compare: 5/12 to 1/12 which one is greater

Given that the length of one of the sides of the triangle is the radius, the length of the other leg of the triangle is also 6 units.

Therefore, this is an instance of a 45-45-90 triangle. The value of x can now be solve by

Given that the side length of the 45-45-90 triangle is 6 units, the length of the hypotenuse x is

The null and alternative hypotheses are-

The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.

A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.

For this assertion, we form:

Null hypothesis H₀; μ ≤ 9

Alternative hypothesis Hₐ: μ > 9

The assertion is represented by the alternative hypothesis in this right-tailed test.

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The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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The scale factor used to create the dilation is -4.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

When dilation is not about the origin then in order to find the scalar factor, we need to find the ratio of the corresponding lengths.

2 Vertices of smaller triangle (Pre-image):

(1,-1) and (1,1)

Length of side:

Distance=√(x₂-x₁)²+(y₂-y₁)²

√(1-1)²+(1-(-1))²=√4=±2

Since distance is always positive so its 2 units.

2 Vertices of bigger triangle(Image):

(1,-1) and (1,-9)

√(1-1)²+(-9-(-1))²=√64=±8

Since distance is always positive so its 8 units.

For the given figure we see that the dilated image is rotated 180° from the original position. Thus, for such dilation the scalar factor is taken negative.

Thus the scalar factor can be calculated as: -8/2=-4

Hence, the scale factor used to create the dilation is -4.

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The remaining angles of triangle are A = 40.8° ,B = 60.6° , C = 78.6°

To determine the remaining angles of a triangle with sides a = 6, b = 8, and c = 9, we can use the Law of Cosines and the Law of Sines.

The Law of Cosines states that for any triangle with sides a, b, and c and angles A, B, and C, respectively:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

Using the given side lengths, we can calculate the value of cos(C):

\(c^2 = 6^2 + 8^2 - 2(6)(8)cos(C)\)

81 = 36 + 64 - 96cos(C)

81 = 100 - 96cos(C)

96cos(C) = 100 - 81

96*cos(C) = 19

cos(C) = 19/96

Using the inverse cosine function (cos^(-1)), we can find the measure of angle C:

C = \(cos^{-1}(19/96)\) = 78.6°

To find the measure of angle A, we can use the Law of Sines:

sin(A)/a = sin(C)/c

sin(A) = (asin(C))/c

sin(A) = (6sin(C))/9

Using the calculated value of angle C and substituting the side lengths, we can find sin(A):

sin(A) = \((6*sin(cos^{-1}(19/96)))/9\) = 40.8°

Finally, the measure of angle B can be determined by subtracting the measures of angles A and C from 180 degrees:

B = 180 - A - C = 60.6°

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Answer:

tank a

Step-by-step explanation:

The limit of the sequence (13\(n^3\))/(15\(n^6\)) as n approaches infinity is equal to 0, which implies that the sequence converges to 0.

To determine whether the sequence \(a_n\) = (13\(n^3\))/(15\(n^6\)) converges or diverges, we can first simplify it by canceling out \(n^3\) from the numerator and denominator, which yields \(a_n\) = 13/15\(n^3\).

To determine if the sequence converges, we need to find its limit as n approaches infinity. As n gets larger and larger, the denominator of \(a_n\)becomes much larger than the numerator, causing \(a_n\) to approach zero. We can use the limit laws to evaluate the limit of \(a_n\) as n approaches infinity:

lim n->∞ 13/15\(n^3\) = 13/15 * lim n->∞ 1/\(n^3\)

Since the limit of 1/\(n^3\) as n approaches infinity is 0, we can substitute it into the above expression and obtain:

lim n->∞ 13/15\(n^3\) = 13/15 * 0 = 0

Therefore, the sequence \(a_n\) converges to 0 as n approaches infinity.

In conclusion, the sequence \(a_n\) = (13\(n^3\))/(15\(n^6\)) converges to 0. This result makes intuitive sense, as the numerator grows much slower than the denominator as n gets larger, causing the fraction to approach 0.

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Answer:

Step-by-step explanation:

These are really difficult, but one thing I noticed pretty much across the board is that we state our trig ratios in terms of sin and cos using the Pythagorean identity:

\(sin^2x+cos^2x=1\), even this one where tangents are involved. Let's begin:

If tan⁻1(x) = u (this is just a substitution to make things easier down the road), then tan(u) = x

If tan⁻1(y) = v, then tan(v) = y.

If that be the case, what we have as a rewrite from our original problem is

sin(u + v) which, according to the identity is:

\(sin(u-v)=sin(u)cos(v)-sin(v)cos(u)\) which also tells us that we need those tangents in terms of sines and cosines, as stated earlier. We will take the Pythagorean identity and solve it for both sinx and cosx. Sinx first:

If \(cos^2x+sin^2x=1\) then solving for sin:

\(\frac{cos^2x}{sin^2x}+\frac{sin^2x}{sin^2x}=\frac{1}{sin^2x}\) (as you can see, I just divided everything by sin-squared):

\(cot^2x+1=\frac{1}{sin^2x}\) and

\(\frac{1}{tan^2x}+1=\frac{1}{sin^2x}\) and work on eliminating the denominators by multiplying through by sin-squared times tan-squared:

\(sin^2x*tan^2x(\frac{1}{tan^2x}+1=\frac{1}{sin^2x})\) which simplifies to

\(sin^2x+sin^2x*tan^2x=tan^2x\) and factor out on the left:

\(sin^2x(1+tan^2x)=tan^2x\) and solve for sin-squared:

\(sin^2x=\frac{tan^2x}{1+tan^2x}\) and take the square root of both sides:

\(sinx=\frac{tanx}{\sqrt{1+tan^2x} }\) .  Do the same to solve for cos(x) to get:

\(cosx=\frac{1}{\sqrt{1+tan^2x} }\) and now we're ready to fill in our formula for sin(u + v):

\(\frac{tanu}{\sqrt{1+tan^2u} }*\frac{1}{\sqrt{1+tan^2v} }\)  -  \(\frac{tanv}{\sqrt{1+tan^2} }*\frac{1}{\sqrt{1+tan^2u} }\)  and...

since tanu = x and tanv = y:

\(\frac{x}{\sqrt{1+x^2}}*\frac{1}{\sqrt{1+y^2}}-\frac{y}{\sqrt{1+y^2}}*\frac{1}{\sqrt{1+x^2} }\) which, in the end, simplifies to

\(\frac{x-y}{\sqrt{1+x^2}*\sqrt{1+y^2} }\) and you're done! Yikes to that!!!!

Answer:

the number is 28

Step-by-step explanation:

A mathematical description of hexagon is given above.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is hexagon.

In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Therefore, a mathematical description of hexagon is given above.

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As the y-intercept increases, the graph of the line shifts up;

As the y-intercept decreases, the graph of the line shifts down

There are two perspectives on this issue. The graphical technique would be the first method.

If we merely alter the y-intercept, the slope remains unchanged;

The vertical axis is the y-axis;

A higher or lower y-intercept can be obtained by shifting the line's point of intersection with the y-axis, respectively.

Now, using algebraic reasoning, a line has the general form of the following equation:

When x = 0, the y-intercept is essentially computed as follows:

y = b:

The graph shifts up or down depending on how much we change the b value, which also affects how much the y value changes.

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Answer:

Step-by-step explanation:

P + 4.5 = - p + 5

Bringing like terms on one side

P + p = 5 - 4.5

2p = 0.5

p = 0.5/2 = 0.25

In my opinion the answer is one solution

Answer:

1 solution.

Step-by-step explanation:

1/2(2p + 9) = -p + 5

lets solve for p

1/2 * 2p + 1/2 * 9 = -p + 5

1p + p + 9/2 = - p + p + 5

2p + 9/2 = 5

Multiply by 2 on both sides to get rid of the fraction 9/2.

4p + 9 = 10

4p = 1

p = 1/4

Therefore, there is only 1 solution.

You can now check by plugging in 1/4 for p in the original equation.

Answer:

1)10

2)-4

3)-9

4)6

5)-14

6)10

7)8

8)6

9)-22

10)0

Step-by-step explanation:

I included pics of my work

hope this helps :)

(btw I just realized that I forgot to make the answer for number 3 negative so sorry)

Answer:

x= 1.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(x−2 2/5) = −5.2

1. We need to use distibutaive property

5×x and 5×-2.4

5x - 12 = -5.2

2. We need to get x alone.

5x - 12 = -5.2

    -12      -12

5x = 6.8

3. We need to divide

5x = 6.8

/5     /5

x = 1. 36

check:

5(1.36−2 2/5)=−5.2

6.8 - 12 = 5.2

Answer: it is the median

Step-by-step explanation:

Answer:

it is the Mode,Median,and Mean.

Step-by-step explanation:

There are ALWAYS three measures of the “center"

Answer:
45.2x0.784

Step-by-step explanation:

This problem equals 35.4368, which has four decimal points

The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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(a) The critical value (t*) for a 99% confidence level is t* = 3.499.

(b) The margin of error for a 99% confidence interval is approximately 1.633.

To solve the problem step by step, we'll use the provided information to find the critical value (t*) for a 99% confidence level (CL) and the margin of error for a 99% confidence interval (CI).

(a) Find the critical value, t*, for a 99% confidence level (CL):

Step 1: Determine the confidence level (CL). In this case, it is 99%, which corresponds to a significance level of α = 0.01.

Step 2: Determine the degrees of freedom (df). Since we have a sample size of 8, the degrees of freedom is given by df = n - 1 = 8 - 1 = 7.

Step 3: Find the critical value, t*, using a t-distribution table or statistical software. The critical value is the value that separates the middle 99% of the t-distribution. For a two-tailed test with α = 0.01 and 7 degrees of freedom, the critical value is approximately t* = 3.499.

Therefore, the critical value (t*) for a 99% confidence level is t* = 3.499.

(b) Find the margin of error for a 99% confidence interval (CI):

Step 1: Calculate the standard error (SE) using the formula: SE = (standard deviation) / √(sample size).

Given that the standard deviation is 1.32 hours and the sample size is 8, we have SE = 1.32 / √8 = 0.4668.

Step 2: Determine the margin of error (ME) by multiplying the standard error by the critical value: ME = t* × SE.

Using the previously calculated critical value (t* = 3.499) and the standard error (SE = 0.4668), we have ME = 3.499 × 0.4668 = 1.633.

Therefore, the margin of error for a 99% confidence interval is approximately 1.633.

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The question is -

A random sample of 8-size AA batteries for toys yields a mean of 3.79 hours with a standard deviation, of 1.32 hours.

(a) Find the critical value, t*, for a 99% Cl. t* = ________

(b) Find the margin of error for a 99% CI. _________

The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.

What is ratio ?

Ratio can be defined as the given value divided by the total value.

The easiest thing to do first is convert all of these fractions to common denominators, and figure out the rest of the problem from there.

So the common denominator between 1/3 and 1/4 is 12, so convert these to fractions to /12 and continue on.

Think of the whole book being 12/12, and Sarah read 4/12 of it in the morning, so we know she has 8/12 left of it. Since we know she still has 3/12 left to read by the end of the day, we can subtract 8/12 - 3/12 to find out how much she read at night, which is 5/12. This makes sense because when we add all the fractions up (4/12 + 3/12 + 5/12) it comes out to 12/12, which is the whole book.

Therefore, The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.

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Answer: there are 432 bars of soup in 12 packages and there are  432 toothbrushes also

Answer:

\(\huge\boxed{\sf x = 3}\)

Step-by-step explanation:

According to intersecting chord theorem, if two chords intersect each other, the product of lengths of each chord will be equal.

Such that,

\(a \times b = c \times d\)

\(x \times 2 = 1 \times 6\\\\2x = 6\\\\Divide \ both \ sides \ by \ 2\\\\x = 6/2\\\\x = 3\\\\\rule[225]{225}{2}\)

Answer:

The answer would be 5x-18=13

Step-by-step explanation:

When given five times than a number, 5 would be multiplied by (x) since x can be any number. Less than 18 means subtract 18. Is equal to means an eual sign and the equation is equal to 13.

Answer:

bfcfbdgbcbcvgb

Step-by-step explanation:

Answer:

B. 259.8 u²

Step-by-step Explanation:

The area of a regular hexagon is given as:

\( Area = \frac{3\sqrt{3} }{2} a^{2} \)

Where a = side length of the hexagon

Thus, the area of the regular hexagon with a given side length, a = 10, is calculated as follows:

\( Area = \frac{3\sqrt{3} }{2} a^{2} \)

\( Area = \frac{3\sqrt{3} }{2}* 10^{2} \)

\( = \frac{3\sqrt{3} }{2}* 100 \)

\( = \frac{3*1.7321 }{2}* 100 \)

\( = \frac{5.1963 }{2}* 100 \)

\( = \frac{519.63 }{2} \)

\( Area = 259.815 \)

The area of the regular hexagon ≈ 259.8 u²

Answer:

Height of the goalpost is 9.25 m.

Step-by-step explanation:

As per the rule of reflection in physics,

Angle of incidence = Angle of reflection

As we can see in the picture attached, both the angles (θ) are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

\(\frac{AB}{ED}= \frac{CB}{CD}\)

\(\frac{1.75}{ED}=\frac{2.6}{13.75}\)

ED = \(\frac{1.75\times 13.75}{2.6}\)

ED = 9.25 m

Height of the goalpost is 9.25 m.

Answer:

9.9cm

Step-by-step explanation:

If side h cm is opposite of 51° and side 8cm is adjacent to 51°, use the tangent function to calculate the opposite side h cm:

tan(51°)=opposite/adjacent=h/8

tan(51°)=h/8

8tan(51°)=h

9.879177252=h

9.9=h

Therefore, the value of h is 9.9cm

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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