OR THEME QQ ZOOM
albertos monthly income is $2,400. Part of Alberto's monthly budget is shown in the
below
Category
groceries
savings
Payment
ultilities
Monthly Budget
Amount of Money
$900
$350
$165
5865
$120
percentage of Alberto's income is used to pay for his utilities?

40%
28%
64%
5%

a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.

b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.

c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.

The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set  B or including more sets

For the first problem, the sets  contain:

n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0

So,  n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

               = 10 +15+25-0-0-0-0-0

              =  50

For the second  problem, since no student can have  more than one major.

So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)

As  we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17

So ,  (A∪B∪C∪D∪E∪F∪G) =  31+88+19+11+41+22+17= 229

For the third problem,  we have

n(A)=5

n(B)=3

n(C)=2

n(D)=7

n(E)=6

So, the number of elements will be (A∪B∪C∪D∪E) =  5+3+2+7+6 =23

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Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question the original line is

y = - 1/4x - 6

Comparing with the general equation above

Slope = - 1/4

Since the lines are parallel their slope are also the same

Slope of parallel line = - 1/4.

Equation of the line using point (12,4) and slope - 1/4 is

\(y - 4 = - \frac{1}{4} (x - 12) \\ y - 4 = - \frac{1}{4} x + 3 \\ y = - \frac{1}{4} x + 3 + 4\)

We have the final answer as

\(y = - \frac{1}{4} x + 7\)

Hope this helps you

In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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The equation that represents the growth or change in the population is p = p =254.9t + 38,655 and it will take 44.5 years to reach 50,000 people.

First, let's determine the growth per year:

41,204 people - 38, 655 people= 2,549 people/ 10 years = 254.9 people per year. Now, based on this, we can write the equation as follows : 254.9t + 38,655 (initial population)

Now, let's calculate the value of t when p is 50,000:

50,000 = 254.9t + 38,655

50,000 - 38,55= 254.9t

11,345/ 254.9= t +

t= 44.5 years

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Answer:

A = 24.15cm2 ~ 24.2cm2

Step-by-step explanation:

Area is calculated by

\(a = l \times w\)

a = area

l = length = 6.9cm

w = width = 3.5cm

A= 3.5cm × 6.9cm

A = 24.15 cm2

so the area is 24.15cm2 ~ 24.2cm2

Therefore, the percentage of girls in the school is approximately 49.02% and the percentage of boys in the school is approximately 50.98%.

Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. It is often used to represent a portion or a part of a whole as a percentage. For example, if there are 20 red balls out of a total of 100 balls, then the percentage of red balls is (20/100) x 100% = 20%. It is a common way of expressing ratios, proportions, and changes in quantity.

Here,

To find the percentage of girls and boys in the school, we need to first find the total number of students in the school.

Total number of students = 250 (girls) + 260 (boys) = 510

Percentage of girls = (Number of girls / Total number of students) x 100%

= (250 / 510) x 100%

= 49.02%

Percentage of boys = (Number of boys / Total number of students) x 100%

= (260 / 510) x 100%

= 50.98%

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Given: x = -2; y = -3; z = 5

It is clear that a numerical term can only be evaluated from an expression filled with numbers (no variables). In the expression provided, we have two variables, where y is being subtracted from x.

The expression can't be simplified because there is no like terms in the expression. However, since there are specific numerical values for each variable, we can substitute the numerical values for the variables in the expression and simplify the expression.

As planned, let's substitute the variables into the expression

Here, we know that x = -2 and y = -3.

If -2 is being subtracted by a negative integer, the negative integer will become positive, and the "minus sign" will be converted to a "plus sign".

We can conclude that 1 is the solution to the expression.

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The value of the probability density function (pdf) at 0 for a uniform random variable between 5 and 15 is 0, because the pdf for a uniform distribution is constant between its minimum and maximum values, and is 0 elsewhere.

To explain further, a uniform distribution is a continuous probability distribution where every value within a certain range has an equal chance of being selected. In this case, the range is between 5 and 15. The pdf for a uniform distribution is constant within the range of the distribution and is 0 outside of it.

Since 0 is not within the range of the uniform distribution, the pdf at 0 is 0. This means that the probability of selecting a value of 0 from this uniform distribution is 0. The area under the pdf curve between 5 and 15 is equal to 1, which means that the probability of selecting a value within this range is 1.

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Answer: all real numbers

Step-by-step explanation: got it right on edguenity

The vector field is not conservative since its curl is non-zero. Therefore, there is no function \( f \) such that \( \vec{F} = \nabla f \).



To determine if the vector field \( \vec{F} = \langle 3x+4y, 4x+6y \rangle \) is conservative, we can check if its curl is zero. If the curl is zero, then the vector field is conservative. Let's calculate the curl of \( \vec{F} \):

The curl of \( \vec{F} \) is given by:

\( \nabla \times \vec{F} = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right) \times \langle 3x+4y, 4x+6y \rangle \)

Expanding the cross product, we get:

\( \nabla \times \vec{F} = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right) \times \langle 3x+4y, 4x+6y \rangle \)

\( = \left( \frac{\partial}{\partial y} (4x+6y) - \frac{\partial}{\partial z} (4x+6y), \frac{\partial}{\partial z} (3x+4y) - \frac{\partial}{\partial x} (4x+6y), \frac{\partial}{\partial x} (4x+6y) - \frac{\partial}{\partial y} (3x+4y) \right) \)

\( = \langle 6-6, 0-4, 4-3 \rangle \)

\( = \langle 0, -4, 1 \rangle \)

Since the curl of \( \vec{F} \) is not zero (it has non-zero components), the vector field \( \vec{F} \) is not conservative.

Therefore, the vector field is not conservative since its curl is non-zero. Therefore, there is no function \( f \) such that \( \vec{F} = \nabla f \).

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9514 1404 393

Answer:

  y = 5x -2

Step-by-step explanation:

The slope is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (8 -3)/(2 -1) = 5

The y-intercept is given by the formula:

  b = y -mx

  b = 3 -5(1) = -2

Then the slope-intercept form equation is ...

  y = mx +b

  y = 5x -2 . . . . . . . . using the m and b we found above

The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

In this question,

The differential equation is

yʹ=y(3−ty) ------- (1)

Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.

By Euler's method,

\(y_{n+1}=y_n+hf_n\)

where \(f_n=f(t_n,y_n)\)

For, t = 0, y = 0,

\(y_{1}=y_0+hf_0\) and

\(f_0=f(t_0,y_0)\)

Substitute in equation 1,

⇒ f(0,0.5) = 0.5(3-(0)(0.5))

⇒ f(0,0.5) = 0.5(3-0)

⇒ f(0,0.5) = 0.5(3)

⇒ f(0,0.5) = 1.5

Then, \(y_{1}=y_0+hf_0\) becomes,

⇒ y₁ = 0.5 + (0.1)(1.5)

⇒ y₁ = 0.5 + 0.15

⇒ y₁ = 0.65

For, t = 1, y = 1,

\(y_{2}=y_1+hf_1\) and

\(f_1=f(t_1,y_1)\)

⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))

⇒ f(0.1,0.65) = 0.65(3-0.065)

⇒ f(0.1,0.65) = 1.90

Then, \(y_{2}=y_1+hf_1\) becomes,

⇒ y₂ = 0.65+(0.1)(1.90)

⇒ y₂ = 0.84

For t = 2, y = 2,

\(y_{3}=y_2+hf_2\) and

\(f_2=f(t_2,y_2)\)

⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))

⇒ f(0.2,0.84) = 0.84(3-0.168)

⇒ f(0.2,0.84) = 2.3788

Then, \(y_{3}=y_2+hf_2\)

⇒ y₃ = 0.84+(0.1)(2.3788)

⇒ y₃ = 1.0778

For t = 3, y = 3,

\(y_{4}=y_3+hf_3\) and

\(f_3=f(t_3,y_3)\)

⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))

⇒ f(0.3,1.0778) = 1.0778(3-0.32334)

⇒ f(0.3,1.0778) = 2.8848

Then, \(y_{4}=y_3+hf_3\) becomes

⇒ y₄ = 1.0778+(0.1)(2.8848)

⇒ y₄ = 1.3584

For t = 4, y = 4,

\(y_{5}=y_4+hf_4\) and

\(f_4=f(t_4,y_4)\)

⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))

⇒ f(0.4,1.3584) = 1.3584(3-0.5433)

⇒ f(0.4,1.3584) = 3.3372

Then, \(y_{5}=y_4+hf_4\) becomes

⇒ y₅ = 1.3584 + (0.1)(3.3372)

⇒ y₅ = 1.6921

For t = 5, y = 5,

\(y_{6}=y_5+hf_5\) and

\(f_5=f(t_5,y_5)\)

⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))

⇒ f(0.5,1.6921) = 1.6921(3-0.84605)

⇒ f(0.5,1.6921) = 3.6447

Then, \(y_{6}=y_5+hf_5\) becomes

⇒ y₆ = 1.6921 + (0.1)(3.6447)

⇒ y₆ = 2.05657

Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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The acceleration of the car at t = 3 seconds is 110 m/s^2.To find the acceleration of the car at t = 3 seconds,

we need to take the second derivative of the position function s(t).

Given the position function s(t) = 2t^4 - 5t^3 - 8t^2 - 5, we first find the velocity function by taking the derivative of s(t) with respect to t:

v(t) = s'(t) = d/dt (2t^4 - 5t^3 - 8t^2 - 5)

Taking the derivative term by term, we get:

v(t) = 8t^3 - 15t^2 - 16t

Next, we find the acceleration function by taking the derivative of v(t) with respect to t:

a(t) = v'(t) = d/dt (8t^3 - 15t^2 - 16t)

Taking the derivative term by term, we get:

a(t) = 24t^2 - 30t - 16

Now we can find the acceleration at t = 3 seconds by substituting t = 3 into the acceleration function:

a(3) = 24(3)^2 - 30(3) - 16

    = 216 - 90 - 16

    = 110

Therefore, the acceleration of the car at t = 3 seconds is 110 m/s^2.

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Answer:

8

Step-by-step explanation:

4 × 16= 64

√64 = 8

hope this helps...

Answer:

the Answer should be 8

Step-by-step explanation:

16×4= 64 = 8

The angle between two vectors a = 5i + j and b = 2i - 4j is approximately 52.125°.

The angle between two vectors can be calculated using the following formula: cosθ = (a · b) / (||a|| ||b||)

where θ is the angle between the vectors, a · b is the dot product of the vectors, and ||a|| and ||b|| are the magnitudes of the vectors.

In this case, the dot product of the vectors is 13, the magnitudes of the vectors are √29 and √20, and θ is the angle between the vectors. So, we can calculate the angle as follows:

cos θ = (13) / (√29 * √20) = 0.943

The inverse cosine of 0.943 is approximately 52.125°. Therefore, the angle between the two vectors is approximately 52.125°.

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Answer:

3x^3 -16x^2 +27x -10

Step-by-step explanation:

(x^2+6x-5) (-3x+2) = -3x(x^2+6x-5)+2(x^2+6x-5) = -3x^3 -18x^2 +15x + 2x^2+12x-10 = -3x^3 -18x^2 +2x^2+15x+12x-10 = -3x^3 -16x^2 + 27x -10

The value os x in the following right triangles and trigonometry are:-

Question 6: x= 13.74

question 7: x= 18.52

question 8: x= 60.12

question 9: x= 3.7

Question 6:

tan θ = opposite/adjacent

tan 58° = 22/x

xtan58° = 22

x = 22/ tan58°

Since tan 58° = 1.6003345

x= 22/ 1.6003345

x ≈ 13.74

question 7:

tan θ = opposite/adjacent

tan 51° = x/15

15tan51° = x

x = 15 * 1.2348971

Since tan 51° = 1.2348971

x ≈ 18.52

question 8:

cosθ = adjacent/hypotenuse

cos 37° = 48/x

xcos37° = 48

x = 48/ cos37°

Since cos 37° = 0.79863551004

x= 48/ 0.79863551004

x ≈ 60.12

question 9:

sinθ = opposite/hypotenuse

sin 24° = x/9

9sin24° = x

Since sin 24° = 0.40673664307

x= 9 * 0.40673664307

x ≈ 3.7

The complete question is:-

Unit 8: Right Triangles & Trigonometry

Homework 3: Trigonometry:

Ratios & Finding Missing Sides

Answers for the remaining four problems?

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Given: 68 x 20

The product of the question will be = 1,360

68

x 20

=====

1360

Step-by-step explanation:

\( {14}^{2} = 2 {a}^{2} \\ 2 {a}^{2} = 196 \\ {a}^{2} = 98 \\ a = \sqrt{98 } = \sqrt{49 \times 2} \\ = 7 \sqrt{2} \)

The inverse of matrix B is: \(B^(-1)\)= [1 -2 1/2; -3/2 3/2 -1; -4/3 4/3 -5/12] . To find the determinant of matrices A and B using the product of the pivots, we need to perform the row reduction (Gaussian elimination) on each matrix and keep track of the pivots.

Let's start with matrix A: A = [2 3; 1 4]. Performing row reduction, we can subtract twice the first row from the second row: R2 = R2 - 2R1

The resulting matrix is: A = [2 3; 0 -2]. The product of the pivots is the determinant of matrix A: det(A) = (2)(-2) = -4 . Now, let's move on to matrix B: B = [1 2 3; 4 5 6; 7 8 9]

Performing row reduction, we can subtract 4 times the first row from the second row and subtract 7 times the first row from the third row:

R2 = R2 - 4R1

R3 = R3 - 7R1

The resulting matrix is: B = [1 2 3; 0 -3 -6; 0 -6 -12]

The product of the pivots is the determinant of matrix B: det(B) = (1)(-3)(-12) = 36. Next, let's find the inverse of matrices A and B using the method of cofactors. For matrix A:A = [2 3; 1 4]

The determinant of A is det(A) = -4. The cofactor matrix C is obtained by taking the determinants of the submatrices of A:C = [4 -3; -1 2]

To find the inverse of A, we divide the cofactor matrix C by the determinant of A: A^(-1) = (1/det(A)) * C.

\(A^(-1)\) = (1/-4) * [4 -3; -1 2] = [-1 3/4; 1/4 -1/2]

So, the inverse of matrix A is: \(A^(-1)\)= [-1 3/4; 1/4 -1/2]

For matrix B: B = [1 2 3; 4 5 6; 7 8 9]

The determinant of B is det(B) = 36. The cofactor matrix C is obtained by taking the determinants of the submatrices of B:

C = [(-3)(-12) 6(-12) (-6)(-3); 6(-9) (-6)(9) (-6)(6); (-6)(8) 6(8) (-3)(5)] = [36 -72 18; -54 54 -36; -48 48 -15]

To find the inverse of B, we divide the cofactor matrix C by the determinant of B:

\(B^(-1)\)= (1/det(B)) * C

\(B^(-1)\) = (1/36) * [36 -72 18; -54 54 -36; -48 48 -15] = [1 -2 1/2; -3/2 3/2 -1; -4/3 4/3 -5/12]

So, the inverse of matrix B is: \(B^(-1)\) = [1 -2 1/2; -3/2 3/2 -1; -4/3 4/3 -5/12]

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Using proportions, it is found that the radian measure of the central angle is given as follows:

\(\frac{4\pi}{3}\) radians.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The entire circumference is equivalent to a central angle of \(2\pi\) radians. Hence the radian measure of the central angle considering two-thirds of the circumference is given as follows:

\(\frac{2}{3} \times 2\pi = \frac{4\pi}{3}\)

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Answer:

Step-by-step explanation:

c edge

Answer:

D. \(\frac{(x-7)^2}{8^2} -\frac{(y-2)^2}{7^2}\)

Step-by-step explanation:

hope this helps

Answer:  D has the largest perimeter

Step-by-step explanation:

The top numbers of fractions describe the vertex and  the bottom number square rooted tells you how long each or wide each part of the asymptote rectangle is.

A.

P = 2(11) + 2(3)

P = 22+6

P=28

B.

P = 2(4) + 2(9)

p = 8 +18

P = 26

C.

P = 2(5) + 2(9)

P = 10 +18

P = 28

D.

P =  2(8) + 2(7)

P = 16 +14

P = 30

Answer:

f²r-nr=d

Step-by-step explanation:

f²r-N=d/r

multiply both sides by r to get d by itself

f²r-nr=d

(all variables need to be there in your final equation)

The partial product of the expression → 13 x 45 given is 585.

A product obtained by multiplying a multiplicand by one digit of a multiplier having more than one digit.

Given is the following expression -

13 x 45

Given expression is 13 x 45.

13 x 45

For partial product, we can write it as -

(10 x 40) + (10 x 5) + (3 x 40) + (3 x 5)

400 + 50 + 120 + 15

585

Therefore, the partial product of the expression → 13 x 45 given is 585.

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Answer: There are 27 trees he can plant in one row. There is one pine tree and 2 oak trees in each row

Step-by-step explanation:

(12x+5y)/3z

substitute in values

(12(12) + 5(6)) / 3(3)

simplify

(144 + 30) / 9

add

174 / 9

factor out a 3

58 / 3

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The given problem is asking for a test to see if the sample mean is significantly different from 85 at the 0.05 level. To solve the problem, we can use the following formula:$$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$$where$\bar{x}$ = sample mean$\mu$ = population mean$s$ = sample standard deviation$n

$ = sample sizeTo calculate the t-value, we need to calculate the sample mean and the sample standard deviation. The sample mean is calculated as follows:$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$where $x_i$ is the score of the $i$th student and $n$ is the sample size.

Using the given data, we get:$$\bar

{x} = \frac{78+89+67+85+90+83+81+79}{8}

= 81.125$$The sample standard deviation is calculated as follows:$$

s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}$$Using the given data, we get:$$

s = \sqrt{\frac{(78-81.125)^2+(89-81.125)^2+(67-81.125)^2+(85-81.125)^2+(90-81.125)^2+(83-81.125)^2+(81-81.125)^2+(79-81.125)^2}{8-1}}

= 7.791$$Now we can calculate the t-value as follows:$$

t = \frac{\bar{x} - \mu}{\frac{s}

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