Please solve asap pls x

Answer:

9

Step-by-step explanation:

Each rectangle is the average of the ones around it.

given that v1,v2 ,v3,v4 is linearly independent vector so in order for a set of vectors to be linearly independent it must satisfy the below conditon:

   \(x_1v1+x_2v2+x_3v3+x_4v4\) =0  --(i)

  where \(x_1, x_2,x_3 ,x_4\) is some real numbers.

a) so in order to show that v1,v2+v4,v3 is linearly independent we have to

check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have :

   \(x_1v1+x_2(v2+v4) +x_3v3\)   ---(ii)

    where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (ii) we have:

     \(x_1v1+x_2v2+x_3v3+x_2v4\)  

     so the above equation is now transformed in the form of equation (i) where \(x_2 = x_4\)  

and hence \(x_1v1+x_2v2+x_3v3+x_2v4\) =0  ----(iii)

equation (iii) shows that the set of given vectors are linearly independent.

b)  so in order to show that v1 +v2, v3, v4  is linearly independent we have to check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have this equation:

   \(x_1(v1+v2)+ x_2v3 + x_3v4\)      where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (iv) we have:

     \(x_1v1+x_1v2+x_2v3+x_3v4\)  

     so the above equation is now transformed in the form of equation (i) where the cofficient of v2 is also \(x_1\)  

and hence \(x_1v1+x_1v2+x_2v3+x_3v4\) =0  ----(v)

equation (v) shows that the set of given vectors are linearly independent.

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Complete question :

let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors a) v1, v2+v4, v3 and   b) v1 +v2, v3, v4 are also linearly independent.

The vectors v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent is hence proved.

let v be a real vector space.

The v1, v2, v3, v4 are vectors in v which are linearly independent.

V={v1, v2, v3, v4} then set V is called  linearly independent if \(\forall \alpha_i \in F \\\).

∝1v1+∝2v2+∝3v3+..........+∝nvn=0

then, \(\forall \alpha_i =0 \\\) i=1,2,3......n.

let ∝1,∝2,∝3,∝4 ε F

∝1v1+∝2(v1+v2)+∝3(v1+v2+v3)+∝4(v1+v2+v3+v4)=0

v1(∝1+∝2+∝3+∝4)+v2(∝2+∝3+∝4)+v3(∝3+∝4)+v4.∝4=0

Since  v1, v2, v3, v4 are linearly independent vectors.

So ∝1+∝2+∝3+∝4=0......(1)

∝2+∝3+∝4=0....(2)

∝3+∝4=0....(3)

∝4=0...(4)

Solving eq(1), (2), (3), (4)

we get ∝1=∝2=∝3=∝4=0

So according to definition of linearly independent vectors.

A set of vectors is called linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set. If any of the vectors can be expressed as a linear combination of the others, then the set is said to be linearly dependent.

So v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent vectors hence proved.

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It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Answer:

$45

Step-by-step explanation:

Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours?

f(x) = 5| x - 8| + 20

solve for when x = 3

f(3) = 5| 3 - 8| + 20

f(3) = 5| -5| + 20

f(3) = 25 + 20

f(3) = 45

Answer:

-5.5 and 0.4 (first option in your list)

Step-by-step explanation:

Please see attached image where we have graphed the expression \(y=6x^2+31x\\\)  and the expression \(y=12\)  and looked for the two points of intersection of the parabola (representing the first expression) with the horizontal line (second expression)

From the graphing we extract that one solution for "x" is approximately -5.5, and the other one around 0.36, which can be rounded to one decimal to: 0.4. then the closest solution is that one shown as the first option in your list.

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

13.81 in

Step-by-step explanation:

the radius is equal to 1.875  and the height is equal to 1.25   .  Put these dimensions into the cylinder volume formula and you get 13.81 inches .  (plus i got this question right on one of my tests )

Answer:

Still a segment

Step-by-step explanation:

When a segment is dilated by a scale factor of r = 1, then the segment and its image would be the same length. When the points P and Q are on a line containing the center, then the dilated points P' and Q' will also be col linear with the center producing an image of the segment that is a segment.

The most reasonable estimate of the total sale of the wooden boxes would be= $147

The total number of small wooden boxes= 8

The price for the small boxes= $12.

The total price for the small boxes= 12×8 = $96

The total number of larger wooden boxes= 3

The price for the larger boxes= $17

The total price for the larger boxes= 17×3 = $51

The total price for all the boxes = 96+51 =$147

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suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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First we need to take the - signal

So the difference between the graphs y = -4x and y = 4x is that they are mirrored by the y-axis

Now we have the graph y = 4x and want the graph y = 4x + 3

We just need to move the graph y = 4x 3 units to the left

So the transformations we need is to move it 3 units to the left and to mirror it by the y-axis

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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i believe the answer would be c.

Answer:

i think its b or c

Step-by-step explanation:

The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

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The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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Answer:

1/3

Step-by-step explanation:

The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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Answer:

20/3 * 10.50 = 70

Step-by-step explanation:

Answer:

Step-by-step explanation:

We khow that 3 gallons of gasolone are worth 10.50 dollars and it takes 20 gallons to do the one way trip .

we can say that :

        20 gallons⇒ x

          =70

we deduce that : the familly badget must be equal to 70 dollars

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.

The basic mathematical operations are subtraction, addition, division, and multiplication.

These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.

In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.

The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds

For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)

The quantity of cement per pound of gravel = ²/₅ pounds or 0.4

For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)

Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.

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After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

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The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

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Answer:

$15.48

Explanation:

100 ÷ 6.46 = 15.479876

Answer:

5/36 is the simplest answer

Step-by-step explanation:

i did the math and searched it up i hope this helps

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:7 · 0 = 0 7 · 1 = 7 7 · 2 = 14

7 · 5 = 35 7 · 6 = 42 7 · 7 = 49

10 · 0 = 0 10 · 1 = 10 10 · 2 = 20

10 · 5 = 50 10 · 6 = 60 10 · 7 = 70

Step-by-step explanation:

C=5

Explain explain Explain

Answer:

the drop in the level of water in the container is 2.03 cm

Step-by-step explanation:

The volume of a cylinder can be written as;

\(V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter\)

the change in height when the volume changes can be derived by differentiating the equation.

\(dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}\)

substituting the given values;

\(\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.\)

\(dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm\)

the drop in the level of water in the container is 2.03 cm