A piece of wood is cut into three pieces in the ratio 6: 5: 2. If the log is 61/2 feet long, what will be the length of the longest piece

Explanation:

The general sine equation is

y = A*sin(B(x-C)) + D

where the D variable directly determines the midline. In this case, D = -3, so that corresponds to a midline of y = -3

The sine curve oscillates going up and down, passing through this middle horizontal line infinitely many times. See the graph below.

Answer:

A) y = –3

Step-by-step explanation:I took the test

Answer:

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

10 machines means that [tex]n = 10[/tex]

2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]

Seven are selected, which means that [tex]n = 7[/tex]

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]

0.0667 = 6.67% probability that all seven machines are nondefective.

Set the proportion as shown:

2660/4.75 = x/1

Cross multiply:

4.75x = 2660

Divide both sides by 4.75

x = 560

Answer: 560 miles per hour

Answer:

Categorical or Continuous.

Step-by-step explanation:

Because the red appears in each colours (continuous)

Answer:

C

Step-by-step explanation:

Convert the equation into slope intercept form : y=mx+b

2y=x+4

y=1/2x + 2

The m is the slope and the b is the y intercept

In this equation, the slope is 1/2 and the y intercept is 2

The only graph with y intercept 2 is C

Answer:

3 seconds

Step-by-step explanation:

First, let's calculate the approximate speed of light.

3 · 10^14 = 3 · 100,000,000,000,000

              = 300,000,000,000,000

Approximately, light travels 300,000,000,000,000 centimeters per second.

Now, let's simplify 9x10^14.

9 · 10^14 = 9 · 100,000,000,000,000

              = 900,000,000,000,000

To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.

900,000,000,000,000/300,000,000,000,000 = 3

Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.

It will take 3 seconds to cover the distance of 9×10¹⁴ cm.

We use the scientific notation of numbers to write very large numbers in compact form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given the speed of light s approximately 3×10¹⁴ cm/sec.

∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.

We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.

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Answer:

x=7

Step-by-step explanation:

AB=BC[ because two sides of isosceles triangles are equal  ]

or, 2x+9=5x-12

or,9+12=5x-2x

or,21=3x

or,x= 21/3

therefore, x=3

Answer:

44.85

Step-by-step explanation:

There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85

Answer:

n=1

Step-by-step explanation:

-36 = 6(2-8n)

-36=12-48n

-36-12=-48n

-48=-48n

n=1

Answer:

D. 130

Step-by-step explanation:

The lines are tangent to the circle therefore 90º which makes 65º + 25º.  The small triangle with C is iso so the angle of C would be 130 and equivalent to x

Answer:

[tex]D.\ \ 130[/tex]

Step-by-step explanation:

1. Approach

Refer to the attached diagram of the figure for further explanation. In this problem, one is asked to solve for the degree measure of arc (x). The easiest method to do so is to use the triangle (CAB). One can solve for the measure of angle (<CBA) by using the tangent to radius theorem. Then one can solve for the measure of angle (CAB) by using the base angles theorem. Then one can use the sum of angles in a triangle theorem to solve for angle (<BCA). Finally, one can use the central angles theorem to solve for the arc (x).

2. Find the measure of angles in the triangle

A. Find the measure of angle (<CBE)

As per the given image, lines (BE) and (AE) are tangent. This means that they intersect the circle at exactly one point. A radius is the distance from the center of a circle to the circumference or outer edge of a circle. All radii in a single circle are congruent. The radius of tangent theorem states that, when a tangent intersects a circle at a point of tangency, and a radius also intersects the point of tangency, the angle between the radius and the tangent is a right angle. One can apply this here by stating the following:

[tex]m<CBE = 90[/tex]

Express angle (<CBE) as the sum of two other angles:

[tex]m<CBE = m<CBA + m<ABE[/tex]

Substitute with the given and found information:

[tex]m<CBE = m<CBA + m<ABE[/tex]

[tex]90 = m<CBA + 65[/tex]

Inverse operations,

[tex]90 = m<CBA + 65[/tex]

[tex]25= m<CBA[/tex]

B. FInd the measure of angle (<CAB)

As stated above all radii in a single circle are congruent. This means that lines (CB) and (CA) are equal. Therefore, the triangle (CAB) is an isosceles triangle. One property of an isosceles triangle is the base angles theorem, this theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. Applying this theorem to the given problem, one can state the following:

[tex]m<CBA = m<CAB = 25[/tex]

C. Find the measure of angle (<ACB)

The sum of angles in any triangle is (180) degrees. One can apply this theorem here to the given triangle by adding up all of the angles and setting the result equal to (180) degrees. This is shown in the following equation:

[tex]m<CAB + m<CBA + m<ACB = 180[/tex]

Substitute,

[tex]m<CAB + m<CBA + m<ACB = 180[/tex]

[tex]25 + 25 + m<ACB = 180[/tex]

Simplify,

[tex]25 + 25 + m<ACB = 180[/tex]

[tex]50 + m<ACB = 180[/tex]

Inverse operations,

[tex]50 + m<ACB = 180[/tex]

[tex]m<ACB = 130[/tex]

3. Find the measure of arc (x)

The central angles theorem states that when an angle has its vertex on the center of the circle, its angle measure is equivalent to the measure of the surrounding arc. Thus, one apply this theorem here by stating the following:

[tex]m<ACB = (x)\\130 = x[/tex]

Answer:57*91547

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are ten sides on this die. As stated in your question, there are five even numbers and five odd numbers. If we take the amount of even numbers over the total, you get 5/10, which simplifies to 1/2.

The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the data set be S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ​}

So , the number of elements in the data set = 10 elements

Now , in order to get an even number when dolling the dice ,

The set of possible outcomes P = { 2 , 4 , 6 , 8 , 10 }

The number of elements in the data set P of outcomes = 5 elements

So , the probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) =
number of elements in the data set P of outcomes / number of elements in the data set

The probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) = 5 / 10

The probability P ( x ) = 1/2

                                   = 0.5

Hence , The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5

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9514 1404 393

Answer:

Step-by-step explanation:

When looking for extremes, one must consider both the turning points and the ends of the interval. Here, there is a relative minimum at x=7, and a relative maximum at x=3. However, the values at the ends of the interval are more extreme than these.

The absolute minimum on the interval is 2 at x=0.

The absolute maximum on the interval is 10 at x=10.

Answer:

1. 3-5

2. 5-3

3. 3-5

4. 5-3

Step-by-step explanation:

This is simple! Just get rid of the parenthesis for each of the expressions shown.

3 + (-5)

the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes

3 - 5

Now do the same for the rest!

For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]

Hope this helps !!

-Ketifa

Answer:

2x-1 = 5x-14

Step-by-step explanation:

5(2x−1) = 5(5x−14)

Divide each side by 5

5/5(2x−1) = 5/5(5x−14)

2x-1 = 5x-14

Answer:

A.

Step-by-step explanation:

5(2x−1) = 5(5x−14)

10x - 5 = 25x - 70

65 = 15x

x = 13/3.

Take Option A.

2x - 1 = 5x - 14

3x = 13

x = 13/3 so its this one.

B: 10x - 5 = 5x - 14

5x = -9

x = -9/5 so NOT B.

C. simplifies to x = 3. so NOT C.

[tex] {a}^{m} \times {b}^{m} = ( {ab)}^{m} [/tex]

please mark this answer as brainlist

Answer:

All have exactly one solution

Step-by-step explanation:

a) -13x + 12 = 13x - 13

   +13x         +13x

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

          12 = 26x - 13

         +13           +13

         -------------------

           25 = 26x

          -----   ------

           26     26

          25/26 = x

b) 12x + 12 = 13x - 12

   -12x          -12x

  -----------------------

          12 = x - 12

        +12       +12

        -----------------

            24 = x

c) 12x + 12 = 13x + 12

  -12x          -12x

 -----------------------------

           12 = x + 12

           0 = x

d) -13x + 12 = 13x + 13

   +13x           +13x

 -----------------------------

         12 = 26x + 13

        -13             -13

      -----------------------

          -1  = 26x

          ---      -----

          26       26

          -1/26 = x

The values of a, b, c are obtained from the given equation, by equation

in the form in which it is equal to 0.

The correct substitution of the values a, b, and c from the equation -2 = -x + x² - 4 is the option;

Given:

The quadratic formula is presented as follows;

[tex]x = \mathbf{ \dfrac{-b \pm \sqrt{b^2 - 4 \cdot a \cdot c} }{2 \cdot a}}[/tex]

The given equation is presented as follows;

-2 = -x + x² - 4

Which gives;

0 = -x + x² - 4 + 2 = -x + x² - 2

-x + x² - 2 = 0

Therefore, we have;

The correct option is therefore;

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9514 1404 393

Answer:

  (x, y) ⇒ (x +(-1), y +(-1))

Step-by-step explanation:

Reflection over the y-axis is the transformation ...

  (x, y) ⇒ (-x, y)

After that reflection, the figure is translated left 1 and down 1. That transformation is ...

  (x, y) ⇒ (x -1, y -1)

_____

Additional comment

The composition of the two transformations is ...

  (x, y) ⇒( -x -1, y -1)

Answer: x-1, y-1

Step-by-step explanation:

Answer:

The correct answer is "Test 20%, Service 10%".

Step-by-step explanation:

As we know,

The coefficient of variation (CV) is:

⇒ [tex]CV=\frac{Standard \ deviation}{Mean}\times 100[/tex]

Now,

CV of test will be:

= [tex]\frac{40}{200}\times 100[/tex]

= [tex]20[/tex] (%)

CV of service will be:

= [tex]\frac{2}{20}\times 100[/tex]

= [tex]10[/tex] (%)

Step-by-step explanation:

-4b-24-2b+8b2

8b2-6b-24=0

Answer:

x=−16/3 or x=2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x2+10x−8=24

Step 2: Subtract 24 from both sides.

3x2+10x−8−24=24−24

3x2+10x−32=0

Step 3: Factor left side of equation.

(3x+16)(x−2)=0

Step 4: Set factors equal to 0.

3x+16=0 or x−2=0

Answer:

They will hike 16% of the trail in Georgia.

Step-by-step explanation:

We have that:

The hiking trail is of 2600 miles.

416 of those miles are in Georgia?

What percent of the trail will they hike?

Georgia distance multiplied by 100% and divided by the total distance. So

416*100%/2600 = 16%

They will hike 16% of the trail in Georgia.

Answer:

The standard error of the estimated difference is of 0.0313.

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Brand A:

33 out of 197, so:

[tex]p_A = \frac{33}{197} = 0.1675[/tex]

[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]

Brand B:

25 out of 290, so:

[tex]p_B = \frac{25}{290} = 0.0862[/tex]

[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]

What would be the standard error of the estimated difference?

[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]

The standard error of the estimated difference is of 0.0313.

Answer:

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use.

At the null hypothesis, we test that at least 28% do not fail, that is:

[tex]H_0: p \geq 0.28[/tex]

At the alternative hypothesis, we test if the proportion is of less than 28%, that is:

[tex]H_1: p < 0.28[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.28 is tested at the null hypothesis:

This means that [tex]\mu = 0.28, \sigma = \sqrt{0.28*0.72}[/tex]

Sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use.

This means that [tex]n = 1800, X = 0.25[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.25 - 0.28}{\frac{\sqrt{0.28*0.72}}{\sqrt{1800}}}[/tex]

[tex]z = -2.83[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.25, which is the p-value of Z = -2.83.

Looking at the z-table, z = -2.83 has a p-value of 0.0023.

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Answer:

x-1/2x-3

Step-by-step explanation:

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