An 18-foot ladder is leaning against a wall. The bottom of the ladder is 4.5 feet from the base of the wall.


How high up the wall does the ladder reach? Round your answer to the nearest tenth, if necessary.

A

13.5 feet

B

18.6 feet

o

С

22.5 feet

D

17.4 feet

Answer:

I got you buddy!

1. 20

2. 200

3. 2000

Step-by-step explanation:

So when you see a number with a little number you multiply the number by itself the same amount of times as the little number up top for example.

10x1= 10

10x10=100

10x10x10=1000

then what you do is take those numbers we multiplied and multiply them again by 2

so its.

2x10=20

2x100=200

2x1000=2000

Hope this helped you buddy!

Volume of a Cylinder = pi * r^2 * h

V / (pi*r^2) = h

12157 / (pi * 9^2) = h = 47.774

Performing operations on the given matrix,

a) F = [17, 12, 17, 23, 18, 17]

b) S = [[1, 1], [1, 1]]

c) T = 72

a) To calculate F, we need to perform two operations:

1. A(2, odd): This selects the elements from the 2nd row of matrix A at odd column indices.

  A(2, odd) = [4, 8]

2. A(even, 3): This selects the elements from even rows of matrix A at the 3rd column index.

  A(even, 3) = [13, 4, 4]

Now, we can perform element-wise addition between A(2, odd) and A(even, 3):

F = A(2, odd) + A(even, 3)

 = [4, 8] + [13, 4, 4]

Since the dimensions do not match, we need to align the vectors by repeating the shorter one:

F = [4, 8] + [13, 4, 4] = [4, 8] + [13, 4, 4, 13, 4, 4] = [4+13, 8+4, 13+4, 10+13, 14+4, 13+4]

 = [17, 12, 17, 23, 18, 17]

Therefore, F = [17, 12, 17, 23, 18, 17].

b) To calculate S, we need to perform element-wise division:

S = A([1, 3], [3, 4]) ÷ A([1, 3], [3, 4])

This means we select the elements from the 1st and 3rd rows, and from the 3rd and 4th columns of matrix A:

S = [[13, 8], [14, 6]] ÷ [[13, 8], [14, 6]]

Element-wise division simply divides corresponding elements from the two matrices:

S = [[13/13, 8/8], [14/14, 6/6]]

 = [[1, 1], [1, 1]]

Therefore, S = [[1, 1], [1, 1]].

c) To calculate T, we need to multiply the element at position (3, 5) with the element at position (4, 3) in matrix A:

T = A(3, 5) × A(4, 3)

 = 12 × 6

 = 72

Therefore, T = 72.

To know more about matrix, refer here:

https://brainly.com/question/29132693

#SPJ4

Complete Question:

Given this A matrix

A = [[12 9 13 10 14] [ 4 3 4 8 5] [8 3 14 6 12] [11 4 6 13 12] [ 14 13 3 9 6] [15 4 4 9 9]]

We wish to do the following

a) F=A(2, odd )+A( even, 3)

b) S=A([ 1 3 ],[ 3 4 ]) ÷ A([ 1 3 ],[ 3 4 ]) Hint: Use element-wise division

c) T=A(3,5)×A(4,3)

Answer:

-8x-28 is after the distributive prop simplified

Step-by-step explanation:

4(-2x-7)

(4×-2x)-(4×-7)= -8x-28

Answer: $0.06 per inch

Concept:

When encountering questions that ask for unit price, follow the statements to get the answer. For example, this question asks the price per inch. Therefore, in the actual answer, use the total price given divided by the number of inches.

Solve:

Price = $6.48

Inch = 9 × 12 = 108 in

Price / Inch = 6.48 / 108 = $0.06 per inch

Hope this helps!! :)

Please let me know if you have any questions

Answer:

14.25 hours

Step-by-step explanation:

We know

2.25 hours = 1 yard

13.5 hours = 6 yards

1/3 yard = 2.25 / 3 = 0.75 hours

To find how long it takes him to complete 6 1/3 yards, we take

13.5 + 0.75 = 14.25 hours

So, he spent 14.25 hours mowing yards.

Answer: angle 1 = 22 degrees

============================================

Work Shown:

x = measure of angle 1 = unknown

y = measure of angle 2 = 49

x+y = measure of angle PQS = 71

x+y = 71

x+49 = 71

x+49-49 = 71-49 .... subtract 49 from both sides

x = 22

angle 1 is 22 degrees.

Answer:

\(m \angle 1\) = 49º.

Step-by-step explanation:

We are given that \(m\angle PQS\) is 71º and \(m \angle 2\) is 49º. Since \(m \angle 1 + m \angle 2\) must equal \(m\angle PQS\), we have that 49º + \(m \angle 1\) = 71º. Therefore, \(m \angle 1\) = 71º - 49º = 22º.

The energy of each photon is:
a) 239.3 kJ/mol
b) \(4.97 * 10^-4 kJ/mol\)
c) \(5.07 * 10^-4 kJ/mol\)

To calculate the energy of each photon in kilojoules per mole, we'll use the following equation:
E = h × ν × (Avogadro's number) / 1000
where E is the energy, h is Planck's constant (6.626 × 10^-34 Js), ν is the frequency in \(s^-1,\) and Avogadro's number is \(6.022 * 10^23 mol^-1.\)

For part c, we'll first convert the wavelength to frequency using the speed of light equation:
ν = c / λ
where c is the speed of light (3.00 × 10^8 m/s) and λ is the wavelength in meters.
a) ν = \(5.92 * 10^19 s^-1\)
E = \((6.626 * 10^-34 Js) * (5.92 * 10^19 s^-1) * (6.022 * 10^23 mol^-1) / 1000\)
E ≈ 239.3 kJ/mol
b) ν \(= 1.24 * 10^6 s^-1\)
E =\((6.626 * 10^-34 Js)\) * \((1.24 * 10^6 s^-1)\) * \((6.022 * 10^23 mol^-1) / 1000\)
E ≈ 4.97 × 10^-4 kJ/mol
c) λ = 265 m
ν =\((3.00 * 10^8 m/s) / (265 m)\)
ν ≈ 1.13 × 10^6 s^-1
E = \((6.626 * 10^-34 Js)\) *\((1.13 * 10^6 s^-1)\) * \((6.022 * 10^23 mol^-1) / 1000\)
E ≈ 5.07 × 10^-4 kJ/mol.

For similar question on energy.

https://brainly.com/question/22236101

#SPJ11

Without further details or measurements, it is not possible to determine the exact value of y that would satisfy the similarity theorem for triangles to be similar.

In order for triangles to be similar by the similarity theorem, the value of y must satisfy the condition of proportional sides. The similarity theorem states that if two triangles have their corresponding angles equal and their corresponding sides in proportion, then the triangles are similar.

Let's consider two triangles, Triangle ABC and Triangle DEF, where the corresponding sides are AB and DE, BC and EF, and AC and DF. If we want these triangles to be similar, then the ratio of the lengths of corresponding sides must be equal.

For example, if we want the ratio of AB to DE to be equal to the ratio of BC to EF, we have AB/DE = BC/EF. Similarly, for the other pairs of corresponding sides, we have AB/DE = AC/DF and BC/EF = AC/DF.

To find the value of y, we need to set up an equation based on the given information. However, without any specific information or measurements for the triangles, it is not possible to determine the exact value of y. The value of y will depend on the specific lengths of the sides of the triangles and the ratios they form.

for more such question on measurements

https://brainly.com/question/27233632

#SPJ8

Answer:

 d. AlcoholContent =β0​+β1​ Calories +ϵ 

Step-by-step explanation:

The population model would be the equation that models the relationship between two variables, in this case AlcoholContent and Calories. Since the objective is to use Alcohol Content to predict Calories, the population model we are estimating should be d. AlcoholContent =β0​+β1​ Calories +ϵ.

The population model we are estimating in this scenario is option d: AlcoholContent = β0 + β1 Calories + ϵ.  In linear regression, we aim to estimate the relationship between two variables by fitting a line to the data points.

The population model represents the true underlying relationship between the predictor variable (AlcoholContent) and the response variable (Calories).

In this case, the equation AlcoholContent = β0 + β1 Calories + ϵ suggests that the AlcoholContent is the dependent variable, and it is being predicted based on the independent variable Calories. The β0 and β1 coefficients represent the intercept and slope of the regression line, respectively. The ϵ term represents the error or residual term, which captures the variability in the data that is not accounted for by the regression model.

So, the population model we are estimating is AlcoholContent = β0 + β1 Calories + ϵ, where β0 and β1 are the coefficients to be estimated.

Learn more about population here: https://brainly.com/question/30935898

#SPJ11

Answer:

$331.02

Step-by-step explanation:

Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

mark my answer as brainliest

The height of the tree is 6.77 meters.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

Given that, the height of the person is 1.25 meters, the length of the tree's shadow is 24.65 meters, and the distance between the person and the tree is 20.1 meters.

Let the height of the tree be x.

Note that the scenario makes two similar triangles.

Since the ratio of the side lengths of similar triangles is proportional, it follows:

(24.65 - 20.1)/1.25 = 24.65/x

3.64 = 24.65/x

x = 24.65 / 3.64

x = 6.77

Hence, the height of the tree is 6.77 meters.

Learn more about similar triangles here:

https://brainly.com/question/24173643

#SPJ1

Answer:

16 cm3

Step-by-step explanation:

4 x 4 x 8 = 128

2 x 2 x 4 = 16

Answer:16 cm

Step-by-step explanation:

Answer:

A) 20

B) 28%

Step-by-step explanation:

A) In order to find percentages you need to make them in to decimals. 80% as a decimal is .8, if you multiply 25 by the decimal .8, you get 20.

B) To find the percentage all you do is divide, 7/25, this gives you the decimal .28, this as a percentage is 28%.

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

  Learn more about Derivations

  brainly.com/question/30365299

  #SPJ11

The vector equation for the line is:

r(t) = (1, 0, 6) + t(-4, 1, 4)

The parametric equations for the line.

x(t) = 1 - 4t

y(t) = t

z(t) = 6 + 4t

To find a vector equation and parametric equations for the line passing through the point (1, 0, 6) and perpendicular to the plane x + 4y + z = 7, we can first determine the direction vector of the line.

The normal vector of the plane x + 4y + z = 7 is (1, 4, 1) since the coefficients of x, y, and z represent the normal vector.

Any line perpendicular to this plane must have a direction vector orthogonal to the normal vector of the plane.

Let's call the direction vector of our line (a, b, c).

We know that the dot product of the direction vector and the normal vector of the plane is zero:

(a, b, c) ⋅ (1, 4, 1) = 0

This equation gives us a condition for the direction vector.

We can choose any values for a, b, and c as long as they satisfy this condition.

For simplicity, we can choose a = -4, b = 1, and c = 4, which gives us a direction vector (-4, 1, 4) orthogonal to the plane.

Now, let's denote the position vector of the given point (1, 0, 6) as (x₀, y₀, z₀) = (1, 0, 6).

The vector equation of the line can be written as:

r(t) = r₀ + t × v

where r₀ is the position vector of a point on the line (which is (1, 0, 6)), t is the parameter, and v is the direction vector of the line (-4, 1, 4).

Therefore, the vector equation for the line is:

r(t) = (1, 0, 6) + t × (-4, 1, 4)

Expanding this equation, we get:

x(t) = 1 - 4t

y(t) = t

z(t) = 6 + 4t

These are the parametric equations for the line passing through the point (1, 0, 6) and perpendicular to the plane x + 4y + z = 7.

Learn more about vector equation and parametric equations click;

https://brainly.com/question/30550663

#SPJ4

Answer:

5 full bowls

Step-by-step explanation:

Set up a proportion where x is the number of bowls with 17 avocados:

\(\frac{3}{1}\) = \(\frac{17}{x}\)

Cross multiply and solve for x:

3x = 17

x = 5.67

This means that 5 full bowls of guacamole can be made with 17 avocados.

Answer: 5 full bowl

Step-by-step explanation:

17 divided by 3 = 5 full bowls 2 avocados

Answer:

2. 7238.23 mm

3. 55.42 ft

4. 703.86 ft

Step-by-step explanation:

Answer:

1. 7234.56mm^2 2. 55.39ft^2 3. 706.5ft^2

Answer:

17.2x + 16.4

Step-by-step explanation:

→ Perimeter = All sides added together

8.6x + 3 + 8.6x + 3 + 5.2 + 5.2

→ Simplify

17.2x + 6 + 10.4

→ Simplify further

17.2x + 16.4

Answer:

Row n ---> 27th term is 27.

Row T ---> 27th term is 80.

Step-by-step explanation:

To find the 27th term for the top row, row n, you will use this formula:

an = a1 + f × (n-1)

The first number = 1

The common difference (f) = 1

a27 = 1 + 1 × (27-1)

a27 = 1 + 27 - 1

a27 = 28 - 1

a27 = 27

So, the 27th term is 27.

We will do the same for the row T.

an = a1 + f × (n-1)

The first number = 2

The common difference (f) = 3

a27 = 2 + 3 × (27-1)

a27 = 2 + 81 - 3

a27 = 83 - 3

a27 = 80

So, the 27th term is 80.

6c^2=4,\:v^3 so yeah that is it

Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

53

Step-by-step explanation:

A random variable X has a probability distribution as follows:

X = 0, 1, 2, 3

P(X) = 2k, 3k, 13k, 2k

where k is a positive constant. The probability P(X < 2.0) is 0.25.

What is random variable?

A quantity or item that depends on random events is formalised mathematically as a random variable, also known as a random quantity, aleatory variable, or stochastic variable. It is a function or mapping from potential outcomes to a quantifiable space, frequently to real numbers.

We know that probability sum of all events is 1

Therefore here sum of all probability events =P(X=0)+P(X=1)+P(X=2)+PX=3)=1

2k+3k+13k+2k=1

20k=1

k=1/20=0.05

For P(x<2)=P(X=0)+P(X=1)=2k+3k =5k=5*(1/20)=0.25

Hence the correct answer is b, 0.25

To learn more about random variable from the given link

https://brainly.com/question/17217746

#SPJ1

Answer:

Step-by-step explanation:

(x - y)² = x² - 2xy + y²

x = b  ; y = 3

(b - 3)² = b² - 2 *b * 3 + 3²

          = b² - 6b + 9

Answer:

a)  OA = 1 unit

b)  BC = 3 units

c)  OD = 2 units

d)  AC = 3√2 units

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{2}{x}-2\)

Point A is the x-intercept of the curve.

To find the x-intercept of the curve (when y = 0), set the function to zero and solve for x:

\(\begin{aligned}f(x) & = 0\\\implies \dfrac{2}{x}-2 & = 0\\\dfrac{2}{x} & = 2\\2 & = 2x\\\implies x & = 1\end{aligned}\)

Therefore, A (1, 0) and so OA = 1 unit.

If OB = 2 units then B (-2, 0).  Therefore, the x-value of Point C is x = -2.

To find the y-value of Point C, substitute x = -2 into the function:

\(\implies f(-2)=\dfrac{2}{-2}-2=-3\)

Therefore, C (-2, -3) and so BC = 3 units.

Asymptote: a line that the curve gets infinitely close to, but never touches.

The y-value of Point D is the horizontal asymptote of the function.

The function is undefined when x = 0 and therefore when y = -2.

Therefore, D (0, -2) and so OD = 2 units.

From parts (a) and (c):

To find the length of AC, use the distance between two points formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}\)

Therefore:

\(\sf \implies AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\)

\(\sf \implies AC=\sqrt{(-2-1)^2+(-3-0)^2}\)

\(\sf \implies AC=\sqrt{(-3)^2+(-3)^2}\)

\(\sf \implies AC=\sqrt{9+9}\)

\(\sf \implies AC=\sqrt{18}\)

\(\sf \implies AC=\sqrt{9 \cdot 2}\)

\(\sf \implies AC=\sqrt{9}\sqrt{2}\)

\(\sf \implies AC=3\sqrt{2}\:\:units\)

Your teacher must have made a typo somewhere. The expression 5^(2n-1) is not divisible by 8.

The expression 5^(2n-1) is composed of 2n-1 copies of "5" multiplied together. The key here is that 5 is the only unique prime factor of this number.

On the other hand, 8 = 2*2*2 = 2^3 showing that 2 is the only prime factor for this number. At this point, we can see that there's no way that 5^(2n-1) is divisible by 8. It all comes down to the clash of the primes 5 and 2 not matching up, and having nothing in common.

Let's consider a few concrete examples:

I'll let you try other natural numbers for n, and you'll find that \(\frac{5^{2n-1}}{8}\) isn't an integer.

Answer:

0.85

Step-by-step explanation:

I just need 20 characters

Answer: .85

Step-by-step explanation:

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

Learn more about Stratified random sampling:

https://brainly.com/question/20544692

#SPJ11