Simplify a polynomial: (3x–4y)²–(3x–4y)(3x+4y)

Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer:

function

Step-by-step explanation:

domain: -inf to +inf

range: -inf to +inf

Answer:

y=-4/3 + 2

Step-by-step explanation:

So first we need to find the slope which is rise over run or rise/run. We already know the slope is negative because it is slanted to the left \.

The equation should be in this form y = mx+ b

m = slope

b = y- intercept

The slope is -4/3

The y-intercept is 2

y= -4/3 + 2

Answer:

2(7) - 1/4 = 4 + 1/3x

x = 117/4

Step-by-step explanation:

solving an equation with one missing variable

step 1: multiply 2 * 7

ex: 14 - 1/4 = 4 + 1/3x

step 2: subtract 14 from 1/4

ex: 55/4 = 4 + 1/3x

step 3: subtract 4 from both sides of the equation

55/4 - 4 = 4 + 1/3x - 4   (39/4 = 1/3x)

step 4: divide both sides of the equation by 1/3

ex: 39/4 / 1/3 = 1/3x / 1/3   (x = 117/4 or x = 29 1/4)

step 5: to check your answer add the answer you got from the last equation which was 117/4 or 29 1/4 and input it into the original equation and get your final answer

ex: 2(7) - 1/4 = 4 + 1/3(117/4)

14 - 1/4 = 4 + 39/4

55/4 = 55/4 (if both sides of the equation are the same numbers like 55/4 = 55/4 then your answer is true)

Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

The completion of the table showing the different percentages of the days that Kimmimela and her foster brother fed the rabbits this year is as follows:

Person     Time (days)    Percentage

Kimimela         350             95.9%

Foster Brother   15                4.1%

A percentage is a mathematical expression of a number or ratio as a fraction of 100.

A percentage is often denoted with the percent sign, "%."

Most importantly, a percentage shows the relative value of a variable out of the hundredth parts of the class.

For instance, this question showed that Kimimela fed her rabbits 350 out of 365 days of this year. This implies that her foster brother fed the rabbits for 15 days (365 - 350).

Person     Time (days)    Percentage

Kimimela         350             95.9% (350/365 x 100)

Foster Brother   15                4.1% (15/365 x 100)

Total               365               100%

Thus, we can conclude that Kimimela fed the rabbits 96% of the days.

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Answer: p = 4.1

Step-by-step explanation:

Answer:

x=9

y=3

Step-by-step explanation:

since all three sides of an equlateral triangle are equal:

3x+y=30   then y=30-3x

4x-2y=30

4x-2(30-3x)=30

4x-60+6x=30

10x=90

x=9

3x+y=4x-2y

x=3y

y=3

Answer:

negative  

Step-by-step explanation:

Have an amazing day!

Hope this helps!

Answer:

0.37 rad m

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc length formula:

We have:

Finding the length of arc AB:

Answer:

Answer

5.0/5

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Answer:

): "x2" was replaced by "x^2". 4 more similar replacement(s).

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

x6 - x5 + x4 - x3 + x2 - x =

x • (x5 - x4 + x3 - x2 + x - 1)

2.2 Factor x5 - x4 + x3 - x2 + x - 1

Try to factor this 6-term polynomial into (2-term) • (3-term)

Begin by splitting the 6-term into two 3-term polynomials:

-x2 + x - 1 and x5 - x4 + x3

Next simplify each 3-term polynomial by pulling out like terms:

-1 • (x2 - x + 1) and x3 • (x2 - x + 1)

Note that the two simplified polynomials have x2 - x + 1 in common

Now adding the two simplified polynomials we get

(x3 - 1) • (x2 - x + 1)

If you mean x = 0.666…, then

10x = 6.666…

10x - x = 6.666… - 0.666…

9x = 6

x = 6/9 = 2/3

If you mean x = 0.060606…, then

100x = 6.060606…

100x - x = 6.060606… - 0.060606…

99x = 6

x = 6/99 = 2/33

Answer:

The conditions for a substance to float on liquid are given below:

\( \mathrm{Hope \: I \: helped!}\)

\( \mathrm{Best \: regards!}\)

2yz² - 2xy + y² = - [x³/(3z²) + 2z²/(3(1 - z²))] + C. This equation represents the integral curve of the given equation.

To find the integral curve of the given equation, 4dy(yz - x) - dx(xz - y) + dz(x²(x³ - z³))/(z³(1 - z²)) = 0, we will express it in terms of differentials and separate variables. By rearranging the equation and integrating both sides, we can obtain the solution for the integral curve.

The given equation, after rearranging, becomes 4dy(yz - x) - dx(xz - y) + dz(x²(x³ - z³))/(z³(1 - z²)) = 0. To find the integral curve, we'll express it in terms of differentials:

4(yz - x)dy - (xz - y)dx + (x²(x³ - z³))/(z³(1 - z²))dz = 0.

Now, we'll separate the variables:

4(yz - x)dy - (xz - y)dx = - (x²(x³ - z³))/(z³(1 - z²))dz.

Integrating both sides, we have:

∫[4(yz - x)dy - (xz - y)dx] = ∫[- (x²(x³ - z³))/(z³(1 - z²))dz].

Integrating each term separately, we obtain:

2yz² - 2xy + y² = - [x³/(3z²) + 2z²/(3(1 - z²))] + C.

Where C is the constant of integration. This equation represents the integral curve of the given equation.

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Answer:

75/4=3/100

Step-by-step explanation:

sinple this is on proportion

if you want crisscross the fraction

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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For every hour he works over 40 hours, he is paid an additional $7.50.

Ray’s error when he miscalculated his overtime pay is +$45.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

His normal pay is $15/h

150%/100 = 1.5

Multiply his normal pay by the rate in decimal form;

$15 X 1.5 = $22.5

His OT pay is $22.5/h.

Additional money = (OT pay) - (Normal pay)

= $22.5 - $15

= $7.5

Or $7.5 = $7.50

Thus, For every hour he works over 40 hours, he is paid an additional $7.50.

Ray actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.

Error = measured value - actual value.

Error = $145 -$100 =$45.

Since the value $145 is greater than his actual pay $100, we have to include a positive sign to the error $45.

Therefore, Error = +$45.

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The point in spherical coordinates is (2√17, π/3, π).

a) To convert the point from cylindrical coordinates to Cartesian coordinates, we use the following equations:

x = r * cos(theta)

y = r * sin(theta)

z = z

Given the cylindrical coordinates (r, theta, z) = (3, 4π/3, -4), we can substitute these values into the equations:

x = 3 * cos(4π/3)

y = 3 * sin(4π/3)

z = -4

Evaluating the trigonometric functions, we get:

x = 3 * cos(4π/3) = 3 * (-1/2) = -3/2

y = 3 * sin(4π/3) = 3 * (√3/2) = (3√3)/2

z = -4

Therefore, the point in Cartesian coordinates is (-3/2, (3√3)/2, -4).

b) To convert the point from cylindrical coordinates to spherical coordinates, we use the following equations:

r = √(x^2 + y^2 + z^2)

theta = atan2(y, x)

phi = acos(z / r)

Using the Cartesian coordinates (-3/2, (3√3)/2, -4), we can calculate the spherical coordinates:

r = √((-3/2)^2 + ((3√3)/2)^2 + (-4)^2) = √(9/4 + 27/4 + 16) = √(16 + 36 + 16) = √(68) = 2√17

theta = atan2((3√3)/2, -3/2) = atan2(3√3, -3) = π/3 (since the angle is in the second quadrant)

phi = acos(-4 / (2√17)) = acos(-2√17 / √17) = acos(-2) = π

Therefore, the point in spherical coordinates is (2√17, π/3, π).

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Answer:

The equation of a line in slope-intercept form is y=mx+b. “m” is the slope and “b” is the y-intercept. To find the slope, take two points and plug them into the slope formula. The slope formula is Y2-Y1/X2-X1.

You can use any two points on the graph but I will use (3,-2) and (6,-3).

-3-(-2)/6-3

-3+2/3

-1/3

The slope is -1/3. To find the y-intercept, look the y-value where the line touches the y-axis. In this graph, the line touches the y-axis at (0,-1).

So, the equation of the line in slope-intercept form is y=-1/3-1.

Hope this helps! :)

The calculated radius of the cylidner when approximated is 8.0 meters

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, h is the height, and π is a constant approximately equal to 3.14.

To find the radius of a cylinder with volume 1607 m³ and height 8 m, we can rearrange the formula as:

r^2 = V / (πh)

Substituting the given values, we get:

r^2 = 1607 / (3.14 x 8)

r^2 ≈ 63.973

Taking the square root of both sides, we get:

r ≈ 8.0

Therefore, the radius of the cylinder is approximately 8.0meters.

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Answer:

$3.45

Step-by-step explanation:

cost of grapes x quantity

Answer:

8.20

Step-by-step explanation:

4x0.75=3

3+4=7

0.6=60%

60% of 0.75= 0.45

0.75+0.45=1.20

7+1.20=8.20

Answer: 4 times 3 equals 12, and that plus 6 is 18.  18 divided by 5 is not 4, sorry if i interpreted your statement wrong, but that is incorrect, or my brain is melting. Help.

Step-by-step explanation:

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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Answer:

less

Step-by-step explanation:

Answer:

less than the answer is less then

The odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test if the probability is 0.20

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents impossibility (an event that cannot occur) and 1 represents certainty (an event that is certain to occur).

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 0.5 (or 1/2) because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

The odds of an event happening are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. Mathematically, odds can be expressed as:

odds = P(event happening) / P(event not happening)

In this case, the probability of the employee passing the test is 0.20, so the probability of the employee not passing the test is 0.80 (since the sum of probabilities of all possible outcomes must be 1).

Therefore, the odds of the employee passing the test can be calculated as:

odds = 0.20 / 0.80 = 0.25

So the odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test (since 0.25 can be written as a fraction of 1/4).

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Answer:

Step-by-step explanation:

17, is the answer.

The area of a regular octagon with sides 1/3 the length of sides of the larger octagon is 173.82 ft sq.

The area of a polygon = n side^2 / (4 tan(180/n))

where "n" is the number of sides

To calculate area for side = 2

area = 8 x 2^2 / (4  tan(180/8))

area = 32 / (4  tan(22.5))

area = 32 / 4 x 0.41421

area = 19.3138746047

To calculate area for side = 6

area = 8*6^2 / (4 * tan(180/8))

area = 288 / 1.65684

area = 173.824871442

173.824871442 / 19.3138746047 =  9

So, the area would be 9 times larger.

Therefore, if we increase the side length is increased by 1/3, then the area increases by 1/9.

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Answer: hope it helps

Step-by-step explanation:The balloon will not reach 2,500 feet after 4 minutes.

Step-by-step explanation:

The equation of the line in the point-slope form is

A hot air balloon in flight begins to ascend at a steady rate of 120 feet per minute, then the slope is

After  minutes, the balloon is at an altitude of  feet. This means, the line passes through the point (1.5, 2,150).

Substitute the slope and point coordinates into the equation:

We know that after 3 minutes, the balloon is at an altitude of 2,330 feet. Check this:

Now, find the height after 4 minutes:

Thus, the balloon will reach only 2,450 feet after 4 minutes.

The area to the right of the z-score 0.0833 is approximately 0.4671

To calculate the proportion of women with hypertension (diastolic blood pressure greater than 90 mmHg), we can use the standard normal distribution.

Given:

Mean (μ) = 80.2 mmHg

Standard deviation (σ) = 9.6 mmHg

We need to calculate the z-score for the threshold value of 90 mmHg, and then find the area under the standard normal curve beyond that z-score.

The z-score formula is:

z = (x - μ) / σ

Plugging in the values:

z = (90 - 80.2) / 9.6

z = 0.8 / 9.6

z ≈ 0.0833

Using a standard normal distribution table or a calculator, we can find the area to the right of this z-score, which represents the proportion of women with diastolic blood pressure greater than 90 mmHg.

The area to the right of the z-score 0.0833 is approximately 0.4671.

Therefore, approximately 0.4671 (or 46.71%) of women have hypertension (diastolic blood pressure greater than 90 mmHg).

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