Tyler takes a piece of plywood that is 72 centimeters long and uses a table saw to make a 78-
centimeter cut from corner to opposite corner. What was the width of the piece of plywood?

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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Answer:

tan 50 =

\( \frac{opposite}{adj} \)

1.1918 = x/10

= 1.19×10 = x

length = 11.9

The fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

Let w be the weight of the bag in pounds, and let x be the weight over the limit.

The first airline charges 28 + 7x dollars for the bag, and the second airline charges 14 + 9x dollars for the bag.

Since the fees are the same with both airlines, we can set these two expressions equal to each other:

28 + 7x = 14 + 9x

Solving for x, we find that x = 7.

Substituting this value back into either of the original expressions, we find that the fee with each airline is 28 + 7x = 35.

Therefore, the fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

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Answer:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Exact Form:

x

=

25

+

√

130

3

,

25

−

√

130

3

Decimal Form:

x

=

12.13391808

…

,

4.53274858

…

Step-by-step explanation:

Answer:

x=\frac{25-\sqrt{130}}{3}

Step-by-step explanation:

x_{1,\:2}=\frac{-100\pm \sqrt{100^2-4\left(-6\right)\left(-330\right)}}{2\left(-6\right)}

x_{1,\:2}=\frac{-100\pm \:4\sqrt{130}}{2\left(-6\right)}

x_1=\frac{-100+4\sqrt{130}}{2\left(-6\right)},\:x_2=\frac{-100-4\sqrt{130}}{2\left(-6\right)}

x=\frac{25-\sqrt{130}}{3},\:x=\frac{25+\sqrt{130}}{3}

The letter on the number line that represents the given number is B.

A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.

Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.

Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.

Therefore, the letter on the number line that represents 1 85/100 is B.

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Answer:

80

Step-by-step explanation:

\( \sin(80) = \cos(10) \\ 90 - x = 10 \\ x = 80\)

Answer:

3.1567 * 10^-4 miles

Step-by-step explanation:

1 ft = 1.894 * 10^-4 miles , so

1 inch = 1.894 * 10^-4 / 12  miles

= 0.15783 * 10^-4

= 1.5783* 10^-5 miles  ( in scientific form).

Multiplying this by 20 we get

31.567 * 10^-5

= 3.1567 * 10^-4 miles.

The value of CPI will be 178.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Now,

Since, In 1983, a pair of jeans cost $66.35.

And, A pair of jeans costs $118.10 today.

Hence, The value of CPI will be;

CPI = 118.10 × 100 / 66.35

      = 11810 / 66.35

       = 178

Thus, The value of CPI will be 178.

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The length of the line segment AB is 11/2 mm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.

Therefore, AC/AB = EC/ED.

22/AB = 44/11.

2/AB = 4/11.

4AB = 22.

AB = 11/2.

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Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).

To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.

The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.

Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.

The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).

The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).

The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).

The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).

Therefore, the total number of ways the lights can be arranged on the string is:

14! / (2! * 4! * 5! * 2!)

You can calculate this expression to find the specific number of arrangements.

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Answer:

1/2 gal

Step-by-step explanation:

A. The acceleration due to gravity is represented by a negative number because it acts in the opposite direction of the upward motion of the projectile. It pulls the object downward, causing it to decelerate and eventually fall back to the ground.

B. The formula to represent the height of a projectile at any given time t is: h = (0.5 * a * t^2) + (v * t) + h0, where h is the height, a is the acceleration (-32 ft/s^2), t is the time, v is the initial velocity, and h0 is the initial height.

C. To find the time when the projectile is at a height of 320 feet, we can set h = 320 in the formula and solve for t. 320 = (0.5 * -32 * t^2) + (192 * t) + 0. Solve the quadratic equation to find the value of t.

D. To find the time it takes for the object to reach its maximum height, we need to find the time when the velocity becomes zero. Set v = 0 in the formula and solve for t. Then substitute the value of t into the formula to find the maximum height.

E. To find the time when the projectile lands on the ground, we need to find the time when the height becomes zero. Set h = 0 in the formula and solve for t.

F. If the initial velocity stays the same but the height the projectile is launched from changes, the amount of time it takes for the projectile to reach its maximum height will remain the same. However, the maximum height will change based on the initial height.

G. To increase the amount of time it takes for the projectile to return to the ground by one second, we need to find the height that corresponds to that additional time. Set the time to (t + 1) in the formula and solve for h. Subtract the initial height from the result to find the height above the ground from which the projectile needs to be launched.

Comment if you need more help!

~~~Harsha~~~

Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

9514 1404 393

Answer:

Step-by-step explanation:

a) The 36000 -23000 = 13000 difference in salary is being made up at the rate of 3000 -2000 = 1000 per year. It will take 13000/1000 = 13 years for the salaries to be the same.

__

b) After 13 years, the salary will be ...

  23000 +13(3000) = 23000 +39000 = 62,000 . . . dollars

  36000 +13(2000) = 36000 +26000 = 62,000 . . . dollars

Answer:

after the first company, her salary would be 48000 in 5 years

after the second company, her salary would be 48000 in 4 years

Step-by-step explanation:

Answer:

  4372 cm³

Step-by-step explanation:

You want the volume of a symmetrical right rectangular pyramid whose lateral faces make angles of 73° and 54° with the base, and whose short side is 15 cm.

The height of the pyramid can be found using the tangent relation. The distance from the center to the steep face is (15 cm)/2 = 7.5 cm. The height will satisfy ...

  Tan = Opposite/Adjacent

  tan(73°) = height/(7.5 cm)

  height = (7.5 cm)tan(73°) ≈ 24.5314 cm

A similar relation can be used to find the longer side length:

  tan(54°) = height/(side/2)

  side = 2·height/tan(54°) = (15 cm)tan(73°)/tan(54°) ≈ 35.6462 cm

The volume is ...

  V = 1/3Bh

  V = 1/3(15 cm)(35.6462 cm)(24.5314 cm) ≈ 4372 cm³

The volume of the pyramid is about 4372 cm³.

<95141404393>

Answer:

x+v

Step-by-step explanation:

brainlest?

The only positive integers n that satisfy the condition for every good coloring of a sphere with n great circles, where the sum of the areas of black regions is equal to the sum of the areas of white regions, are powers of 2.

Let's consider the case where n is not a power of 2. If n has an odd prime factor p, then the coloring of the sphere can be arranged in a way that creates a contradiction. We can divide the sphere into p equal parts using p great circles. In each part, we can color half of it black and the other half white. Since p is odd, we will have a larger number of black regions than white regions, leading to an imbalance in their areas.

On the other hand, if n is a power of 2, we can prove by induction that it satisfies the condition. For n = 2, we can divide the sphere into two equal hemispheres and color them differently. Now, assume that for some k, the condition holds for n = \(2^k\). To prove it for n = \(2^{(k+1)}\), we can take the sphere divided by \(2^k\) great circles and replicate it k times, creating a larger sphere divided by \(2^{(k+1)}\) great circles. By alternating the colors of the replicated regions, we ensure that adjacent regions have different colors, and the areas of black and white regions remain balanced.

Hence, the only positive integers n that satisfy the condition are powers of 2.

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Answer & Step-by-step explanation:

% = \(\frac{75}{150}\)(100)

% = 0.5(100) = 50%

Answer:

70 degrees

Step-by-step explanation:

The angle opposite x and x itself are vertical angles, meaning that they have the same angle measure. Since the sum of the interior angles of a triangle is 180 degrees:

x+55+55=180

x+110=180

x=180-110=70

Hope this helps!

Answer:

532.5

Step-by-step explanation:

I really hope this answer helps you!!

Answer:

Addition property

Adding 5 to the each side makes it

x -5 + 5 = 15 +5

x = 20

Answer:

See below.

Step-by-step explanation:

Della is correct. 1, in decimals, is 1.00, or 100. So, if the decimal is 1.4(1.40), it is equal to 140%.

-hope it helps

Della is correct here 1.4 is equivalent to 140%.

Percentage is the value per hundredth.If we have give 10% this means per hundredth it is 10 and we have to calculate for the amount or something that is given.

According to the given question

robbie says 1.4 is equivalent to 14% della says 1.4 is equivalent to 140%

When we are given some value in fraction or in decimals to convert them into percentage we multiply the given fraction or decimals by 100.

∴ 1.4 is equivalent to (1.4 × 100)% which is

= 140 % so della is correct here.

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Answer:

See below.

Step-by-step explanation:

Part A:

y = -3x + 2

y = -3x + 10

y = -3x

Part B:

y =  2x + 5

y = -3x + 5

y = -2x + 5

Part C:

y = -3x + 5

There can only be one line with this slope and intercept because the expression is very simple.  There are only two pieces of information that define a straight line:  slope and intercept.  There is nothing else that can be altered to impact the line.  

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

a= 12

Step-by-step explanation:

Use pythagorean theorem

a^2 + b^2 = c^2 where c is the hypotenuse

so 9^2 + a^2 = 15^2

81 + a^2 = 225

a^2 = 144

square root both sides to get a = 12

Answer:

1/6

Step-by-step explanation:

If you roll a 1 then on the second roll (for a fair 6 sided die) the probability that the second roll is a 1 is 1/6 (assuming independence.

Answer:

1/6

Step-by-step explanation:

If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes ( A standard die has 6 Number { 1,2,3,4,5,6 } ) , the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.

[RevyBreeze]

Answer:

1 and 7/8 in two hours

Step-by-step explanation:

Answer:

the answer to that would be 0.

Step-by-step explanation:

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

Explanation:

The dot plot is of these values

3, 4, 5, 5, 5, 5, 5, 5, 6, 7

The unique values are 3,4,5,6,7 where the '5' shows up six times while the other values only show up exactly one time.

Adding up those values gets us

3 + 4 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 7 = 50

Then we divide by 10 because there are 10 items in the original list. So that leads to the arithmetic mean 50/10 = 5

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

The next step is to subtract the mean from each data value

We'll apply absolute value to ensure the results are never negative. So this is where the "absolute" comes from in "mean absolute deviation". The "deviation" portion is another way of saying distance. Specifically, we're looking for the distance from the mean.

We then have the new set {2,1,0,0,0,0,0,0,1,2} where there are 6 copies of "0" in the middle. We also have two copies of "1" and "2" each.

Let's find the arithmetic mean of this new set

Add the values: 2+1+0+0+0+0+0+0+1+2 = 6

Divide by 10 to get: 6/10 = 0.6 which is the final answer

This represents the average absolute value distance each value is from the mean.