​One- equals the quotient of a number and . Find the number.

Answer:

Step-by-step explanation:

We observe the pattern:

It can be put as:

or

The nth term is going to be:

The sum of the 31 terms will be:

or

Use the formula for sum of the first n squares:

The sum N equals:

And the value of N/31 is:

Answer:

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Step-by-step explanation:

Let \(\vec u\) and \(\vec a\), from Linear Algebra we get that component of \(\vec u\) parallel to \(\vec a\) by using this formula:

\(\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a\) (Eq. 1)

Where \(\|\vec a\|\) is the norm of \(\vec a\), which is equal to \(\|\vec a\| = \sqrt{\vec a\bullet \vec a}\). (Eq. 2)

If we know that \(\vec u =(2,1,1,2)\) and \(\vec a=(4,-4,2,-2)\), then we get that vector component of \(\vec u\) parallel to \(\vec a\) is:

\(\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

Lastly, we find the vector component of \(\vec u\) orthogonal to \(\vec a\) by applying this vector sum identity:

\(\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}\) (Eq. 3)

If we get that \(\vec u =(2,1,1,2)\) and \(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\), the vector component of \(\vec u\) is:

\(\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

\(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\)

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

The length of the fencing is 62.4 feet.

The width of the fencing is 17.6 feet.

Given,

The measurement of the Christmas garland = 160 feet

The width of the fencing = w

The length of the fencing, l = 4w - 8

We have to find the length and width of the fencing.

Here,

Perimeter can be taken as 160. Because garland will cover the entire fencing.

Perimeter = 2(l + w)

160 = 2(4w - 8 + w)

160 = 2(5w - 8)

160/2 = 5w - 8

80 + 8 = 5w

88/5 = w

width = 17.6 feet

Now,

l = 4w - 8

l = 4 × 17.6 - 8

l = 70.4 - 8

length = 62.4 feet

That is,

The length of the fencing is 62.4 feet.

The width of the fencing is 17.6 feet.

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14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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Answer: about 1.6 or 1.7

Answer:

-9 feet

Step-by-step explanation:

The turtle was already at -2 feet below sea level, then the turtle went 7 more feet down. Which means that -2 +7 = -9

The common step to draw any polygon whether it is a hexagon, a square, and a equilateral triangle in a circle is constructing an arc using an end points of the diameter and the center of the circle

If a polygon is drawn in an circle so that every corner of the polygon lies on the circle, the polygon is called an inscribed polygon or cyclic polygon, and the circle is called circumcircle.

If we draw a hexagon, square and equilateral triangle in a circle.

Then all the corners of the polygon lies on the circle and are called cyclic polygon.

The common step to draw any polygon whether it is a hexagon, a square, and a equilateral triangle in a circle is constructing an arc using an end points of the diameter and the center of the circle.

Thus, option D is correct.

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The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

C is the answer!

Step-by-step explanation:

Have a Great Day! ;) Mark me as brainliest!

Answer:

Step-by-step explanation:

-5 - 9x = 3-9x-8  (Used distributive property)

-5 - 9x = -9x-5  (-8+3 = -5)

- 9x = -9x  (Add 5 to both sides)

0 = 0 (Add 9x to both sides)

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

Answer:

I still got negative 3

Step-by-step explanation:

Answer:

The probability that exactly 2 don't grow is 0.075 or 7.5%

Step-by-step explanation:

Binomial Distribution

Let's consider a random experience with only two possible outcomes. Call p to the probability that the event has a successful outcome and q to the unsuccessful outcome.

It's clear that p+q=1, or q=1-p.

Now repeat the random experience n times. We want to calculate the probability of getting x successful outcomes. This can be done with the following formula:

\(\displaystyle P_{x} = {n \choose x} p^{x} q^{n-x}\)

Where  

\(\displaystyle {n \choose x}\)

Is the number of combinations:

\(\displaystyle {n \choose x} =_nC_x=\frac{n !}{x ! (n-x) !}\)

For the problem to solve, each seed has a p=0.95 probability of growing into a healthy plant. The value of q=1-0.95=0.05.

The experience is repeated n=10 times and we want to estimate the probability that 2 of them don't grow. Note this last data is not directly the value of x because it's not related to success but with no success. The value of x is x=10-2=8. That means, 8 out of 10 seeds grow.

Apply the formula:

\(\displaystyle P_{8} = {10 \choose 8} \cdot 0.95^{8} \cdot 0.05^{10-8}\)

\(\displaystyle P_{8} = 45\cdot 0.95^{8} 0.05^{2}\)

\(\displaystyle P_{8} = 0.075\)

The probability that exactly 2 don't grow is 0.075 or 7.5%

Answer:

I believe the answer would be 186

Step-by-step explanation:

241-55=186

nearest tenth = 0.2

2/9 is in its simplest form.

Hence, we use a calculator to find the fraction in decimal

2/9 = 0.2222 (a repeating decimal)

0.2222 to the nearest tenth = 0.2

Answer:

Step-by-step explanation:

2/9 as a decimal is 0.2222

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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Answer:

0

Step-by-step explanation:

=1/2 × -5,6 × 0

=-8,4×0

=0

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Everytime, you add a value number 2 greater than the previous.

1+3=4

4+5=9

9+7=16

16+9=25

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▹ Answer

25

▹ Step-by-Step Explanation

1 + 3 = 4

4 + 5 = 9

9 + 7 = 16

16 + 9 = 25

The pattern is increasing the value of which is added by two each time:

3 + 2 = 5

5 + 2 = 7

7 + 9 = 16

9 + 16 = 25

Hope this helps!

CloutAnswers ❁

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Work Shown:

f(x) = 3x-1

f(x) = 3( x ) - 1

f( g(x) ) = 3( g(x) ) - 1 ... replace every x with g(x)

f( g(x) ) = 3(x^3-5x^2) - 1 ... plug in g(x) = x^3-5x^2

f( g(x) ) = 3x^3-15x^2-1

(f o g)(x) = 3x^3-15x^2-1

The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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$32.89

15% tip

Is $4.94

Making the total of the bill

$37.83

Answer:

an=an−1+10, where a1=8

Step-by-step explanation:

it is

Answer:

an=an−1+10 , where a1=8

Step-by-step explanation:

I just took the test and I got it right!! :)

Answer:

Between 4 and 5

Step-by-step explanation:

Given

See attachment for graph

Required

Between which points is g(x) = 0

From the attachment, we can see that the graph crosses the x-axis at 4... and -1...

This means that

g(x) = 0 between 4 and 5

g(x) = 0 between -1 and -2

Going by the available options,

g(x) = 0 between 4 and 5

Explanation:

m = 1/4

slope = (1, 2)

If we are to find the equation of the line, we apply the formula:

Equation of line: y = mx + c

where m = slope

c = intercept

Inserting the points and slope into the equation, we will find the intercept

(1, 2) = (x, y)

2 = 1/4 (1) + c

2 = 1/4 + c

c = 2 - 1/4

c = 1 3/4

The equation of line becomes:

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

\(D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0\)

Solving for k,

\(k=\pm\sqrt{36}=\boxed{\pm{6}}\).

Hope this helps.

The shipping container shaped like a cuboid is 9.5 feet tall.

Let's call the height of the shipping container "h".

As per the given information, the shipping container can be described as a cuboid.

We are aware that the container's volume is given by the formula:

V = lwh,

where l stands for length, w for width, and h for height.

Substituting the values provided yields:

3040 = 8 x 40 x h

Simplifying, we get:

3040 = 320h

Dividing both sides by 320, we get:

h = 9.5

Therefore, the height of the shipping container is 9.5 feet.

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The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x

The given equation −(5−x) = 5−x

The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together.

The distributive property of addition

A(B+C) = AB + AC

The distributive property of subtraction

A(B-C) = AB - AC

The given equation is  −(5−x) = 5−x

Apply distributive property in the equation

−(5−x) = 5−x

-5+x = 5-x

Hence, The equation is equivalent to −(5−x) = 5−x is -5+x = 5-x

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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