The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
a) 95% of the widget weights lie between _______ and ________.
b) What percentage of the widget weights lie between 37 and 67 ounces?c) What percentage of the widget weights lie above 49 ?

Answer:

The interest rate = 1.68%

Step-by-step explanation:

Sue invests £9000 in an account for one year.

She pays £30.24 at a rate of 20%

So 20% of the interest =£ 30.24

Let the interest be x

X0.2= 30.24

X=£ 151.2

The total interest was£ 151.2

The rate R at which generated this interest

R = (100*151.2)/(1*9000)

R= 15120/9000

R= 1.68%

The interest rate = 1.68%

Answer:

P= $3.5x -$30

Step-by-step explanation:

Let the number of roses Thomas bought and sold be x.

Hence the total selling price would be;

$3.5 × x= $3.5x

The profit = selling price-expenses

P= $3.5x -$30

Answer:

V = V = 175 pi units^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V =pi ( 5)^2 ( 7)

V = 175 pi units^3

Answer:

1.4650  (the first option in the list of possible answers)

Step-by-step explanation:

Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:

[tex]2+3^x=7\\3^x=7-2\\3^x=5[/tex]

Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":

[tex]3^x=5\\x=log_3(5)[/tex]

In order to find this logarithm, we use the change of base formula:

[tex]log_3(5)=\frac{log(5)}{log(3)} =1.46497...[/tex]

which rounded to four decimals gives: 1.4650

Answer:

Step-by-step explanation:

There are four options given above.

P specifies the probability that a couple turns their head to the right when kissing. P is 0.5 because the probability of turning right when kissing is 75÷150 = 1/2 = 0.5

Assuming that the given confidence intervals are an instance of a random interval computed upon observing the given data,

The correct statements are statements 1 and 4

Answer:

Population

Step-by-step explanation:

In mathematics, when we talk about the people, places, or things under consideration, we are referring to the population. The Population is the entire sum of objects in a study. When a researcher wants to study factors that concern a particular set of people, places, or things, the group under study is the population. For example, the researcher might want to do a study on the amount of food consumed by Brazilian students in the year 2019. The Brazilian students represent the population, because they are the group of people being studied.

The population under study might sometimes be difficult to study as a whole. For example, the study of the entire Brazilian students might be cumbersome. In such cases, a sample can be drawn from the population and studied, or the population narrowed down a little more, so that it can be easily studied.

Answer:

Step-by-step explanation:

item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm

You did not state the diameter or radius of the window

so, i will use 90cm as the diameter of the window

First, I'd calculate the half circumference of the window.

The formula for circumference is [tex]c = 2\pi r[/tex],

Half of it would just be [tex]c/2 = r\pi[/tex]

Since our diameter is 90 cm, our radius is 45 cm.

Circumference =

[tex]=45\pi \\= 141.37 cm[/tex]

circumference is also the same with perimeter

Answer:

141.4cm

Step-by-step explanation:

=>

please give barinlist

Answer:

it is

Step-by-step explanation:

Answer:

x=-3 y=6

Step-by-step explanation:

it was a easyone ,don't forget to mark me as a brainlinest .☺️

Answer:

f(x) = 2x^4 - 3

Step-by-step explanation:

First multiplying by 2 giving f(x) = 2x^4 stretches it vertically by factor 2.

Then subtract 3 to move it down 3 units:

f(x) = 2x^4 - 3.

Answer:

g(x)=2x^4-3

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

since it is divided to 8 equal parts then the first tick is 1/8

Answer:

32 units

Step-by-step explanation:

The large triangle on top has an area of 20, cause 4*10 = 40

40/2 = 20.

the square on the bottom has an area of 4, well, cause 2*2 = 4.

The smaller triangle on the left has an area of 2, cause 2*2=4

4/2=2

The triangle on the right, has an area of 6, because 6*2=12

12/2=6

20+4+2+6 = 32

Answer:

32 Units =)

Step-by-step explanation:

Answer: g(x) = -f(x)

Step-by-step explanation:

When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y)

In this case we have a function reflected, and we know that we can write a function as (x, f(x))

So when we reflect it, the result will be (x, g(x)) = (x, -f(x))

So we have g(x) = -f(x)

Answer:

4

4

Step-by-step explanation:

x litres of 15% solution + y litres of 19% solution= 8 gallons of 17% solution

disinfectant content of the final solution= 8*0.17= 1.36 gallons

0.15x+0.19y=1.36

x+y= 8 ⇒ x=8-y

Answer:

C.

Step-by-step explanation:

60° in Radians = 1.047

Using Formula

s=rθ

s= 7(1.047)

s ≈ 7.36

Answer:

z=2

Step-by-step explanation:

56-35z+17=3

73-35z=3

-35z=-70

z=2

Answer:

Since there was a dilation, the two triangles will be similar. The scale factor is less than one and is a reduction, therefore, the image will be smaller than the pre-image.

Answer:

(-∞,∞)

Step-by-step explanation:

It's just a line

Answer:

INFINITIE, INFINITIE

Step-by-step explanation:

Answer:

PQ AND SR on ED

Step-by-step explanation:

Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.

For the given situation,

Angles PTQ and STR are vertical angles and congruent.

Line segments T P, T Q, T R, and T S are radii.

So, T P = T Q = T R = T S.

The two sides T P = T Q and T R = T S and [tex]\angle PTQ = \angle RTS[/tex],

then by SAS similarity theorem two triangles,

Δ PTQ ≅ Δ STR.

When two triangles are congruent, then the corresponding arc are also congruent.

The congruent central angles intercept congruent arcs PQ and SR.

Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

Learn more about vertical angle theorem here

https://brainly.com/question/17702030

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Answer:

S20 ≈ 4.942

Step-by-step explanation:

Sum of a geometric series is expressed as Sn = a(1-rⁿ)/1-r if r<1

a is the first term

r is the common ratio

n is the number of terms

Given the geometric series

1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}

Given a = 1,

r = 0.8/1 = 0.8²/0.8 = 0.8

n = 20 (The total number of terms in the series is 20)

Substituting this values in the formula above.

S20 = 1(1-0.8^20)/1-0.8

S20 = 1-0.01153/0.2

S20 = 0.9885/0.2

S20 ≈ 4.942

Answer:

20 minutes

Step-by-step explanation:

Distance= 40 km

Speed= 120 km/h

Time= distance/speed= 40/120= 1/3 hour= 20 min

Answer:

Time = 0.33 hrs

Step-by-step explanation:

Given:

Speed = 120 km/hr

Distance = 40 km

Required :

Time = ?

Formula:

Speed = Distance/Time

Solution:

Time = Distance / Speed

Time = 40/120

Time = 0.33 hrs

Answer:69

Step-by-step explanation:

Because i am smart.

Answer:

[tex](4x-3)(3x^2)+2)[/tex]

Step-by-step explanation:

Answer:

The greatest common factor for the first parenthesis is 3 and the greatest common factor for the second parenthesis is 2

Step-by-step explanation:

Hope this helps plz mark brainliest!

Answer:

60, 62, 64

Step-by-step explanation:

Let x, (x + 2) & (x+ 4) be three consecutive even integers.

[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]

Hence, the three consecutive even integers are 60, 62 and 64.

Answer:

68% of the lengths of pregnancies fall between 250 days and 282 days.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 266

Standard deviation = 16.

What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?

250 = 266 - 16

So 250 is one standard deviation below the mean.

282 = 266 + 16

So 282 is one standard deviation above the mean.

By the Empirical Rule, 68% of the lengths of pregnancies fall between 250 days and 282 days.

Answer:

[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]

And we can find this probability with this difference and using the normal standard table or excel:

[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]

So then we will have approximatetly 68.26% of the values between 250 and 282 days

Step-by-step explanation:

Let X the random variable that represent the The length of human pregnancies from conception to birth, and for this case we know the distribution for X is given by:

[tex]X \sim N(266,16)[/tex]  

Where [tex]\mu=266[/tex] and [tex]\sigma=16[/tex]

We are interested on this probability

[tex]P(250<X<282)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]

And we can find this probability with this difference and using the normal standard table or excel:

[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]

So then we will have approximatetly 68.26% of the values between 250 and 282 days

Answer:

Future value = $755.61 ( to the nearest cent)

Step-by-step explanation:

The formula for calculating the future value of an invested amount compounded periodically for a number of years is given as:

[tex]FV = PV (1+\frac{r}{n} )^{n*t}[/tex]

where:

FV = future value = ???

PV = present value = $575

r = interest rate in decimal = 5.5% = 0.055

n = number of compounding periods per year = quarterly = 4

t = time of investment = 5 years

∴ [tex]FV = 575 (1+\frac{0.055}{4} )^{4*5}[/tex]

[tex]FV = 575 (1+0.01375)^{20}\\FV = 575 (1.01375 )^{20}\\FV = 575 * 1.3141\\FV = 755.607[/tex]

∴ Future value = $755.61 ( to the nearest cent)

Answer:

DE= 39°

Step-by-step explanation:

(4w+ 4 )+(4w+8)= 180

Solve for w

8w + 12 = 180

8w = 180-12

8w = 168

W= 21°

(4w+ 4)+(2w+11)+DE = 180

But w= 21°

((4*21 )+4)+((2*21)+11)+DE = 180

88 + 53 + DE = 180

DE = 180-88-53

DE= 39°

Answer:

job cost sheet.

Step-by-step explanation:

When planning or working on a specific project/job all the actual costs that are incurred for that job are written down in the job cost sheet. This report is an entire compilation that should be created by the accounting department and then distributed to all the members of the management department who then analyze it and determine whether the job was correctly bided. This sheet  gets updated as the job is undergoing and fully completed when the job is closed.

Answer:

k= 80%

Step-by-step explanation:

Jar A contains 4*0.45 L acid, and 4 L of a solution  of acid.

Jar B contains 5*0.48 L acid., and 5 L of a solution of acid.

Jar C contains 1*k/100 = k/100 acid, and 1 L of a solution.

50% = 0.5

For jar A.

(2/3)*k/100 L acid  is added to jar A.

Now jar A contains   4*0.45 L + (2/3)*k/100 L acid, and it has (4+2/3)L of a solution.

L solute/L solution = 0.5

[4*0.45 L + (2/3)*k/100 L]/(4+2/3)L = 0.5

[1.8 + (2k/300)]/[(12+2)/3] = 0.5

[1.8 + (2k/300)]/[14/3] = 0.5

[1.8 + (2k/300)]= 0.5*(14/3)

(2k/300) = 0.5*(14/3) - 1.8

2k = (0.5*(14/3) - 1.8)*300

k = (0.5*(14/3) - 1.8)*300/2 =80

k= 80%

We also can find k using jar B.

(1/3)k/100 L acid is added  to jar B.

Now jar B contains 5*0.48 L+ (1/3)k/100 L acid, and it has (5+1/3) L of a solution.

L solute/L solution = 0.5

[5*0.48 L+ (1/3)k/100 L ]/(5+1/3)L= 0.5

[5*0.48 + (1/3)k/100 ]/(5+1/3)= 0.5

This equation also gives k=80%

Check.

We can check at least for jar A.

Jar A has 4L solution and 4*0.45=1.8 L acid.

2/3 L of the solution from jar C was added, and now we have 4 2/3 L of solution.

(2/3)* 80%= (2/3)*0.8 acid was added from jar C.

Now we have [1.8 +(2/3)*0.8] L acid in jar A.

L solute/L solution =  [1.8 +(2/3)*0.8] L /(4 2/3) L = 0.5 or 50%  as it is given that jar A has 50% at the end.