given vectors: p= 3i, q= j
find: 1. p+q, 2. p-q, 3. 2p-3q

Answer:

f = 3

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

Using (6,8) and (f,-7) then

m = (-7 - 8)/(f - 6) = 5

- 15 = 5(f - 6)

-15 = 5f - 30

5f = 30 - 15

5f = 15

f = 3

Let's see

#a

Take 28

#2

Take 9,10

Answer:

Two-digit number greater than 25:   32

Rewrite 32 as the difference of 2 numbers: 40 - 8

Therefore, x = 40  and  y = 8

\(\begin{aligned}\implies (40-8)^2 & =40^2-2(40)(8)+8^2\\ & = (4 \cdot 10)^2-(80)(8)+64\\ & = 4^2 \cdot 10^2-640+64\\ & = 16 \cdot 100-640+64\\ & = 1600-640+64\\ & = 960+64\\ & = 1024\end{aligned}\)

Let a = 10

Let b = 11

\(\begin{aligned}\implies 10^3+11^3 & =(10+11)(10^2-10 \cdot 11+11^2)\\& = 21(100-110+121)\\ & = 21(-10+121)\\ & = 21(111)\\& = 21 (100 + 10 + 1)\\ & = (21 \cdot 100)+(21 \cdot 10)+(21 \cdot 1)\\ & = 2100 +210+21\\ & = 2310 + 21\\ & = 2331\end{aligned}\)

Answer:

The maximum height of the ball is 380.25 feet in the air.

Step-by-step explanation:

The quadratic function:

\(h(t)=-16t^2+132t+108\)

Models the ball's height h(t), in feet, above the ground t seconds after it was thrown.

We want to determine the maximum height of the ball.

Note that this is a quadratic function. Therefore, the maximum or minimum value will always occur at its vertex point.

Since our leading coefficient is leading, we have a maximum point. So to find the maximum height, we will find the vertex. The vertex of a quadratic equation is given by:

\(\displaystyle \left(-\frac{b}{2a},f\left(\frac{b}{2a}\right)\right)\)

In this case, a = -16, b = 132, and c = 108. Find the t-coordinate of the vertex:

\(\displaystyle t=-\frac{132}{2(-16)}=-\frac{132}{-32}=\frac{33}{8}=4.125\)

So, the maximum height occurs after 4.125 seconds of the ball being thrown.

To find the maximum height, substitute this value back into the equation. Thus:

\(h(4.125)=-16(4.125)^2+132(4.125)+108=380.25\text{ feet}\)

The maximum height of the ball is 380.25 feet in the air.

Answer:

$7500

Step-by-step explanation:

Let x = amount of monthly sales.

Choice A:

"monthly salary of $500 plus a bonus of 25% of his monthly sales"

monthly salary = 0.25x + 500

Choice B:

"$2,000 monthly salary with a 5% bonus on sales"

monthly salary = 0.05x + 2000

We set the total monthly salaries equal and solve for x.

0.25x + 500 = 0.05x + 2000

0.2x = 1500

x = 1500/0.2

x = 7500

Answer: $7500

Answer:

12.5

Step-by-step explanation:

A=HbB/2=5*5/2=12.5

Answer:

The ladder will go 6 feet up.

Answer:

1)

The hypotenuse is the longest side of a triangle. It is ALWAYS the one across from the right angle (depicted as the box in the corner at 90 degrees). Therefore the 2 sides that intersect the 90-degree angle are "leg" and "leg" and the longest side is the"hypotenuse"

2)

The Pythagorean theorem states: \(a^{2} + b^{2} = c^{2}\)  where a and b are sides and c is the hypotenuse.

\(a^{2} + b^{2} = c^{2} \\8^{2} + 6^{2} = c^{2} \\64 + 36 = c^{2} \\100 = c^{2} \\\sqrt{100} = c\\10 = c\)

For your purposes, a and b do not matter which number you choose as long as you make sure that they are sides and not the hypotenuse.

3)

The Pythagorean theorem states: \(a^{2} + b^{2} = c^{2}\)  where a and b are sides and c is the hypotenuse.

\(a^{2} + b^{2} = c^{2} \\4^{2} + 7^{2} = c^{2} \\16 + 49= c^{2} \\65 = c^{2} \\\sqrt{65} = c\\8.0622 = c\)

Hope that helps!

T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

The number of baskets that were made is 4.

The first step is to form a pair of simultaneous equations using the information provided in the question:

x - 6y = 16 equation 1

x - 8y = 8 equation 2

Where:

The elimination method would be used to solve for the number of baskets :

Subtract equation 2 from equation 1:

2y = 8

Divide both sides of the equation by 2L

y = 8 / 2

y = 4

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Answer:

y =5

Step-by-step explanation:

2y + 4y = 30

6y = 30

Divide both sides by six

y = 30/6

y = 5

Answer:

= 5

Explain: Combine like terms

3 0 = 2 + 4

30=6y

Divide both sides of the equation by the same term

3 0 = 6

30/6 = 6y/6

Simplify:

1)Divide the numbers

2)Cancel terms that are in both the numerator and denominator

3)Move the variable to the left

= 5

The value of 'x' is highlighted in the box

inverse operations = x=.5

simplify = x=1/2

inverse operations = x=.5

solution = x=1/2

check:

Let x = 3/2

10×3/2-5=10

use this rule = a×b/c=ab/c

10×3/2-5=10

Simplify  10×3  to 30.

30/2-5=10

Simplify 30/2 to 15

15-5=10

Simplify 15-5=10

10=10

Checked✅

Answer:

1/6

Step-by-step explanation:

4/9 live in Wells, so the probability of ONE winner being from Wells is 4/9.  Now there are 8 people left, and 3 live in Wells.  The odds of another person being chosen from Wells is 3/8.

4/9x3/8=12/72

12/72=1/6

Answer:

θ = \(\frac{\pi }{3}\) (60° )

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

cos²θ - sin²θ = 2 - 5cosθ

cos²θ - (1 - cos²θ) = 2 - 5cosθ

cos²θ - 1 + cos²θ = 2 - 5cosθ

2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )

2cos²θ + 5cosθ - 3 = 0 ← in standard form

(cosθ + 3)(2cosθ - 1) = 0 ← in factored form

Equate each factor to zero and solve for θ

cosθ + 3 = 0

cosθ = - 3 ← not possible as - 1 ≤ cosθ  ≤ 1

2cosθ - 1 = 0

cosθ = \(\frac{1}{2}\) , so

θ = \(cos^{-1}\) (\(\frac{1}{2}\) ) = \(\frac{\pi }{3}\) ( or 60° )

Answer:

\( \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}\)

Step-by-step explanation:

\( \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation\)

In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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The value of x for the given triangle will be 4√3.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle,

The unknown third angle will be 180° - 60° - 30° = 90°.

Thus, it is a right-angle triangle so a trigonometric ratio will apply.

By sin60°  = x/8

x = 8(√3/2) = 4√3

Hence "The value of x for the given triangle will be 4√3".

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Answer: newtons

Step-by-step explanation:

Answer:

I believe it is Newtons :)

Step-by-step explanation:

Answer:

310559.29375

Step-by-step explanation:

i multiplied the original 700,000 times 0.15 to see what that would equal which was 105,000 then took that away from 700k which was 595,000 then multiplied that by 0.15 which was 89,250 i did this process 5 times and came up with 310,559. 29375

Building the Cartesian Plane with the proper scale we can conclude that

Answer:

x = -18

Step-by-step explanation:

1/2x = -9

(21)1/2x = -9(2/1)

x = -9/1(2/1)

x = -18/1

x = -18

Answer:

x = -18

Step-by-step explanation:

1/2x = -9

Multiply each side by 2

1/2x * 2 = -9*2

x = -18

The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of "P-Value."

A null hypothesis is a sort of statistical hypothesis which asserts that there is no statistical significance in a particular set of observations.

Using sample data, hypothesis testing is performed to determine the believability of a theory. It really is expressed as H0 and is also known to simply as "null."

Some key features regarding null hypothesis are-

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Answer:

-22

Step-by-step explanation:

Plug in 5 for x.

y = -3(5) - 7

y = -15 - 7

y = -22

The features of the sine function are given as follows:

The equation is given as follows:

y = 3sin(0.25πx) + 1.

The standard definition of a sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The minimum value is of -2, while the maximum value is of 4, hence the midline is given as follows:

y = (-2 + 4)/2

y = 1.

The difference between the minimum and the maximum value is of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

The function with no vertical shift would oscillate between -A = -3 and A = 3, while this function oscillates between -2 and 4, hence the vertical shift is given as follows:

C = 1.

The shortest distance between repetitions of the function is of 8 units, hence the period is of 8, the frequency is of 1/8, and the coefficient B is given as follows:

2π/B = 8

8B = 2π

B = π/4.

B = 0.25π.

Hence the function is defined as follows:

y = 3sin(0.25πx) + 1.

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Answer:

-9 = d

Step-by-step explanation:

Answer:

d= -9

Step-by-step explanation:

Answer:

Hello Darling! Answer: 14%

Step-by-step explanation:

Now I'm not always accurate, I can re-check myself if you think it isn't right! c;

The probability that a randomly selected day in June will be foggy if it is cloudy can be determined by calculating the conditional probability of foggy days given cloudy days.

Let's denote the events as follows: C represents a cloudy day, and F represents a foggy day. We are given that the probability of a day being cloudy is 0.87 (87%) and the probability of a day being both cloudy and foggy is 0.73 (73%).

To find the probability of a day being foggy given that it is cloudy, we use the formula for conditional probability:

P(F | C) = P(F and C) / P(C)

In this case, P(F and C) represents the probability of a day being both foggy and cloudy, which is given as 0.73 (73%), and P(C) represents the probability of a day being cloudy, which is given as 0.87 (87%).

Therefore, the probability of a randomly selected day in June being foggy if it is cloudy can be calculated as:

P(F | C) = 0.73 / 0.87 ≈ 0.839

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Answer:

k750×60x=Ohio

Step-by-step explanation:

Swag like Ohio down in Ohio