Which expression represents the length of the spring after Gerard removes some weight? Gerard adds weight to the end of the hanging spring D-- The song stretches to a length of p centimeters. Gerard removes some weight and the song moves up by a 8 E-p) - 9 D-9--​

By supposing that 7₁, 72 are linearly dependent in a vector space V. The coefficient of 7₁ is 1 and the coefficient of 72 is 0, while in the second linear combination, the coefficient of 7₁ is 0 and the coefficient of 72 is 1. Therefore, we can conclude that V₁ + V2, V₂ - V₁ is also linearly dependent.

To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we will begin by using the given linear combination of vectors to determine whether they are linearly dependent or independent. Suppose that 7₁, and 72 are linearly dependent in a vector space V.

Let us recall that a set of vectors is linearly dependent if it can be represented as a linear combination of other vectors in the vector space. This implies that if 7₁, 72 are linearly dependent, then there exist scalars α and β, not all zero, such that α7₁ + β72 = 0. To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we need to use the definitions of vector addition and subtraction to writing each of these vectors as a linear combination of 7₁ and 72. Let's begin with V₁ + V2.

Using the definition of vector addition, we have

V₁ + V2 = 1 · 7₁ + 1 · 72 = 7₁ + 72.

Similarly, using the definition of vector subtraction, we have

V₂ - V₁ = -1 · 7₁ + 1 · 72 = -7₁ + 72.

Now we can write V₁ + V2, V₂ - V₁ as linear combinations of 7₁ and 72:

V₁ + V2 = 1 · (7₁ + 72) + 0 · (-7₁ + 72)V₂ - V₁

= 0 · (7₁ + 72) + 1 · (-7₁ + 72)

Notice that the coefficients in each linear combination are not all zero. We can say that V₁ + V2, V₂ - V₁ is linearly dependent.

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answer:

3 plants are left !

step-by-step explanation:

hi there!

first lets use our times table to see which number gets use closest to 35 when it is multiplied by 4

4, 8, 12, 16, 20, 24, 28, 32,

4 * 8

= 32

then you can just subtract 35 by 32 to get you final answer of

35 - 32

= 3 plants are left over

( i hope i did the problem right since the wording of it was kinda hard to understand it )

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i made a table with each number being the plant! just in case your a visual learner like me!

but i hope this help you and if i made anything confusing or if i made a mistake please let me know! but other then that i hope you have a good rest of your day :)

There are 3 plants left.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Total number of plants = 35

And, You want to split them equally between 4 sections of your garden.

Now,

To find the left plants after splitting into 4 sections, we can divide and find the remainder as;

The number of left plants = 35 ÷ 4

 4 ) 35 ( 8

    - 32

    -------

         3

Clearly, The remainder = 3

Thus, There are 3 plants left.

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Answer:

The answer is 7 (A)

Step-by-step explanation:

Answer:

D. The length is the same as line MN.

Step-by-step explanation:

Even if the line is moved any one bit, the length of the line will not change. So as a result, A, B & C are already out. That leaves D as our answer.

[tex]f+44^{\circ}[/tex] and [tex]71^{\circ}[/tex] are opposite angles.

Therefore

[tex]f+44^{\circ}=71^{\circ}\\f=27^{\circ}[/tex]

27°

Using information about angles, we can create an equation to solve for f.

Verticle Angles

There is a special angle relationship known as vertical angles. Vertical angles are opposite angles made by interesting lines. The left angle  (made up of f and 44°) and the right angle (71°) are vertical angles. We know this because they are opposite each other and formed by the same interesting lines. Verticle angles are always congruent. This means that their measurements are equal.

Solving for f

We can use the information above to create an equation. Since we know that the left and right angles are congruent, we can set the equal to each other.

Now, we can subtract 44 from both sides and solve for f.

So, angle f must equal 27°.

Answer: 11

Step-by-step explanation:

Sooooo all I did was take the formula for the area of a triangle ( A= 1/2(b)(h) 0 and plug In the values. So 'b' would be 4 and 'h' would be 5.5. I assumed this rectangle had equal widths and equal heights.

Answer:

B its B

Step-by-step explanation:

a) the reading on the thermometer after 3 more minutes will be -3 degrees Celsius.

b) the thermometer will read 6 degrees Celsius after 1.5 minutes.

To solve the given problem, we can assume that the temperature change follows a linear pattern based on the given information.

(a) To find the reading on the thermometer after 3 more minutes, we need to determine the rate of temperature change per minute. From the initial reading of 21 degrees Celsius to the reading after one minute of 15 degrees Celsius, there was a temperature decrease of 6 degrees Celsius in one minute.

Therefore, the rate of temperature decrease is 6 degrees Celsius per minute. If this rate remains constant, after 3 more minutes, the thermometer will show a further temperature decrease of:

3 minutes * 6 degrees Celsius per minute = 18 degrees Celsius

Thus, the reading on the thermometer after 3 more minutes will be 15 degrees Celsius - 18 degrees Celsius = -3 degrees Celsius.

(b) To find when the thermometer will read 6 degrees Celsius, we need to determine the time it takes for the temperature to decrease from 15 degrees Celsius to 6 degrees Celsius.

The initial reading is 15 degrees Celsius, and the final desired reading is 6 degrees Celsius. Therefore, we need to calculate the time it takes for a temperature decrease of:

15 degrees Celsius - 6 degrees Celsius = 9 degrees Celsius

Since the rate of temperature decrease is 6 degrees Celsius per minute, we can set up the equation:

9 degrees Celsius = 6 degrees Celsius per minute * t minutes

Solving for t (the time it takes to reach 6 degrees Celsius):

t = 9 degrees Celsius / 6 degrees Celsius per minute = 1.5 minutes

Therefore, the thermometer will read 6 degrees Celsius after 1.5 minutes.

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Answer:

Select all possible values for x in the equation.

x cubed=375.

5*the cubed root of 3

the cubed root of 375

75*the cubed root of 5

125*the cubed root of 3

I am trying to do a practice test to prepare for my real test tomorrow and I don't understand the question. Can anyone help explain it plz any help would be great.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D

Answer:

D. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 69bpm.

Step-by-step explanation:

Hypothesis testing is used in statistics to confirm the validity of a statement or observation. Null hypothesis is the original observation for which the test is being conducted. Alternative hypothesis is set against the null hypothesis to reach a conclusion whether to accept or reject the null hypothesis. In the given scenario there is sufficient evidence to reject the null hypothesis.

Answer:

2 laborers and 33 ops

Step-by-step explanation:

Given

Let:

L = Laborers

P = Ops

From the statements, we have:

[tex]L + P = 35[/tex] -- total people hired; and

[tex]140P + 100L = 4820[/tex] ---number of hirees

Required

Solve for L and P

Make L the subject in: [tex]L + P = 35[/tex]

[tex]L = 35 - P[/tex]

Substitute [tex]L = 35 - P[/tex] in [tex]140P + 100L = 4820[/tex]

[tex]140P + 100(35 - P) = 4820[/tex]

[tex]140P + 3500 - 100P = 4820[/tex]

Collect like terms

[tex]140P - 100P = 4820 - 3500[/tex]

[tex]40P = 1320[/tex]

Solve for P

[tex]P = 1320/40[/tex]

[tex]P = 33[/tex]

Substitute [tex]P = 33[/tex] in [tex]L = 35 - P[/tex]

[tex]L = 35 - 33[/tex]

[tex]L = 2[/tex]

(a) The probability that a randomly chosen wedge of cheddar cheese is greater than 10.14 is found using the standard normal distribution as follows:

P(Z > z) = P(Z > (10.14 - µ)/σ)

= P(Z > (10.14 - 10.2)/0.2)

≈ 0.3085.

Therefore, the probability is approximately 0.3085.

(b) If a sample of 16 is randomly chosen, then the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of σ/√n,

Where n = 16.

The sample standard deviation is given by σ = 0.2, so the standard deviation of the sample mean weight is:

σ/√n = 0.2/√16

= 0.05.

Therefore, the distribution of the sample mean weight is approximately normal with a mean of 10.2 ounces and a standard deviation of 0.05 ounces.

(c) The probability that the sample mean weight of this sample of 16 is less than 10.14 is found using the standard normal distribution as follows:

P(Z < z) = P(Z < (10.14 - µ)/(σ/√n))

= P(Z < (10.14 - 10.2)/(0.2/√16))

≈ P(Z < -1.6)

≈ 0.0548.

Therefore, the probability is approximately 0.0548.

(d) The probability that the sample mean weight of this sample of 16 is greater than 10.14 is found using the standard normal distribution as follows:

P(Z > z) = P(Z > (10.14 - µ)/(σ/√n))

= P(Z > (10.14 - 10.2)/(0.2/√16))

≈ P(Z > -1.6)

≈ 0.9452.

Therefore, the probability is approximately 0.9452.

(e) The probability that the sample mean weight of this sample of 16 is between 10.14 and 10.3 is found

Using the standard normal distribution as follows:

P(a < Z < b) = P((a - µ)/(σ/√n) < Z < (b - µ)/(σ/√n))

= P((10.14 - 10.2)/(0.2/√16) < Z < (10.3 - 10.2)/(0.2/√16))

≈ P(-1.6 < Z < 2)

≈ 0.9452 - 0.0548

= 0.8904.

Therefore, the probability is approximately 0.8904.

(f) Let x be the average weight of a sample of these 16 cheese wedges that is below some value z.

Then, the probability that x is less than z is 0.07.

Using the standard normal distribution, we can find the z-score such that

P(Z < z) = 0.07 as follows:

z = inv Norm(0.07)

≈ -1.4758.

Therefore, the average weight of a sample of these 16 cheese wedges that is below the value z is:

x = µ + z(σ/√n)

= 10.2 + (-1.4758)(0.2/√16)

≈ 10.0625.

Therefore, there is only a 7% chance that the average weight of a sample of these 16 cheese wedges will be below 10.0625.

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The level of measurement used in the operationalization of extracurricular participation is categorical/nominal.

In the operationalization of extracurricular participation, the measurement of students' involvement in university-based clubs is done using categorical/nominal level of measurement.

This is evident from the variable created to reflect whether students were involved in at least one activity, indicating a binary (yes/no) response. The subsequent breakdown of the activities listed into different categories, such as sports/recreation, fraternities/sororities, cultural, departmental/professional, campus programs, special interest, service, and religious, further supports the use of categorical measurement.

Each activity falls into a distinct category, and the percentages represent the proportions of students engaged in each category. Categorical/nominal measurement allows for classifying and organizing data into mutually exclusive categories, without any inherent order or numerical value associated with the category.

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$105

15*3=45

12*5=60

60+45=105

(12*5)+(15*3)=105

Can i get brainliest

The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

At a hardware store, DVDs are at a bargain. A few DVDs cost $15.00 each and some expenses $12.00 each. Bart bought 8 DVDs and spent a sum of $105.00.

Let 'x' be the number of $15 DVDs and 'y' be the number of $12 DVDs. Then the equations are given as,

x + y = 8                     ...1

15x + 12y = 105         ...2

From equations 1 and 2, then we have

15x + 12(8 - x) = 105

15x + 96 - 12x = 105

3x = 9

x = 3

Then the value of y is given as,

y = 8 - 3

y = 5

The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.

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The value of limits after using limit laws is [tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]

What are Limit Laws?

Limit laws, also known as limit properties or limit theorems, are a set of rules and principles that allow us to simplify and evaluate limits of functions. These laws provide a systematic approach to finding the limit of a more complex expression by breaking it down into simpler parts.

Given:

[tex]\lim_{x \to 2} f(x) &= -3 \\\lim_{x \to 2} g(x) &= 4 \\\lim_{x \to 2} h(x) &= 7\end{align*}\textbf{(a) Calculate} $\lim_{x \to 2} (f(x) - 2g(x))$:[/tex]

Using the limit laws, we can split the expression and apply the limit laws individually:

[tex]\lim_{x \to 2} (f(x) - 2g(x)) &= \lim_{x \to 2} f(x) - \lim_{x \to 2} (2g(x)) \\&= \lim_{x \to 2} f(x) - 2 \lim_{x \to 2} g(x) \\&= (-3) - 2(4) \\&= -3 - 8 \\&= -11[/tex]

Therefore,[tex]$\lim_{x \to 2} (f(x) - 2g(x)) = -11$.[/tex]

[tex]\textbf{(b) Calculate} $\lim_{x \to 2} (h(x))^2$:[/tex]

Again, using the limit laws, we can apply the limit to the expression:

[tex]\lim_{x \to 2} (h(x))^2 &= \left(\lim_{x \to 2} h(x)\right)^2 \\&= (7)^2 \\&= 49[/tex]

Therefore,

[tex]\lim_{x \to 2} (h(x))^2 = 49$.\textbf{\\\\(c) Calculate} $\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)}$:[/tex]

Applying the limit laws, we can evaluate the limit as follows:

[tex]\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} &= \frac{\lim_{x \to 2} h(x) \cdot \lim_{x \to 2} g(x)}{\lim_{x \to 2} f(x)} \\\\&= \frac{7 \cdot 4}{-3}\\ \\&= \frac{28}{-3}[/tex]

Therefore,[tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]

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At a certain compound interest rate, the amount of 100 will increase to 200 in x years, 200 will increase to 300 in y years, and 300 will increase to 1,500 in z years. We need to find an expression for n, the number of years it takes for 600 to increase to 1,000.

The given information implies that the ratio of the final amount to the initial amount after a certain number of years is constant. We can express this ratio as follows:

(200 / 100) = (300 / 200) = (1500 / 300)

Simplifying this equation, we get:

2 = 3/2 = 5

Now, let's calculate the value of n. We know that 600 will increase to 1,000 in n years. We can set up a ratio using the same constant ratio calculated above:

(1000 / 600) = (300 / 200)

Simplifying the equation, we have:

5/3 = 3/2

Cross-multiplying, we get:

(5 * 2) = (3 * 3)

10 = 9

Since the equation is not valid, it means there is no value of n that satisfies the given conditions. Therefore, we cannot express n in terms of x, y, and z.

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Answer:

Step-by-step explanation:

If they are added, they are supplementary. If anything else is done to them, there is no answer.

89 + 91 = 180 Supplementary angles add to 180.

Answer:

answer is 1

Step-by-step explanation:

Step-by-step explanation:

The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.

The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)

The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)

The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)

Hope that helps :)

Answer:

x=20

Step-by-step explanation:

Hello There!

Remember the exterior angle of a triangle rule:

An exterior angle of a triangle is equal to the sum of the opposite interior angles

Knowing this, we can create an equation to solve for x

exterior angle (100) = sum of opposite interior angles (3x+2x)

100 = 2x+3x

now we solve for x

step 1 combine like terms

2x+3x=5x

now we have 100=5x

step 2 divide each side by 5

5x/5=x

100/5=20

we're left with x = 20

Answer:

With their steel hoofs, their long legs, their stag-like muscles, their thick skins, their powerful horns, they could walk the roughest ground, cross the widest deserts, climb the highest mountains, swim the widest rivers, fight off the fiercest bands of wolves, endure hunger, cold, thirst and punishment as few beasts of the earth have ever shown themselves capable of enduring.

Answer : a) a random variable X can only take the six values (1,2,3,4,5, and 6 ). If each value has equal probability, then p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6

b) The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9

Explanation :

A probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.[1] Sometimes it is also known as the discrete density function.

The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

a) If each value has equal probability, the pmf of the random variable X which can only take the six values (1,2,3,4,5, and 6) is : p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6

b)If the probabilities of X(0,1,2, and 3) are 1/9,2/9,2/9, and 4/9. The pmf of the random variable X is:p(0) = 1/9p(1) = 2/9p(2) = 2/9p(3) = 4/9

The sum of these probabilities is:p(0) + p(1) + p(2) + p(3) = 1/9 + 2/9 + 2/9 + 4/9 = 9/9 = 1

So, the pmf is defined for all X.

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Answer:

[tex]f(t) = 1450(1.025)^{t}[/tex]

Step-by-step explanation:

Given

[tex]P =1450[/tex] -- principal

[tex]r = 2.5\%[/tex] --- rate

[tex]n = 1[/tex] --- compounded once a year

Required

Determine the function for compound interest

Compound interest f(t) is calculated as:

[tex]f(t) =P(1 + r/n)^{nt[/tex]

So, we have:

[tex]f(t) = 1450(1 + 2.5\%/1)^{1 * t}[/tex]

[tex]f(t) = 1450(1 + 2.5\%)^{t}[/tex]

[tex]f(t) = 1450(1 + 0.025)^{t}[/tex]

[tex]f(t) = 1450(1.025)^{t}[/tex]

Answer:

DON'T LOOK AT THE PICTURE!!

Step-by-step explanation:

Answer:

Micheal surveyed 60 students.

Answer: Look at the explanation please.

Step-by-step explanation:

Please note that I am using what is in the Mathematics textbook.

So we need to know for the students who play Exactly 1 sport.

So you have to make an equation. It will look like this...

15/60 = x/300

Note that we get the 15 from the table of the number of students. We get 60 from adding 13+15+32 which is all the students Michael has surveyed.   Lastly we get 300 from the question There are 300 students in his school.

x = 75 when you do the math. Cross multiply and divide.

Hope this helps :)

The angle of incidence for a beam of light in air striking a slab of crown glass, where the angle of reflection is twice the angle of refraction, can be determined using the laws of reflection and refraction. The angle of incidence is approximately 39.2 degrees.

we can apply the laws of reflection and refraction to find the relationship between the angles. Let's denote the angle of incidence as θ, the angle of reflection as θ_r, and the angle of refraction as θ_t.

According to the law of reflection, the angle of reflection is equal to the angle of incidence: θ_r = θ.

According to Snell's law of refraction, the relationship between the angles of incidence and refraction is given by: n_1 × sin(θ) = n_2 × sin(θ_t), where n_1 and n_2 are the refractive indices of the two media.

In this case, the light travels from air (with a refractive index of approximately 1) to crown glass (with a refractive index of 1.52). Substituting the values, we have: sin(θ) = (1.52 / 1) × sin(θ_t).

Since the angle of reflection is twice the angle of refraction, we can write: θ = 2θ_t.

Substituting this relation into the previous equation, we get: sin(2θ_t) = (1.52 / 1) × sin(θ_t).

Using the double-angle trigonometric identity, sin(2θ_t) = 2sin(θ_t)cos(θ_t), we have: 2sin(θ_t)cos(θ_t) = 1.52sin(θ_t).

Dividing both sides by sin(θ_t), we obtain: 2cos(θ_t) = 1.52.

Solving for cos(θ_t), we have: cos(θ_t) = 1.52 / 2.

Taking the inverse cosine, we find: θ_t = cos^(-1)(1.52 / 2) ≈ 26.8 degrees.

Finally, substituting this value into θ = 2θ_t, we get: θ ≈ 2 × 26.8 degrees ≈ 53.6 degrees.

Hence, the angle of incidence is approximately 39.2 degrees.

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The probability of three people sharing the same birthdays is approximately [tex]0.0000075[/tex] or [tex]0.00075[/tex]%, and there are three different pairs of people when there are three humans.

In conclusion, the probability of three people sharing the same birthdays is extremely low (approximately [tex]0.0000075 \ or \ 0.00075\%[/tex]), and when there are three humans, there exist three different pairs of people.

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Answer:

125

Step-by-step explanation:

5 to the 3rd power means 5³

5³ = 5x5x5

= 125