A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 27 bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

Answer:

11.68ft or 11.68 feet

Step-by-step explanation:

From the above question, we are told that:

Area of the square and the Area semicircle is to be 190 ft squared.

We are also told in the question that:

The window has the shape of a square with a semicircle mounted on it.

Hence, the Diameter of the semicircle = Width of the Square

Let the Width of the square = x

Area of a square = Width²

= x²

Let the Diameter of the semi circle = x

Radius of the semi circle = Diameter of the semi circle/2 = x/2

Area of a semicircle = πr²/2

Area of a the semi Circle = π ×(x/2)² /2

= (πx²/4)/2

= πx²/8

Therefore,

Area of a square + Area of a semicircle = 190ft²

= x² + πx²/8 = 190

Cross Multiply

x² + πx² = 190

= x² ( 1 + π/8) = 190

x² = (190)/(1 + π/8)

x² = 136.42573798

x = √136.42573798

x = 11.680142892ft

Approximately x ≈ 11.68ft

Therefore, the width of the window = 11.68ft

Answer:

C. [tex] \sqrt {149} [/tex]

Step-by-step explanation:

Coordinates of the endpoints of the segment are (4, 4) & (-6, - 3)

By distance formula

Length of segment

[tex] = \sqrt {(4+3)^2 +(4+6)^2} [/tex]

[tex] = \sqrt {(7)^2 +(10)^2} [/tex]

[tex] = \sqrt {49 +100} [/tex]

[tex] = \sqrt {149} [/tex]

Answer:

See below.

Step-by-step explanation:

1.

Statement 8. triangle SQR is congruent to triangle TQP

Reason 8. ASA

2.

The only way to prove those two sides are congruent is to first prove that the triangles that contain those sides are congruent. Then you can use CPCTC to prove those sides congruent.

The two number with the largest product would be the two numbers closest together.

Divide 23 in half:

23/2 = 11.5

Use the whole numbers on each side of 11.5, so you have 11 + 12 = 23

Multiply: 11x 12 = 132

Answer:

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

Step-by-step explanation:

The question is not properly formatted, here is a good format for proper understanding and readability

[tex]64a^3-27b^3-144a^2+108ab^2[/tex]

let us first collect/ group like terms

[tex]64a^3-144a^2+108ab^2-27b^3[/tex]

we can now bring out the common factors we have

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

The simplified expression is

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

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

Work Shown:

LCM = least common denominator

List out the prime factorization of each denominator

So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.

The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM

The prime 3 shows up at most one time, meaning 3 is also a factor

The prime 11 shows up at most one time, so 11 is another factor

Multiply these factors to get 4*3*11 = 12*11 = 132

The LCM is 132

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

Another Approach:

Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.

The LCM of 1/6 and 10/11 is 66

The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively

The original list of fractions updates to 11/66, 60/66, 5/12

We've gone from 3 different denominators to now 2 different denominators.

Repeat the steps of multiplying the denominators and dividing by the GCF

66*12 = 792

792/(gcf of 66 and 12) = 792/6 = 132

So the LCM of all the fractions is 132.

Answer:

2/11 or approx. 18%

Step-by-step explanation:

There are 2 blue marbles out of 11 total marbles, so the probability will be 2/11.

2/11 = 0.18, or 18%

So, the odds are 2/11 or approx. 18%

Answer:

9:2

Step-by-step explanation:

9 red  and  2 blue

ways that an outcome cannot occur : how many ways it can occur

9 : 2  are the odds against a blue marble

Step-by-step explanation:

If (5) = 3

Then (10) = 6

Because 5 x 2 = 10 so 3 x 2 = 6

False.

Slope is the "rise over run" (y/x) in a linear equation. Because the denominators are the same in both fractions, it means you can just focus on the numerator with the larger number as that one will be the steeper line.

Answer:

$43,350

Step-by-step explanation:

To find the increase in the salary we need to find the percentage.

2 percent of $42,500 = $850.

$42,500 + $850 =  $43,350.

New salary = $43,350.

Answer:

7/5

Step-by-step explanation:

rise over run

start at the bottom point and count up along y axis and then count over along x axis

Answer: t = 4.87s

Step-by-step explanation: The vertical position y is given by

[tex]y = -16t^{2}+380[/tex]

If y at the base of the cliff equals 0, then equation is

[tex]-16t^{2}+380=0[/tex]

[tex]-16t^{2}=-380[/tex]

[tex]t^{2}=\frac{-380}{-16}[/tex]

[tex]t=\sqrt{\frac{380}{16}}[/tex]

[tex]t=\sqrt{23.75}[/tex]

t = 4.87

Since it is time we want, the negative value of the square root can be ignored. So, at the base of the cliff, the rock will hit the ground after 4.87 seconds.

Answer:

Step-by-step explanation:

H₀ : The distribution of the sample agrees with the population distribution.

H₁ : the distribution of the does not agree with the population distribution.

Using the  Chi-square test statistics

we will compute the expected frequencies

Now expected frequency for Washington will be

Fe = Npi = 1000×51% = 5100

expected frequency for Oregon

Fe = Npi = 1000×30% = 300

expected frequency for Idaho

Fe = Npi = 1000×11% = 110

expected frequency for  Montana

Fe = Npi = 1000×8% = 80

The Chi=square test statistics is;

x² = ∑ [ (Fo - Fe)² / Fe )

now we substitute

Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question

x² =  (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80

x²= 31.9376

so the chi-square test statistics is 31.9376

Now the chi-square critical value

first we compute for degree of freedom

d.f = k -1 = 4 - 1 = 3

So from the critical value table, degree of freedom 3 and significance level 0.05,

the chi-square critical value is 7.8147

Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.

There is sufficient evidence to warrant rejection  of the claim that the distribution of the sample agrees with the distribution of the state populations.

Answer:

The algebraic equation describing the above

X+y= x-30

Step-by-step explanation:

The initial temperature of the environment= x degrees

Temperature of the front= y degrees

the environment dropped 30 degrees, means loosed 30 degrees.

The final temperature f the environment= x-30

The algebraic equation describing the above

X+y= x-30

Answer:

When finding the y-intercept it indicates that the x-coordinate will be zero.

So,when letting x=0 you will get

y=-3(0)+4

Hence,

y=4

Step-by-step explanation:

Answer:

5 calories.

Step-by-step explanation:

We begin by calculating the rate at which Raquel burns calories while hiking.

This can be obtained as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

In this case, the Rate is simply defined as calories per unit time. Mathematically, it is expressed as:

Rate = Calorie/time

With the above formula, we can obtain the rate at which Raquel burns calories as follow:

Calories burned = 225 calories

Time = 45 mins

Rate =?

Rate = Calorie/time

Rate = 225/45

Rate = 5 cal/min

Therefore, Raquel burns Calories at a rate of 5 cal/min.

Now, we shall determine the calories burned by Raquel in 1 minutes. This is illustrated below:

Rate = 5 cal/min

Time= 1 min

Calorie =.?

Rate = Calorie /time

5 = Calorie /1

Cross multiply

Calorie = 5 x 1

Calorie = 5

Therefore, Raquel burns 5 calories in 1 minute while hiking.

Answer: He doesn't have any money left that period point blank

Step-by-step explanation

7-6=1

1-3= you cant do that

so he doesn't get soda at all.

Answer:

y=-1/4x-1/2

Step-by-step explanation:

When two lines are parallel, they have the same slope.

So for this line, we already know that the slope (m) has to equal -1/4x.

Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

in order to find the equation, we must plug in x and y to solve for b, the y intercept (the value of y when x=0).

Now, let's plug in 2 for x and -1 for y and solve for b:

-1=-1/4(2)+b=-1=-1/2+b=-1+1/2=b

b=-1/2

Hence, the answer is y=-1/4x-1/2

Answer:

The answer is -1/4x - 1/2

Step-by-step explanation:

Just took the Unit Session

Answer:

64000

Step-by-step explanation:

Answer:

64000

Step-by-step explanation:

Answer:

3 / 13

Step-by-step explanation:

Hello!

There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2

52/ 2 = 26

There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount

6/26 we can simplify this

3 / 13

The answer is 3 / 13

Hope this helps!

Answer:

3/13

Step-by-step explanation:

In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.

p(face given black) = 6/26 = 3/13

Answer:

8i+8j

Step-by-step explanation:

3i+4j+5i+4j

i(3+5) + j(4+4)

Therefore 8i +8j

HAPPY TO HELP YOU

Answer:

Step-by-step explanation:

we have :

a=3i+4j

b=5i+4i

so that : a+b=3i+4j+5i+4j

=(3i+5i)+(4j+4j)

so    a+b=8i+8j=8(i+j)

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]

The value of first quartile is 34.75.

Q₃ is at the position:

[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]

The value of third quartile is 44.83.

Then the inter-quartile range is:

[tex]IQR = Q_{3}-Q_{1}[/tex]

        [tex]=44.83-34.75\\=10.08[/tex]

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]

                                 [tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]

Thus, the probability that a student scored at most 50 on the examination is 0.89.

Answer:

D. 8

Step-by-step explanation:

We can see the numbers from 20 (inclusive) to 45 on the plot:

Correct answer choice is: D. 8

Answer:

air conditioning or air cooling or climate control

hope this helps :)

Answer:

0

Step-by-step explanation:

To find the slope of two points, here is the formula (y2-y1)/(x2-x1)

So we have (1,2) and (4,2),

We let y2 = 2 and y1 = 2 and we let x2 = 4 and x1 = 1

So, (2-2)/(4-1) = 0/3

Our slope is 0.

Answer:

$1500

6 hours

Step-by-step explanation:

There is no one off fee, therefore we got (0,0) a starting point.

(1,125) is representing the first hour of rent, so 1 hour rent costs $125.

There is a direct relationship between the time and rental fee.

As a function is will be:

For x= 12, we get:

So, if f(x) = 750, then:

The value of a in the function's equation is 3

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions,

equation of  parabola is :

[tex]y= a (x-h)^{2} + k[/tex]

where ,

h= horizontal coordinate of graph

k = vertical coordinate of graph

a =  the value of the coefficient

According to the question

horizontal coordinate of graph  = -2

vertical coordinate of graph = 2

[tex]y= a (x-h)^{2} + k[/tex]

[tex]y= a (x+2)^{2} + 2[/tex]

now we will take one point from  x and y value from the graph  to take out value of  coefficient a  

from graph (x,y) = (-1,5)

[tex]5= a (-1+2)^{2} + 2[/tex]

[tex]\\3= a (-1+2)^{2}[/tex]

[tex]\\3= a (1)^{2}[/tex]

[tex]a = 3[/tex]

Hence, the value of a in the function's equation is 3

To know more about equation function and parabola here :

https://brainly.com/question/26227783

# SPJ2

Answer:DC=7

Step-by-step explanation:

As it is written △ABC = △DBC.   So the corresonding legs (the legs which are equal ) are as follows:

AC=DC       AB=DB      BC= BC

So DC=7  the same like AC