distribution here:

https://brainly.com/question/29163389

#SPJ6

Identify the sample space in the following tree diagram

A.) H, T
B.) TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
C.) HHH, THH, TTH, TTT
D.) HT, TH, TT, HT

Answers

Answer: Choice B

There are 2 sides per coin, and 3 flips, so 2^3 = 8 total items in the sample space

HHHHHTHTHTHHHTTTHTTTHTTT

Tracing each branch from left to right will help form the 8 different outcomes. For instance, if you go along the upper most path of the upper tree, then you'll get HHH meaning you got 3 heads in a row. The next branch down would be HHT, and so on.

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). y= [tex]\frac{2}{x^2}[/tex]+3

Answers

Answer:

One possible answer is:

f(x) = (2/x) + 3 and g(x) = x².

Step-by-step explanation:

Explanation:

We are to write this equation as y = f(g(x)).  This means we want it to be a composite of functions; in f(x), we take the value of g(x) and use in place of x.

If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x².  To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.

Please help with this, thanks

Answers

Answer:

BDC is half of mBC = 11°

Easily you see that C is A + BDC = 23°

Since C = 23° so mDC is twice = 46°

x

what is 38.4 cm + 38.4 cm ???

Answers

Answer:

76.8 cm

Step-by-step explanation:

Answer:

76.8 cm

Step-by-step explanation:

38.4 cm + 38.4 cm = 76.8 cm

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null



As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.

The sample data support the claim that the population mean is not equal to 88.9.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Answers

Answer:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Step-by-step explanation:

We are given the following hypothesis below;

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9      {means that the population mean is equal to 88.9}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9     {means that the population mean is different from 88.9}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 81.3

             s = sample standard deviation = 13.4

            n = sample size = 7

So, the test statistics =  [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex]   ~ [tex]t_6[/tex]

                                     =  -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

                    P-value = P([tex]t_6[/tex] < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.

Transform the Cartesian (rectangular) equation to a polar equation: x = -9. The selected answer is incorrect.

Answers

Answer:

Solution : Option C

Step-by-step explanation:

We have the equations r² = x² + y², x = r cos(θ), and y = r sin(θ) that can be used to solve this problem. In this case we only need the second two equations (  x = r cos(θ), and y = r sin(θ) ) as we don't need to apply the concept of circles etc here.

Given : x = - 9,

( Substitute r cos(θ) for x )

r cos(θ) = - 9,

r = - 9 / cos(θ)

( Remember that sec is the reciprocal of cos(θ). Substitute sec for 1 / cos(θ) )

r = - 9 sec(θ)

Therefore the third option is the correct solution.

An oblique cylinder is shown.


An oblique cylinder is shown. It has a radius of 5, a height of 12, and a slant length of 13.


Which represents the volume of the cylinder, in cubic units?


120π

130π

300π

325π

Answers

Answer:

 The volume in terms of Pi is 300π

Step-by-step explanation:

This problem is on the mensuration of solid shapes, an oblique cylinder.

the expression for the volume of an oblique cylinder is given as

[tex]volume= \pi r^2h[/tex]

Given data

radius r= 5

height h= 12, and

slant length of 13.

Substituting the given data into the expression we can solve for the volume below

[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]

Answer:

300

Step-by-step explanation:

PLLLEEEASSSSEEEE ANSWER FAST
The shape is based only on squares, semicircles, and quarter circles. Find the area of each shaded part.

Answers

Answer:

36.48 cm²

Step-by-step Explanation:

If you take a careful look at the figure given, you'd realise that the area of the shaded portion is actually created by 2 overlapping quarter circle.

The area of the shaded portion = Area of Square - Area of Unshaded part

Area of square = s² = 8² = 64 cm²

Area of the Unshaded portion = 2(Area of Square - Area of Quarter Circle)

= 2(s² - ¼*πr²)

Where, radius (r) = s = 8 cm, take π as 3.14

Area of unshaded part = 2(8² - ¼*3.14*8²)

= 2(64 - ¼*3.14*64)

= 2(64 - 1*3.14*16)

= 2(64 - 50.24)

= 2(13.76)

Area of unshaded part = 27.52 cm²

Area of shaded part = Area of Square - Area of Unshaded part

Area of shaded part = 64 - 27.52 = 36.48 cm²

Use a​ t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥8 300, α = 0.10
Sample statistics: x = 8000, s = 440, n = 24
A. What are the null and alternative hypotheses?
B. What is the value of the standardized test statistic?
C. What is the p-value?
D. Decide whether to reject or fail to reject the null hypothesis.

Answers

Answer:

A

     

The null hypothesis is  [tex]H_o : \mu \ge 8300[/tex]

The  alternative hypothesis is  [tex]H_a : \mu < 8300[/tex]

B

  [tex]t = -3.34[/tex]

C

 [tex]p-value = P(t< -3.34) = 0.00041889[/tex]

D

 reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 8300[/tex]

    The sample mean is [tex]\ = x = 8000[/tex]

     The  standard deviation is [tex]s = 440[/tex]

      The sample size is  [tex]n = 24[/tex]

       The  level of significance is  [tex]\alpha = 0.01[/tex]

   

The null hypothesis is  [tex]H_o : \mu \ge 8300[/tex]

The  alternative hypothesis is  [tex]H_a : \mu < 8300[/tex]

 The  test statistic is mathematically evaluated as

                     [tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]

=>                  [tex]t = \frac{8000- 8300 }{ \frac{440}{\sqrt{24} } }[/tex]

=>                    [tex]t = -3.34[/tex]

The p-value is obtained from the z -table ( reference calculator dot net ) , the value is

         [tex]p-value = P(t< -3.34) = 0.00041889[/tex]

Looking at the values of  [tex]p-value and \ \alpha[/tex] we see that  [tex]p-value < \alpha[/tex] Hence we reject the null hypothesis  

Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses. Examples to get 0: 0=4+4−(4+4); 0=44−44; 0=4×4−4×4

Answers

Answer:

0=4×4−4×4

Step-by-step explanation:

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

1 = 4 ÷ 4

2 = (4 + 4) ÷ 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 - 4

5 = (4 × 4 + 4) ÷ 4

6 = (4 + 4) - (4 ÷ 4) - (4 ÷ 4)

7 = (4 + 4) - (4 ÷ 4)

8 = 4 + 4

9 = (4 + 4) + (4 ÷ 4)

10 = (4 + 4) + (4 ÷ 4) + (4 ÷ 4)

Hi people, Please if someone can give me a hand, l already have done the first part of the exercise, but l cant make Angle CAB= X^0 c) calculate the lower bound for the value of tan X^0 there is the answer 1.02 (2dp) but l have no clue how to get it thanks i used Toa (Tan = Opp/ adj) but l couldnt find it thanks

Answers

Answer:

  (c) 1.02

Step-by-step explanation:

(c) The tangent is the ratio of Opposite to Adjacent. Its lowest value will be found where Opposite is lowest, and Adjacent is highest:

  min tan(A) = (min BC)/(max AB) = 75/73.5 ≈ 1.020408...(42-digit repeat)

Kathleen ordered a box of different colored light bulbs to use for stage lighting at the concert. Of the 60 bulbs in the box, 20% were red, 30% were orange, 30% were green, and 20% were blue. Of the blue ones, approximately 10% were damaged. What is the closest estimate for the number of blue bulbs that were damaged?

Answers

Answer:

1 bulb

Step-by-step explanation:

First find the number of blue bulbs

60 * 20 %

60 * .2

12 blue bulbs

10 % of the blue were damaged

12 * 10%

12 * .10

1.2

Rounding to the nearest whole number

1 bulb

60 x 0.2 x 0.1 = 1.2
Therefore 1 damaged blue bulb.

Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9

Answers

[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]

state crunchy theorem​

Answers

Answer: it says that if two different paths connect the same two points.

Step-by-step explanation:

It says that is two different paths connect the same two points, and a function holomorphic everywhere in between the two paths, then the two path integrals of the functions will be same.

Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?

Answers

Answer:

2 seconds

Step-by-step explanation:

Given the equation:

[tex]f(x) = -x^2 + x + 2[/tex]

Where f(x) represents the height of each ball thrown by machine.

and x represents the time in seconds.

To find:

The number of seconds after which the machine throws the balls hits the ground = ?

Solution:

In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]

(Because when the ball hits the ground, the height becomes 0).

Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]

[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]

[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.

So, the answer is after 2 seconds, the ball hits the ground.

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