Declan is stacking identical cube-shaped boxes. He stacks 8 boxes to make a tower that is 144 cm tall. He adds 1 more box to the tower. How tall is the tower now? Give your answer in centimetres (cm).

If side a is perpendicular to the third side of the triangle, it implies that a = b * sin(A) since tan(A) = sin(A) / cos(A).

To show that if side a is perpendicular to the third side of the triangle, then a = b * sin(A), we can use the trigonometric relationship involving sine in a right triangle.

Let's consider a triangle ABC, where side a is perpendicular to the third side BC at point D. Angle A is opposite to side a. Side b is adjacent to angle A.

In triangle ABC, according to the definition of sine, we have:

sin(A) = opposite/hypotenuse

Since side a is perpendicular to side BC, it serves as the opposite side to angle A.

Therefore, sin(A) = a/hypotenuse.

Now, let's focus on side AC, which is the hypotenuse of the triangle. By using the definition of cosine, we have:

cos(A) = adjacent/hypotenuse

Since side b is adjacent to angle A, we can rewrite this equation as:

b = cos(A) * hypotenuse.

We can rearrange this equation to solve for hypotenuse:

hypotenuse = b / cos(A).

Now, substituting the value of hypotenuse into the equation sin(A) = a/hypotenuse, we get:

sin(A) = a / (b / cos(A)).

Multiplying both sides by (b / cos(A)), we have:

(b / cos(A)) * sin(A) = a.

Simplifying the left-hand side, we get:

b * (sin(A) / cos(A)) = a.

Using the identity tan(A) = sin(A) / cos(A), we can rewrite the equation as:

b * tan(A) = a.

Finally, dividing both sides of the equation by tan(A), we obtain:

a = b * tan(A).

So, if side a is perpendicular to the third side of the triangle, then a = b * tan(A).

Therefore, if side a is perpendicular to the third side of the triangle, it implies that a = b * sin(A) since tan(A) = sin(A) / cos(A).

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Answer:

4534443242

Step-by-step explanation:

Answer:9,892,247

Step-by-step explanation:

The particular antiderivative that satisfies the given conditions is y(x) = 2x^(3/2) + 5x^(1/2) - 3x.

To find the particular antiderivative that satisfies the given conditions, we will integrate the given function with respect to x and then use the initial condition to determine the constant of integration.

The given function is: (4x + 5) / (3√x).

First, we split the function into two parts:

(4x) / (3√x) + (5) / (3√x).

Now, we integrate each part separately:

∫ (4x) / (3√x) dx = 2x^(3/2) + C1, where C1 is the constant of integration for the first part.

∫ (5) / (3√x) dx = 5x^(1/2) + C2, where C2 is the constant of integration for the second part.

Combining the two parts, we have:

y(x) = 2x^(3/2) + 5x^(1/2) + C, where C = C1 + C2.

Next, we use the initial condition y(1) = 8 to determine the value of C:

y(1) = 2(1)^(3/2) + 5(1)^(1/2) + C = 2 + 5 + C = 7 + C = 8.

Solving for C, we have: C = 8 - 7 = 1.

Therefore, the particular antiderivative that satisfies the given conditions is:

y(x) = 2x^(3/2) + 5x^(1/2) + 1.

The particular antiderivative that satisfies the given conditions is y(x) = 2x^(3/2) + 5x^(1/2) + 1. This antiderivative is obtained by integrating the given function and including the constant of integration determined by the initial condition y(1) = 8.

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Answer:

80

Step-by-step explanation:because u have to multiply 4x3 then that’s 12 add 80 and U get 90 sorry if I’m wrong

Answer:

- 30/91

Step-by-step explanation:

As a result, we can claim with 95% certainty that the genuine proportion of students who would approve an increase in parking places is between 0.591 and 0.809.

A confidence interval is a statistical range of values that, with a particular level of certainty, contains the real value of a population parameter. A 95% confidence interval indicates that if we repeated this process several times, creating confidence intervals for the same population parameter with different samples, about 95% of those intervals would include the genuine population parameter. The researcher or analyst usually chooses the degree of confidence, with 95% being a frequent choice.

Here,

CI =p ± z* (√(p(1-p)/n))

p = 63/90 = 0.7

n = 90

z* = 1.96

CI = 0.7 ± 1.96 * (√(0.7(1-0.7)/90))

Simplifying this expression, we get:

CI = 0.7 ± 0.109

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Answer:

x is less than -6

Step-by-step explanation:

Add 4 to both sides

-2x is greater than 12

Divide both sides by -2 and don't forget to change the sign

x is less than -6

Answer:

x < - 6

Step-by-step explanation:

Given

- 2x - 4 > 8 ( add 4 to both sides )

- 2x > 12

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x < - 6

The assertion that which shows that P(k + 1) is true provided Pk in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that P(n) be the assertion

∑j² = n (n+1)(2n+1)/6

(a) For n = 3, we get

∑j² = 1² + 2²+3² =14

= 3(3+1)(6+1)/6

=14

Hence, P(3) is true.

(b) Expression for P(k) may take the form

∑j² = k (k+1)(2k+1)/6

(c) Expression for P(k + 1) may take the form

∑j² = (k+1) (k+2)(2k+3)/6

(d)Base case:

In base case, we must prove that P(1) is true.

(e) To prove P(n) will be true for every positive integer n, we need to prove that P(k + 1) is true in the inductive step, where k is a positive integer.

(f) In the Inductive step, the Inductive hypothesis is that Pk is true for positive integer k.

(g)Base case:

a) For n=1, we get

RHS= 1(1+1)(2+1)/6

=1

Hence, P(1) is true.

Inductive hypothesis:

Assume P(k) is true:

∑j² = k (k+1)(2k+1)/6

Inductive step:

Now,

∑j² = k (k+1)(2k+1)/6 +(K+1)²

which shows that P(k + 1) is true provided P(k) in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

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Answer: ASA

Step-by-step explanation:

Answer:

Step-by-step explanation:

Height of model = 20 ft ⋅ (2 in)/(5 ft) = 8 in

Answer: m<c is 57 degrees

Step-by-step explanation: A parallelogram must have equivalent opposite interior angles, and <c is a diagonal to <a

therefore its 57

Hope this helps! <3

Answer: Number of small boxes = 7, Number of large boxes =3

Step-by-step explanation:

Let x= Number of small boxes , y = Number of large boxes.

As per given , 30x+55y=375  (i)

x+y=10   (ii)

Multiply (ii) by 30, we get

30x+30y=300    (iii)

Eliminate (iii) from (i), we get

25y=75

⇒ y= 3   [Divide both sides by 25]

Put y=3 in (ii), we get

x+3=10 ⇒ x=7

Hence,  Number of small boxes = 7, Number of large boxes =3

Answer:

80

Step-by-step explanation:

Divide 24 by .3 and u get 80

The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

\($\sin a^{\circ}=\frac{E F}{D E}$\)

If we know that DE=30 and \($\sin a^{\circ}=\frac{4}{5}$\), then the length of the segment EF is:

\(E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\\)

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

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Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

Answer:

the unit cost per rubber tile is $$$$$$$$$$$$$6

Step-by-step explanation:

..

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane.

Describe coordinates using an example?

What are the coordinates for all 3?

the given points on one coordinate plane  are

A . (-4,3)

B. (2,7)

C. (5,-1)

D. (0,-8)

E. (-6,-2)

Graph is attached

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Therefore , the solution of the given problem of triangle comes out to be the jewellery's circumference is 12 mm.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything like this can only be distinguished from a standard triangle form by edges A and B. Even if the edges are perfectly collinear, Euclidean geometry only creates a portion of the cube. A triangle is made up of a quadrilateral and three angles.

Here,

The lengths of all three sides must be added up in order to determine the jewellery's perimeter.

=> c²= a² + b²

where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

=> A = 3mm, and B = 4mm.

Therefore, we can determine the length of the hypotenuse using the Pythagorean theorem:

=> c² = a²+ b²

=> c² = 3² + 4²

=> c² = 9 + 16

=> c² = 25

=> c = √25)

=> c = 5 mm

As a result, the hypotenuse is 5 mm long.

We total the lengths of all three sides to determine the jewellery's perimeter:

=> perimeter = 4mm, 3mm, and 5mm.

=> 12 mm is the diameter.

Therefore, the jewellery's circumference is 12 mm.

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The  situations that can be represented by the opposite of -25 are:

-25 can be seen as represention of the given  situations fro the problem, and exploring the given options, we can see that 25 feet below the sea level with that ones balance can be gets reduced by $25.

But when exploring the But the opposite of (-25)  then we can see that 25 feet above the sea level, and in this case the amount will be raised by $25. and the height by 25 feet with the increase in the debt by $25.

Therefore, option B ,C and E are correct.

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missing options:

A. A scuba diver is 25 feet below sea level. B. Leon gets paid $25. C. An airplane descends 25 feet. D. Sara has a $25 debt. E. A bird flies 25 feet above sea level

A statistical technique called the chi-square test is used to compare actual outcomes with predictions. The goal of this test is to establish whether a discrepancy between observed and expected data is the result of chance or a correlation between the variables you are researching.

T tests and chi-square tests can both evaluate differences between two groups. However, a t test is utilised when there are two groups in a categorical variable and a dependent quantitative variable. In cases where there are two categorical variables, a chi-square test of independence is applied.A statistical technique called the chi-square test is used to compare actual outcomes to predictions.

Typically, it involves a contrast between two sets of statistical data. Karl Pearson developed this test in 1900 for the analysis and distribution of categorical data. As a result, Pearson's chi-squared test was cited.

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one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. Thus,

The lengths of the legs of the triangle are 18 inches,24 inches and  30 inches.

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Given that,

one leg of a right triangle is 6 inches longer than the other leg.

hypotenuse is 30 inches.

Let assume, the other leg be x

It is given that, one leg of a right triangle is 6 inches longer than the other leg. So, One leg = x + 6

Since it is a right angled triangle,

h² = p² + b²

Where, h = hypotenuse

p = perpendicular

B = Base

So, (30)² = (x+6)² + x²

or, x = -24, 18

As, the length of side cannot be negative so x becomes 18.

Thus, x + 6 = 18 + 6 = 24 inches

Hypotenuse = 30 inches

Hence, the lengths of the legs of the triangle are 18 inches, 24 inches and  30 inches.

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⇒To find the midpoint use the formula:

⇒\(M(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})\\M(\frac{3+(-2)}{2} ,\frac{3+(-5)}{2} )\\\\M(\frac{3-2}{2},\frac{3-5}{2} )\\M(\frac{1}{2} ,\frac{-2}{2} )\\M(\frac{1}{2} ,-1)\)

Your midpoint M is given above .

GOODLUCK!!!

Answer:

Midpoint formula : (\(\frac{x1 + x2}{2}\) , \(\frac{y1 + y2}{2}\))

the given points are  (3,3) and (-2,-5).

(3 = x1, 3 = y1) and (-2 = x2, -5 = y2).

we place them in the formula.

(\(\frac{3 + -2}{2}\) , \(\frac{3 + -5}{2}\))

(1/2 , -2/2)

(0.5, -1) is the midpoint.

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a) The number of page faults for the First In First Out (FIFO), Least Recently Used (LRU), and Optimal page replacement (OPT) algorithms with 4 frames in physical memory are compared for the given page reference string. , b) The effect on the page fault rate is discussed when the number of frames is reduced to 3 frames in each algorithm.

a) To compare the number of page faults for the FIFO, LRU, and OPT algorithms with 4 frames, we simulate each algorithm using the given page reference string. FIFO replaces the oldest page in memory, LRU replaces the least recently used page, and OPT replaces the page that will not be used for the longest time. By counting the number of page faults in each algorithm, we can determine which algorithm performs better in terms of minimizing page faults.

b) When the number of frames is reduced to 3 in each algorithm, the page fault rate is expected to increase. With fewer frames available, the algorithms have less space to keep the frequently accessed pages in memory, leading to more page faults. The reduction in frames restricts the algorithms' ability to retain the necessary pages, causing more page replacements and an overall higher page fault rate. The specific impact on each algorithm may vary, but in general, reducing the number of frames decreases the efficiency of the page replacement algorithms and results in a higher rate of page faults.

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Answer:

B) formation of a precipitate
E) change in color

Step-by-step explanation:

just did the assignment on e.d.g.e

Answer:

B and E is correct

Step-by-step explanation:

Angles TRS and TRV are supplementary, that is,

m∠TRS + m∠TRV = 180°

(25x + 30) + (5x) = 180

(25x + 5x) + 30 = 180

30x = 180 - 30

x = 150/30

x = 5

Angles TRV and WRS are vertical angles, then they are congruent, that is,

m∠TRV = m∠WRS

5x = m∠WRS

5*5 = m∠WRS

25° = m∠WRS

The exact value of the cosine ratio with the point P(7.00,−3.00) on the terminal arm is 0.92.

To determine the exact value of the cosine ratio for the given point P(7.00, -3.00), we can use the trigonometric identity:

\(\[ \cos(\theta) = \frac{x}{r} \]\)

where x is the x-coordinate of the point P and r is the distance from the origin to the point P, which can be calculated using the Pythagorean theorem:

\(\[ r = \sqrt{x^2 + y^2} \]\)

In this case, x = 7.00 and y = -3.00.

Plugging these values into the equations, we have:

\(\[ r = \sqrt{(7.00)^2 + (-3.00)^2} = \sqrt{49 + 9} = \sqrt{58} \]\)

Now we can calculate the cosine ratio:

\(\[ \cos(\theta) = \frac{7.00}{\sqrt{58}} = 0.92 \]\)

Thus, the exact value of the cosine ratio is 0.92.

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Answers:

Option two, 5\(y^{4}\)(2\(y^{5}\)) = 10\(y^{9}\) and option 4, 5\(x^{3}\)(6\(x^{4}\)) = 30\(x^{7}\)

Step-by-step explanation:

O1 + O3 = incorrect, the powers have been multiplied together. Laws of indices suggest that if you are multiplying powers together, you must add them, not do 4 x 5 or 2 x 2.

Please remember:

2y squared x 3y cubed = 6y to the power 5

Answer:

Solution(s) : Option # 2 and # 4

Step-by-step explanation:

One quick way to identify which solutions are accurate would be adding the exponents of the terms provided ( b, y, c etc ). As you can see in each example two expressions are being multiplied, and hence the exponents of each term are being added.

Therefore the second and fourth example are correct, as 4 + 5 = 9, the co - efficient of y. And 3 + 4 = 7, the co - efficient of x.

Check :

\(5y^4\left(2y^5\right)\) = \(5\cdot \:2y^{4+5}\) = \(5\cdot \:2y^9\) = \(10y^9\)

\(5x^3\left(6x^4\right)\) = \(5\cdot \:6x^{3+4}\) = \(5\cdot \:6x^7\) = \(30x^7\)

Answer:

3

Step-by-step explanation:

For one batch there is 2 cups so for one person it's one serving so you will need 3 batches for 6 people.