. A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working properly when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared. Is there evidence that the machine should be stopped and production wait for repairs

Answer:

(c)hope

Step-by-step explanation:

2x + 44 = 72

14

hence

2x = 2*14

28

\(\displaystyle\frac{3}{16}\)

Probability represents the likelihood of an event occurring. Complex probability is the likelihood of a series of events occurring.

Independent Events

The question states that the marbles are replaced after being recorded. This means that the separate drawing of marbles is independent of each other. So, the probability of an event occurring does not change based on events that happened earlier.

This is important to this question because it means that probability does not change based on if the one red marble was drawn first or second.

Probability of a Red

First, we need to find the probability of drawing a red marble. Probability is represented as the number of successful outcomes (drawing a red) over the number of possible outcomes (number of marbles). Out of the total 12 marbles, 3 of them are red. So, the probability of drawing a red is \(\displaystyle\frac{3}{12}\).

The Complement

In probability, the complement is the likelihood of an event not occurring. So, in this situation, the complement is the likelihood of not drawing a red. Out of the total 12 marbles, 9 are NOT red. So, the complement is \(\displaystyle\frac{9}{12}\).

Complex Probability

To find the probability of 2 different events both occurring, multiply the probabilities together.

Then, we can simplify the fraction by dividing by 9

This means that the probability of drawing exactly one red is 3/16.

Answer:

a. Without any additional information provided, it is impossible to determine the probability of Manchester United winning the match. The outcome of a football match can be influenced by many factors such as player performance, tactics, and luck.

b. There are 22 players + 3 officials = 25 people on the pitch. The probability that a person selected at random from the pitch is an official is 3/25.

c. i. Since there are 2 goalkeepers on the pitch, the probability that a player selected at random is a goalkeeper is 2/22 = 1/11

ii. Since there are 3 attackers on the pitch, the probability that a player selected at random is an attacker is 3/22 = 1/7

iii. Since there are 8 defenders on the pitch, the probability that a player selected at random is a defender is 8/22 = 4/11

Answer:

(-3,-5)

Step-by-step explanation:

I graphed the two lines and where they intersect is their soluation!

Picture attached!

(u‿ฺu✿ฺ)

each pumpkin costs $10.50

63/6 = 10.5 or $10.50 and $10.50 x 2 = $21

that's all I got sorry ~(>_<。)＼

Answer:

igcwochcd chocho dhvohov dochvo

Answer:

y equals 2/3 x plus 4 is correct.

The equation y= 1/3x  + 4 represents a linear function.

A linear function is a function that can be represented by a straight line. The equation of a linear function is typically in the form y = mx + b, where m represents the slope and b represents the y-intercept.

1. 2x − 4 = 6 is a linear equation, but it is not a function because it does not isolate y.

2. x = −2" represents a vertical line with a slope of infinity, but it does not have the form y = mx + b.

3. y = 1/2x² represents a quadratic function because it contains x raised to the power of 2.

4. y= 1/3x  + 4 represents a linear function.

Therefore, the equation y= 1/3x  + 4 represents a linear function.

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3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

hi ik you dont trust me however id like to say that the answer is A. 41.6

Step-by-step explanation:

hope this helps <3 (also i put this into a calculator to double check my work and it was still 41.6)

Answer:

41.6

Step-by-step explanation:

Move the decimal 1 place to the right according to the laws of exponents.

since the exponent is 1, that's why we move it 1 place right. if the exponent was -1, it would go to the left, and the number would become "0.416".

Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

The axis of symmetry is at x = 1, the domain is (-∞, +∞), the y-intercept c is at 7 and x intercept is not applying .

A parabolic function is one that satisfies the formula f(x) = ax2 + bx + c and, when represented graphically in two dimensions, has the shape of a parabola. Any quadratic equation with just a second degree in x is the equation for a parabolic function.

The following characteristics define a basic parabola:

Thus, from the given graph the value are obtained as:

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The slope of the curve  y⁴ = y² - x² is 1 and repeat the process for the second point.

Find the slopes of the curve y⁴ = y² - x² at the given points, we need to differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation with respect to x, we get:
4y³ * (dy/dx) = 2y * (dy/dx) - 2x
Next, we can solve for (dy/dx) by isolating it on one side of the equation:
4y³ * (dy/dx) - 2y * (dy/dx) = -2x
(2y - 4y³) * (dy/dx) = -2x
(dy/dx) = -2x / (2y - 4y³)
Now, substitute the x and y values for each point into the equation to find the slopes at those points.
For example, if one point is (1, 1), we substitute x = 1 and y = 1 into the equation:
(dy/dx) = -2(1) / (2(1) - 4(1)³)
(dy/dx) = -2 / (2 - 4)
(dy/dx) = -2 / -2
(dy/dx) = 1
Repeat the process for the second point, and you will have the slopes of the curve at both points.

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Answer: the fraction is 4over 12

Step-by-step explanation:

first you multiply the top and bottom number then u divide the number by the bottom.

Answer:

1/2

Step-by-step explanation:

If you were to multiply 1/2 by -50 you would get -25, which is greater than -50.

The same goes for 1/5, if you were to multiply 1/5 by -50, you would get -10.

Another example is 1/10 times -50, that would be -5.

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

JIG and JIL

Step-by-step explanation:

Adjacent angles share a side

I hope this helps :)

Answer:

JIG and JIL

Step-by-step explanation:

cuz adjecent angles add up to 180 degrees.

Hope this helps :)

Answer:

10.83

Step-by-step explanation:

The length of AB to 3 decimal places is 10.83 cm

The given figure is a right triangle

From the triangle, we are given the following parameters

AC = 18cm

m<C = 38 degrees

we need to get the length of AB

Using the SOH CAH TOA identity

\(sin \theta = \frac{opposite}{hypotenuse} \\sin 37 = \frac{AB}{18}\\AB = 18 sin37\\AB =18(0.6018)\\AB =10.832cm\)

Hence the length of AB to 3 decimal places is 10.83 cm

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Answer:

Area of a triangle = l*b

                              = 183/5*50/3

                              = 36.6*16.66

                              = 609.756 m

A two-column proof to show that m∠3 + m∠6 = 180° should be completed with the statements and reasons stated below.

In Mathematics and Geometry, the consecutive interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the interior angles that are formed are congruent and each pair of the consecutive interior angles is supplementary.

In this context, a two-column proof to show that m∠3 + m∠6 = 180° should be completed with the following statements and reasons;

Statement                                                Reasons

l║n                                                           Given

∠6 and ∠7 are linear pair                 consecutive interior angles theorem  

∠3 ≅ ∠7                                                Definition of linear pair  

m∠3 + m∠6 = 180°                                Substitution property

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1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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The two triangles are both right triangles and are both formed by the

intersection of the lines AS and BD and are therefore similar.

Response:

(a) Yes, ΔABC is similar to ΔSDC according AA similarity postulate

(b) The distance from the ship to the shore is approximately 282.6 feet

(a) Yes, Gilligan can conclude that ΔABC and ΔSDC are similar by

Angle-Angle, AA, similarity postulate.

Reason:

Angle ∠SCD in ΔSDC and ∠ACB in ΔABC are vertically opposite angles,

and they are therefore congruent by vertical angles theorem.

∠SDC = 90° and ∠ABC = 90° therefore ∠SDC ≅ ∠ABC because all 90°

are congruent.

Therefore, two angles in ΔABC are congruent to two angles in ΔSDC,

therefore, ΔABC is similar to ΔSDC according to AA similarity postulate

(b) The ratio of corresponding sides in similar triangles are equal,

therefore;

\(\dfrac{BC}{DC} = \mathbf{\dfrac{AB}{SD}}\)

Which gives;

\(\dfrac{23}{130} = \dfrac{50}{SD}\)

\(SD = \dfrac{130}{23} \times 50 \approx 282.6\)

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The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Answer:

Below.

Step-by-step explanation:

sin ((x))-(y)) / cos (x) sin (y)

    sin x cos y - cos x sin y

=  ----------------------------------

           cos x sin y

     sin x cos y

=    ----------------   -   1

     cos x sin y

But tan x = sin x / cos x  and cot y = cos y / sin y

So the above =  tan x cot y - 1.

a) One-tailed test at α = 0.01, we get a critical value of 2.423

b) 99% confident that the true difference between the means of the two populations (μ₁ - μ₂) lies between 3.

Sample data refers to a subset of data that is selected from a larger population of interest, with the intention of using it to draw conclusions or make inferences about the population.

a) Hypotheses: H0: μ₁ ≤ μ₂, Ha: μ₁ > μ₂ (right-tailed test)

Test Statistic: t = (x₁ - x₂) / √((s₁²/n₁) + (s₂²/n₂))

Calculating the test statistic:

t = (47.2 - 38.6) / √((9²/26) + (9.3²/20))

t = 2.77

Degrees of Freedom:

df = {(s₁²/n₁ + s₂²/n₂)² } / {(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)}

Calculating the degrees of freedom:

df = ((9²/26) + (9.3²/20))² / (((9²/26)²/25) + ((9.3²/20)²/19))

df = 42.38 (rounded to nearest integer) = 42

Using a t-distribution table or calculator with 42 degrees of freedom and a one-tailed test at α = 0.01, we get a critical value of 2.423.

b) To construct a 99% confidence interval for μ₁ - μ₂, we can use the following formula:

(x₁ - x₂) ± t(α/2,df) × √((s₁²/n₁) + (s₂²/n₂))

Substituting the values:

(47.2 - 38.6) ± t(0.005,42) × √((9²/26) + (9.3²/20))

Therefore, the 99% confidence interval for μ₁ - μ₂ is:

(47.2 - 38.6) ± 2.718 × √((9²/26) + (9.3²/20))  = 8.6 ± 4.902

= (3.698, 13.502)

Hence, we can be 99% confident that the true difference between the means of the two populations (μ₁ - μ₂) lies between 3.

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9514 1404 393

Answer:

  1/4

Step-by-step explanation:

Each coordinate of H'J'K' is 1/4 of the value for HJK.

The scale factor is 1/4.

Answer:

1/4 would be right I am 100% sure

Answer:

The slope is -7 and the y-intercept is 8.

Step-by-step explanation:

You would subtract 7x from the left side and move it to the right side so y = -7x + 8. The slope is -7 because that is the number in front of the x and the slope is 8.

Answer:

Slope = –7, y-intercept = 8

Step-by-step explanation:

y = mx + b