A bag with 12 marbles has 12 blue marbles. A marble is chosen from the bag at random. What is the probability that it is blue?
Write your answer as a fraction in simplest form.

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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An equilateral triangle is a type of triangles which can always be used as a counterexample to the statement ""all angles in a triangle are acute"".

An acute angle is one that is smaller than 90 degrees in length. If the arms of an angle open up less than a "L," an acute angle is created because a "L" shape forms at 90°.

Angle between 90 to 180 are known as obtuse angle.

Because an equilateral triangle is likewise equiangular, it can be used as a counterexample. So, each angle has a 360/3=60 measurement. Two angles are therefore acute, and the third's measure is also acute.

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Answer:

<RQS = <RSQ

Step-by-step explanation:

IRQ = RS, then QRS is an isosceles triangle and the base angles are equal

<RQS = <RSQ

Answer:

I believe its 32oz because if hes dri king 8oz every 5 cookies and he ate 20 cookies he ate 4 times the first 5 cookies so you would multiply 8x4=32oz of milk

Answer:

32oz

Step-by-step explanation:

Answer:

11x+4

Step-by-step explanation:

To do this, we can substitute 3x+10x for f(x) and 2x-4 for g(x), and we get 13x-(2x-4). By distributing the negative to 2x-4, we just swap the signs, and get 13x-2x+4, which equals 11x+4

Also, is there supposed to be an exponent on the first f(x)? I'm not sure because I haven't seen the real problem.

(Otherwise it would just be f=13x.) Maybe try being a little more clear when asking a question :)

Please let me know if you need more help or explanation on another problem!

The sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

The formula we use for this is

Sum of interior angles of a polygon

= ( n-2)*180

Where “n” is the number of sides of the polygon.

Here n=14

So, sum = (14–2)*180 = 2160 degrees

Therefore, the sum of the measures all the interior angles of a polygon having 14 sides is 2160°.

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What will be the sum of the measures all the interior angles of a polygon having 14 sides?

The expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

The expected probability of a head coming up next given the results of the 25 coin flips is 15/25 = 0.6.

This is due to the fact that 15 of the 25 flips were heads, so the probability of the next head is 15 out of the 25 total flips which is equal to 0.6 or 60%.

However, since the probability of heads (m) is unknown, the expected probability of a head coming up next is still unknown.

Therefore, the expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

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the answers for the y coordinates

-6

-3

-3/2

-3/4

The ratio of x and y will be equal to x:y  = 25:16

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

We know that

The length of Q is 25% more than the length of p

length Q=1.25 x 80--------> 100 cm

The area of Q is 20% less than the area of p

Area Q=100 x y

Area P=80 x x

100 x y=0.80 x [80 x  x]---------> 100 x y = 64 x  x-------> x/y=100/64-->  25/16

Therefore the ratio of x and y will be equal to x:y  = 25:16

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Answer:

25:16

Step-by-step explanation:

Answer:

B. 2

To find MAD, find the mean of the set, then find how far each number is from the mean. Next, find the mean of THAT set of numbers. Yea, I know it's a bit confusing... don't worry!

Find the mean of the set:

12 + 10 + 10 + 8 + 6 + 7 + 7 + 12

72

72 / 8

9

Find how far each number is from 9:

12 - 9 = 3

10 - 9 = 1

10 - 9 = 1

9 - 8 = 1

9 - 6 = 3

9 - 7 = 2

9 - 7 = 2

12 - 9 = 3

Find the mean of that number set:

{3, 1, 1, 1, 3, 2, 2, 3}

3 + 1 + 1 + 1 + 3 + 2 + 2 + 3

16

16 / 8

2

So the answer is 2!

Not so hard after all   :D

Upper Control Limit for R Chart: UCL = D4 * R-Bar , UCL = 2.114 * 1.000, UCL ≈ 2.115 cm. Therefore, the correct answer is 2.115 cm(d).

To calculate the upper control limit for the R Chart, we need to use the following formula:

Upper Control Limit (UCL) = D4 * R-Bar

Where:

- D4 is a constant value based on the sample size (n=5 in this case).

- R-Bar is the average range of the samples, which is given as 1.000 cm.

The value of D4 for a sample size of 5 is 2.114. (You can find this value in statistical reference tables.)

Now, we can calculate the UCL:

UCL = D4 * R-Bar

   = 2.114 * 1.000

   = 2.114 cm

Rounding to 3 decimal places, the upper control limit for the R Chart is 2.114 cm.

Therefore, the correct option is: d. 2.115 cm

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The complete question is :

Repeated sampling of a certain process shows the average of all sample ranges to be 1.000 cm. There are 12 random samples and the sample size has been 5. What is the upper control limit for R Chart? Must compute in 3 dec pl. Select one: O a. 2.745 cm O b. 3.005 cm O c. 1.725 cm d. 2.115 cm e. 2.000 cm

Step-by-step explanation:

The solution to the system is the point that is on BOTH lines....this is the point where they intersect (cross) each other

for this system, from the graph, this is point ( 3,2)  

The standard form of the given equation is -k² + 7k

Quadratic Equation:

A quadratic equation is a quadratic polynomial in variables of type f(x) = ax2 + bx + c = 0, a, b, c, ε R and a ≠ 0. It is the general form of the quadratic equation. 'a' is called the principal coefficient and 'c' is called the absolute term of f(x). The value of x that satisfies a quadratic equation is the root (α, β) of the quadratic equation.

Standard Form of a Number:

A standard form is a way of writing certain mathematical concepts, such as equations, numbers, and formulas, in a form that follows certain rules. Standard forms are used to concisely represent very large or very small numbers. For example, 4.5 billion years is written as 4.5 billion years. As you can see here, writing a large number like 4.5 billion in its numeric form is not only ambiguous and time consuming, it can add or subtract a few zeros when writing in numeric form. There is a nature. In this case, writing the numbers in standard form can be very helpful. For example, 4,500,000,000 = 4.5 × 109 in normal form. You can write not only numbers but also fractions, equations, formulas, polynomials, etc. in standard form.

Now,

Given that:

c = k - 3

b = k² - 6k -3

Now,

C - B = k - 3 - (k² - 6k -3)

        = k - 3 - k² +6k + 3

        = k - k² + 6k

        = -k² + 7k

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Using it's definition, the probabilities are given as follows:

The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

The total number of bulbs in this problem is given as follows:

6 + 9 + 5 = 20.

Six of them are red, hence the probability of a red bulb is:

p = 6/20 = 0.3 = 30%.

Nine of them are blue, hence the probability of a blue bulb is:

p = 9/20 = 0.45 = 45%.

Five of them are green, hence the probability of a green bulb is:

p = 5/20 = 0.25 = 25%.

The probability of a red or blue bulb is:

p = 0.3 + 0.45 = 0.75.

The probability of a blue or green bulb is:

p = 0.45 + 0.25 = 0.6.

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The circumference with radius of 10.4 ft is 65.3 ft. The result is obtained by using the formula for circumference.

Circumference is also called the perimeter of a circle. It can be expressed as

P = 2πr

Where

The circumference with the radius = 10.4 ft.

We have

Find the circumference! (to the nearest tenth)

The circumference will be

P = 2πr

P = 2(3.14)(10.4)

P = 65.3 ft

Hence, the perimeter of the circle to the nearest tenth is 65.3 feet.

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a. To find the intercepts with the coordinate axes, we set each variable to zero and solve for the remaining variables.

For the x-intercept, we set y = 0 and z = 0 in the equation x = 4 - y^2 - 4z^2:

x = 4 - 0^2 - 4(0^2)

x = 4

So, the x-intercept is located at x = 4.

For the y-intercept, we set x = 0 and z = 0 in the equation x = 4 - y^2 - 4z^2:

0 = 4 - y^2 - 4(0^2)

y^2 = 4

y = ±2

Therefore, the y-intercepts are located at y = -2 and y = 2.

For the z-intercept, we set x = 0 and y = 0 in the equation x = 4 - y^2 - 4z^2:

0 = 4 - 0^2 - 4z^2

4z^2 = 4

z^2 = 1

z = ±1

Hence, the z-intercepts are located at z = -1 and z = 1.

b. The xy-trace is obtained by setting z = 0 in the equation x = 4 - y^2 - 4z^2:

x = 4 - y^2

This represents a parabola opening downward in the x-y plane.

The xz-trace is obtained by setting y = 0 in the equation x = 4 - y^2 - 4z^2:

x = 4 - 4z^2

This represents a hyperbola opening left and right in the x-z plane.

The yz-trace is obtained by setting x = 0 in the equation x = 4 - y^2 - 4z^2:

0 = 4 - y^2 - 4z^2

y^2 + 4z^2 = 4

This represents an ellipse in the y-z plane.

c. To sketch the graph of the surface, we can plot the intercepts and use them to guide the shape of the quadric surface. From the intercepts we found, the surface intersects the x-axis at x = 4, the y-axis at y = ±2, and the z-axis at z = ±1. The surface is symmetrical about the x-axis and opens downward in the x-y plane. It is also symmetrical about the y-z plane. The yz-trace forms an ellipse, while the xz-trace forms a hyperbola. Combining all these features, we can sketch the graph of the surface accordingly.

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Answer:

\(36\)

Step-by-step explanation:

Given

\(x^2 - 12x = 21\)

Required

Make a perfect square

First, get the coefficient (k) of x

\(k = -12\)

Divide by 2

\(\frac{k}{2} = \frac{-12}{2}\)

\(\frac{k}{2} = -6\)

Square this result:

\((\frac{k}{2})^2 = (-6)^2\)

\((\frac{k}{2})^2 = 36\)

Hence, 36 when added to the left-hand side makes it a perfect square trinomial

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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Answer:

An acute angle is less than 90°.

An obtuse angle is more than 90°.

Step-by-step explanation:

Sorry if wrong didn't really get the question I'm a little slow

Answer:

No solution

Step-by-step explanation:

Rewrite so  m  is on the left side of the inequality.

8 m − 4 ( 2 m + 5 ) > 46

Simplify  

8 m − 4 ( 2 m + 5 )

Apply the distributive property.

8 m − 4 ( 2 m ) − 4 ⋅ 5 > 46

Multiply  2 by  − 4  .

8 m − 8 m − 4 ⋅ 5 > 46

Multiply  − 4 by  5 .

8 m − 8 m − 20 > 46

Simplify by adding terms.

Subtract  8 m from 8m .

0 − 20 > 46 0 - 20 > 46

Subtract  20 from  0 .

− 20 > 46

Since  − 20 < 46

There are no solutions. No solution

(Hope this helps can I pls have brainlist (crown)☺️)

The amount of interest in 7 years will be $126.

To calculate the interest earned by Buddy after 7 years, we can use the formula for simple interest, which is given by:

I = Prt

Where I is the interest earned, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time period in years.

We are given that Buddy invests $600 in a savings account that pays 3% interest, which means that the annual interest rate r is 0.03. Therefore, we can plug these values into the formula and solve for I:

I = 600 x  0.03 x 7

I = $126

Therefore, Buddy will earn $126 in interest after 7 years.

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Answer:

5.5p-17.6

Step-by-step explanation:

-3.1p + 2(4.3p – 8.8)=-3.1p+8.6p-17.6=5.5p-17.6

Answer:

K = 15t + 19

E = 9t + 49

After 2 days, Evelyn is farther along.

Step-by-step explanation:

K = page Kayla is on

E = page Evelyn is on

t = number of days

K = 15t + 19

E = 9t + 49

After 2 days, t = 2.

K = 15 × 2 + 19 = 49

E = 9 × 2 + 49 = 67

After 2 days, Evelyn is farther along.

Using the equations written we can conclude that: after 2 days, Evelyn is farther along in the book, as she is on page 67, while Kayla is on page 49.

Let's first write the equations for Kayla and Evelyn's progress in terms of "t" days into the month which represents the situation:

For Kayla:

KK = 19 + 15t

For Evelyn:

EE = 49 + 9t

Now, let's find their progress after 2 days:

For Kayla (t = 2):

KK = 19 + 15 * 2 = 19 + 30 = 49

For Evelyn (t = 2):

EE = 49 + 9 * 2 = 49 + 18 = 67

2 days later, Evelyn has progressed to page 67, which is ahead of Kayla's position at page 49 in the book.

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To determine the number of miles Andrew can run in one hour, we need to know the rate at which he runs. From the given information, we know that Andrew can run ½ of a mile in 1 hour.

To calculate the number of miles Andrew can run in one hour, we divide the distance by the time:

Distance ÷ Time = Speed

In this case, the distance is ½ mile and the time is 1 hour. So, we have:

½ mile ÷ 1 hour = ½ mile/hour

Therefore, Andrew can run ½ mile in one hour.

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Answer: 61 apples

Step-by-step explanation:

Given:

1 apple

+2 apples = +10 minutes

1 hour = 60 minutes

60/10 = 6 x 2 = 12 apples/hr

12 x 5 = 60 apples for 5 hours

60 + 1 = 61 apples

I'm not in highschool but I did the math I think it's 18

Answer:

The Answer is D

Step-by-step explanation:

437-18.5=419.5

The algebra word problem method shows that Richard is 22 years old and Teo is 6 years old.

Algebra is used in our daily lives without us even recognizing it. Students can relate to and comprehend the significance of mathematics in the real world by solving algebraic word problems in worksheets.

Algebraic word problems usually comprise interpreting words into numbers, variables, their coefficients, and the use of appropriate arithmetic operations.

From the information given, we can the following system of equations as follows:

r + t = 28     --- (1)

r =  2t + 10   --- (2)

(2t + 10) + t = 28

3t + 10 = 28

3t = 28 - 10

3t = 18

t = 18/3

t = 6

From (1),  r + t = 28

r + 6 = 28

r = 28 - 6

r = 22

Therefore, we can conclude that Richard is 22 years old and Teo is 6 years old.

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Answer:

domain (-3,0,2)

range (3,6,9)

Step-by-step explanation:

the domain is all the numbers on the x-axis or the input side and the range is all the numbers on the y-axis side or the output