When a ribbon is cut into 3 equal pieces,each piece is _______ m long (correct to 2 decimal places).
​

Step-by-step explanation:

y=-3/4 ÷ -4/3

y=+9/16‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌

Answer:

So we have this equation:

\(\frac{-4}{3y}=\frac{-3}{4}\)

We can multiply both sides by 4 and 3y:

\(\frac{-4*4*3y}{3y}=\frac{-3*4*3y}{4}\)

\(-4*4=-3*3y\)

\(-16 = -9y\)

Now we divide both sides by 9:

\(\frac{-16}{-9}=y\)

And we can remove the minus signs:

\(\frac{16}{9}=y\)

If you mean \(\frac{-4}{3}y=\frac{-3}{4}\):

\(-4y*4=-3*3\)

\(-16y = -9\)

\(y=\frac{9}{16}\)

Answer:

The equation is;

y = -2x - 3

Step-by-step explanation:

If two lines are parallel, then they have an equal value of slope

Mathematically we can generally have the equation of a line written as;

y = mx + c

where m

is slope and c is the y-intercept

In the case of the equation given, the slope of the line is -2

So technically, we want to get the equation of a line that has a slope of -2 and it passes through (2,-7)

The point-slope form can be written as;

y-y1 = m(x-x1)

So the equation we want to get is;

y-(-7) = -2(x-2)

y + 7 = -2x + 4

y = -2x + 4 - 7

y = -2x - 3

Answer:

4x² -4xy -4y -4

Step-by-step explanation:

\(\boxed{ {a}^{2} - {b}^{2} = (a + b)(a - b)}\)

In this case, a= 2x -y and b= y +2.

(2x -y)² -(y +2)²

= (2x -y +y +2)[2x -y -(y +2)]

= (2x +2)(2x -y -y -2)

= (2x +2)(2x -2y -2)

= 2x(2x) +2x(-2y) +2x(-2) +2(2x) +2(-2y) +2(-2) (expand)

= 4x² -4xy -4x +4x -4y -4

= 4x² -4xy -4y -4

Alternatively, start by expanding the brackets.

\(\boxed{(a - b)^{2} = {a}^{2} - 2ab \: + {b}^{2} }\)

\(\boxed{(a + b)^{2} = {a}^{2} + 2ab \: + {b}^{2} }\)

(2x -y)² -(y +2)²

= 4x² -4xy +y² -(y² +4y +4)

= 4x² -4xy +y² -y² -4y -4 (expand)

= 4x² -4xy -4y -4 (simplify)

Answer:

angle ODC=30°

Step-by-step explanation:

Parallel to the line now draw another line PQ

Answer:

87.5% increase

Step-by-step explanation:

75 - 40 = 35

Find what percentage 35 is of 40, and you can do so by dividing.

35 ÷ 40 = 0.875

0.875 = 87.5%

Answer:

-5,2

Step-by-step explanation:

it literally represents LM and Shows it on the graph

The crucial value (z) relies on the desired level of confidence and is predicated on a normal distribution when creating a confidence interval for a proportion (p) with a confidence level of 93%.

A 93% confidence level in this instance translates to an alpha level of 0.07 (1 - 0.93 = 0.07) that is split evenly between the two tails. In the usual normal distribution table, we search for the value that falls within the range of 0.07 to find the proper z-value. A 93% confidence level corresponds to a z-value of roughly 1.81. The confidence interval for the proportion p may be calculated using this number and provides a range where the genuine proportion is like to fall.

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The value of x is x = 9/4. The equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4

The equation 2xc = d and 2x + 1 = 9 are similar in that they are both linear equations and involve the variable x.

However, they are different in that they have different constants and coefficients.

How to use 2xc = d to solve 2x + 1 = 9? To use 2xc = d to solve 2x + 1 = 9, you first need to rewrite 2x + 1 = 9 in the form 2xc = d.

To do this, you need to isolate x on one side of the equation. 2x + 1 = 9

Subtract 1 from both sides2x = 8. Divide both sides by 2x = 4Now, we can write 2x + 1 = 9 as 2x * 1/2 = 9/2.

Therefore, we can see that this equation is similar to 2xc = d, where c = 1/2 and d = 9/2.

We can use this relationship to solve for x in the equation 2xc = d as follows: 2xc = d2x * 1/2 = 9/22x = 9/2 * 2x = 9/4 Therefore, x = 9/4.

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Terms in this set (8)

Slope. y2 - y1 / x2 - x1 = slope.

Slope Intercept form. y = mx + b.

Point slope form. y - y1 = m ( x - x1)

Standard Form. Ax + By = C.

x - axis. The horizontal line on a graph.

y - axis. The vertical line on a graph.

X - intercept. The point on a line that intercepts on the x axis.

Y - intercept.

The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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When X=3 a polynomial has a value of 61 and when X=3 a value of 143.

Given that,

Let p(x)=3x²−4x²+7x−5 is our polynomial.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Substitute x=3 in above expression,

∴p(3)=3(3) 3−4(3) 2 +7(3)−5

=3(27)−4(9)+21−5

=81−36+21−5

=61

Now,

p(−3)=3(−3)

3 −4(−3) 2 +7(−3)−5

=3(−27)−4(9)−21−5

=−81−36−21−5

=−143

So, value of polynomial when X=3 is 61 and when x=−3 is −143

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Answer:

Step-by-step explanation:

The correct answer is (a) there is enough evidence to conclude that age and drink preference is dependent.

Using the formula for the chi-square test of independence, we can calculate the test statistic as:

X² = Σ (O-E)^2 / E

Performing this calculation on the given data, we get:

X² = (50-62.5)²/62.5 + (100-87.5)²/87.5 + (200-250)²/250 + (200-200)²/200 + (50-50)²/50 + (200-150)²/150 + (50-37.5)²/37.5 + (150-162.5)²/162.5 + (200-250)²/250 + (50-50)²/50 = 34

Using a chi-square distribution table with (2-1)*(4-1)=3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated test statistic of 34 is greater than the critical value of 7.815, we can reject the null hypothesis of independence and conclude that there is enough evidence to support the alternative hypothesis that age and drink preference are dependent.

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To solve for x and y in this problem, we need to use the formulas for arithmetic and geometric sequences.

For the arithmetic sequence, we know that the difference between each term is the same. Let's call this difference "d". So we have:

-8 + d = x
x + d = y
y + d = 72

For the geometric sequence, we know that the ratio between each term is the same. Let's call this ratio "r". So we have:

x * r = y
y * r = 72

Now we can use these equations to solve for x and y.

First, we'll use the arithmetic sequence equations to find the value of "d". We can subtract the first equation from the second equation to get:

d = y - x

We can then substitute this into the third equation to get:

y + (y - x) = 72

Simplifying this, we get:

2y - x = 72

Now we can use the geometric sequence equations to find the value of "r". We can divide the second equation by the first equation to get:

r = y/x

We can then substitute this into the first equation to get:

x * (y/x) = y

Simplifying this, we get:

y = x^2

Now we have two equations for "y", so we can substitute one into the other to get an equation in terms of "x" only:

2x^2 - x = 72

Solving this quadratic equation, we get:

x = -8 or x = 9

We can then substitute each of these values back into the equation y = x^2 to get:

y = 64 or y = 81

So the solutions are:

x = -8, y = 64
x = 9, y = 81

Therefore, the first three terms of the sequence are -8, -8+17=9, 9+17=26 and the second, third, and fourth terms are 9, 26, 72.
In an arithmetic sequence, the difference between consecutive terms is constant. In a geometric sequence, the ratio between consecutive terms is constant.

Given the arithmetic sequence: -8, x, y, the difference between consecutive terms is constant, so we can say that x - (-8) = y - x. Simplifying, we get x + 8 = y - x, and then 2x = y - 8 (Equation 1).

Now, considering the geometric sequence: x, y, 72, the ratio between consecutive terms is constant. Therefore, y/x = 72/y. By cross-multiplying, we obtain y^2 = 72x (Equation 2).

To determine x and y, we can solve this system of equations. Using Equation 1, y = 2x + 8. Substitute this expression for y in Equation 2:

(2x + 8)^2 = 72x
4x^2 + 32x + 64 = 72x
4x^2 - 40x + 64 = 0
x^2 - 10x + 16 = 0
(x - 8)(x - 2) = 0

From this quadratic equation, we have two possible values for x: x = 8 or x = 2.

If x = 8, then y = 2x + 8 = 24. This would result in the geometric sequence 8, 24, 72, which has a constant ratio of 3.

If x = 2, then y = 2x + 8 = 12. This would result in the geometric sequence 2, 12, 72, which has a constant ratio of 6.

Both solutions are valid, so we have two possible sets of values for x and y: x = 8, y = 24 or x = 2, y = 12.

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The solutions for x and y are: 1. x = 2, y = 12 and

2. x = 8, y = 24

To determine the values of x and y in the sequence -8, x, y, 72, analyze the information given.

First, consider the arithmetic sequence formed by the first three terms: -8, x, y. In an arithmetic sequence, the common difference between consecutive terms is constant.

Therefore, set up the following equation:

x - (-8) = y - x

Simplifying the equation, we have:

x + 8 = y - x

2x + 8 = y

Next, given that the second, third, and fourth terms form a geometric sequence: x, y, 72. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio.

Express this relationship using the following equation:

y / x = 72 / y

Cross-multiplying, we get:

y² = 72x

Now, we have two equations:

2x + 8 = y (Equation 1)

y² = 72x (Equation 2)

To solve for x and y, we'll substitute Equation 1 into Equation 2:

(2x + 8)² = 72x

Expanding and simplifying:

4x² + 32x + 64 = 72x

Rearranging the terms:

4x² + 32x - 72x + 64 = 0

4x² - 40x + 64 = 0

Dividing the entire equation by 4:

x² - 10x + 16 = 0

Factoring the quadratic equation, we have:

(x - 2)(x - 8) = 0

Setting each factor equal to zero and solving for x, we get:

x - 2 = 0 -> x = 2

x - 8 = 0 -> x = 8

So, x can be either 2 or 8.

If we substitute these values back into Equation 1, we can find the corresponding values of y:

For x = 2:

2(2) + 8 = y

4 + 8 = y

12 = y

For x = 8:

2(8) + 8 = y

16 + 8 = y

24 = y

Therefore, the possible solutions for x and y are:

1. x = 2, y = 12

2. x = 8, y = 24

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Answer:

the answer is -10

Step-by-step explanation:

the steps are in the picture

Answer:

The answer to this expression would be negative.

Step-by-step explanation:

-10

Answer:

me neither (TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

c. x <_ -2 or x >_ 4

Step-by-step explanation:

On the number line, the line goes infinity both sides, but stops between x= -2 and x=4

Answer:

100

Step-by-step explanation:

What you need to do is multiply all of the numbers together so the three sides equal 12 so you need to do 12x3 which equals to 36 and 8x8 is 64 and then add 64 and 36 which gives you 100

Solution :

The given figure consists of two shapes that are a triangle and a square . To find the total area of the figure we will first find the area of the triangle then that of the square and add them .

Let's work on this ,

In the given figure the base of the triangle is 12 inches and it's height is 8 inches .

Now lets find the area of the square ,

Total area of the figure

To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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Answer:

\(ABC = 130\)

Step-by-step explanation:

Given

\(ABC=12x - 110\)

\(ABD=3x+40\)

\(DBC=2x - 10\)

Required

Determine the measure of ABC --- Missing part of the question

First, we need to determine the value of x

Since, D is an interior of ABC, then

\(ABC = ABD + DBC\)

\(12x - 110 = 3x + 40 + 2x - 10\)

Collect Like Terms

\(12x - 3x - 2x = 110 + 40 - 10\)

\(7x = 140\)

Solve for x

\(x = 140/7\)

\(x = 20\)

Substitute 20 for x in \(ABC=12x - 110\)

\(ABC = 12 * 20 - 110\)

\(ABC = 240 - 110\)

\(ABC = 130\)

Answer:

145

.8x = 116 (80% of class is 116)

x=145

Step-by-step explanation:

Answer:

The area of a parallelogram with adjacent sides u and v is given by the magnitude of the cross product of u and v:

A = |u x v|

We can find the cross product as follows:

u x v = (8)(-1) - (0)(-2), -(9)(-2) - (-3)(1), (9)(2) - (-3)(8) = (-8, -15, 42)

So the area of the parallelogram is:

A = |(-8, -15, 42)| = √(8^2 + 15^2 + 42^2) ≈ 46.09 square units

(a) The triple scalar product of three vectors u, v, and w is given by:

u . (v x w)

We can find the cross product v x w as follows:

v x w = (2)(1) - (-2)(1), (-2)(3) - (0)(1), (0)(1) - (2)(1) = (4, -6, -2)

So the triple scalar product is:

u . (v x w) = (-3)(4) - (4)(-6) - (-1)(-2) = -12 + 24 - 2 = 10

(b) The volume of a parallelepiped with adjacent edges u, v, and w is given by the scalar triple product of u, v, and w:

V = |u . (v x w)|

We already found u . (v x w) in part (a), so we just need to take the absolute value:

V = |10| = 10 cubic units

To find the distance from point P to the plane, we can use the formula:

d = |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2)

where the equation of the plane is given by ax + by + cz + d = 0. In this case, we have:

a = 4, b = -1, c = 3, and d = -9

So the equation of the plane is 4x - y + 3z - 9 = 0. To find the distance from point P(2, 8, -7), we plug in these values:

d = |(4)(2) + (-1)(8) + (3)(-7) - 9| / sqrt(4^2 + (-1)^2 + 3^2) ≈ 5.61 units

Therefore, the distance from point P to the plane is approximately 5.61 units.

rate5* po and give thanks for more po! your welcome!

the rate of change of y with a linear function is the slope, so we just need to calculate

with the points (x1,y1) and (x2,y2)

now replaced with the points (- 3, 4) and (2, - 6)

So the answer is: -2

Answer:

Jason started scuba diving 5 meters below sea level and is descending at a rate of 2.5  meters per second.

Step-by-step explanation:

Jason is scuba diving at a constant rate toward the ocean floor.

Equation: \(y= -2.5x- 5\)

x = The number of seconds Jason has been swimming.

y=The depth of Jason in meters  below sea level

General equation : y=mx+c

m = Slope = rate of change per unit

On comparing m = -2.5

Negative signs represents the descending .

So, rate of descending per second = 2.5 m/sec

-5 denotes the initial position below sea level

So, Option D is true

So, Jason started scuba diving 5 meters below sea level and is descending at a rate of 2.5  meters per second.

Answer:

write the expression for the perimeter of the 1st rectangle 6x

write the expression for the perimeter of the 2nd rectangle 4x + 30

write the equation 6x = 4x + 30

x= 15

perimeter = 90

Step-by-step explanation:

The perimeter is adding up all the sides of the rectangle.

So for the first one, we know two of the sides: x and 2x. The opposite sides have the same values. So the other two sides are x and 2x.

Therefore, the perimeter is

2x + x + 2x + x

or

6x

Similarly with the second rectangles:

(x+12) + (x+3) + (x+12) + (x+3)

Combine like terms

x + x + x + x + 12 + 3 + 12 + 3

4x + 30

Set these two equal to each other because the two perimeters are equal

6x = 4x + 30

Subtract 4x on both sides

2x = 30

Divide by 2 on both sides

x = 15

Check:

6(15) = 4(15) + 30

90 = 60 + 30

90 = 90

The common perimeter is

6*15 = 90 units

Answer:

8/24 is correct. However, I would simplify 8/24 down to 1/3, since most teachers want you to do that.

The answer is A

Step-by-step explanation:

You multiply when you scale up

Answer:

p+4

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Based on the eigenvalues and the summary of importance, we find that two principal components are enough to summarize the data. These components capture a substantial proportion of the variance and adequately represent the underlying patterns in the dataset.

In the given output, we have the eigenvalues: 6.93107360, 1.78514434, 0.38964992, 0.22952892, and 0.01415498. The eigenvalues represent the amount of variance explained by each principal component. The larger the eigenvalue, the more significant the component.

Additionally, the summary of importance provides the standard deviation, proportion of variance, and cumulative proportion for each principal component.

From the summary, we can see that the first component (Comp. I) has a standard deviation of 2.5369267 and accounts for 74.13% of the variance. The second component (Comp. 2) has a standard deviation of 0.7413268 and explains an additional 19.09% of the variance. The cumulative proportion shows that the first two components together explain 93.23% of the variance.

Based on this information, we can conclude that the first two principal components are sufficient to summarize the data. They capture a significant amount of the total variance (93.23%) and provide a good representation of the underlying patterns in the dataset.

Including additional components would explain a diminishing amount of variance. Therefore, using the first two principal components is a reasonable choice for summarizing the data effectively.

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