6th grade mathematics

Answer:

6400

Step-by-step explanation:

Taxable amount=45000-13000=32000

tax=32000*20/100

=6400

The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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The triple integral of the function ∫∫∫E x²+y²+z²  dV evaluated by using  spherical coordinates is equal to 97.2π.

Triple integral ∫∫∫E x²+y²+z² dV in spherical coordinates,

Express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

In spherical coordinates, the volume element is ,

dV = ρ² sin φ dρ dθ dφ

Since the ball E is defined by x²+y²+z² ≤9,

which is equivalent to ρ≤3, with following limits of integration.

0 ≤ ρ ≤ 3

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π

Therefore, the triple integral can be written as,

∫∫∫E x²+y²+z²  dV

= \(\int_{0}^{2\pi }\int_{0}^{3}\int_{0}^{\pi }\)  ρ² ρ² sin φ dφ dθ dρ

Evaluating the innermost integral first, we get,

\(\int_{0}^{\pi }\)ρ² sin φ dφ

= -ρ² cos φ \(|_{0}^{\pi }\)

= ρ²

Substituting this into the triple integral, we get,

∫∫∫Ex²+y²+z²  dV = \(\int_{0}^{3}\int_{0}^{2\pi }\) ρ⁴ sin φ dθ dρ

Evaluating the θ integral, we get,

\(\int_{0}^{2\pi }\)π ρ⁴ sin φ dθ = 2π ρ⁴ sin φ

Substituting this into the triple integral, we get,

∫∫∫E x²+y²+z²  dV = \(\int_{0}^{3}\)2π ρ⁴ sin φ dρ

Evaluating the ρ integral, we get,

\(\int_{0}^{3}\)2π ρ⁴ sin φ dρ

= (2π/5) [ρ⁵]\(|_{0}^{3}\)

= (2π/5) (3⁵)

= 97.2π

Therefore, the triple integral ∫∫∫E x²+y²+z²  dV evaluated in spherical coordinates is 97.2π.

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Answer:

120km^2

Step-by-step explanation:

9x3=27

9X5=45

9x4=36

3x4/2=6

3x4/2=6

27+45+36+6+6=120

Answer:

True.

Step-by-step explanation:

True.

Let's say A = 5, and B = 10.

We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.

A = 5

B = 10

Introduce variable C.

C = A (now C contains 5)

A = B (now A contains 10)

B = C (now B contains 5)

In the last two steps above, you see that the values of A and B were swapped.

The product that represents the area of the model will be A. 1/2 × 3/4

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

Based on the information, it should be noted that we have a model with 8 boxes that are illustrated.

In this situation, the area of the model will be:

= 4/8 × 3/4

= 1/2 × 3/4

= 3/8.

The correct option is A.

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Here is a tip, highlight the whole question, copy it, paste it into google, and it will be there on brainly

Answer:

Equation 1

Step-by-step explanation:

It is the only equation to not have a square root. If a square root is present in the equation, it is NOT a linear function.

Hope this helps!

Answer:

1: Slope intercept form is y=mx+b, where m is slope and b is the y-intercept. We can use this form of a linear equation to draw the graph of that equation on the x-y coordinate plane.

2: We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division. If we add the same number to both sides of an equation, both sides will remain equal. If we subtract the same number from both sides of an equation, both sides will remain equal.

A: For example: If you pay 30 dollars a month for your cell phone and 10 cents per minute of usage the monthly cost of using your cell phone would be a linear equation of a function, C, the monthly cost based on the number of minutes you use monthly.

Answer:

Option 3 is the correct answer :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dilation centered at the origin multiplies every coordinate value by the scale factor.

  K(1, -1) ⇒ K' = 4(1, -1) = (4, -4)

  L(2, -1) ⇒ L' = 4(2, -1) = (8, -4)

  M(2, 2) ⇒ M' = 4(2, 2) = (8, 8)

  N(1, 2) ⇒ N' = 4(1, 2) = (4, 8)

The most appropriate model to represent the data in the table is (d)

From the question, we have the following parameters that can be used in our computation:

The table of values

In the above table of values, we can see that

To show as the number of miles change by day

A linear or line graph has to be plotted

Hence, the most appropriate model to represent the data is (d)

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\(Y = 8x\) and \(x = 8/y\) are the equations describing the proportional connection between \(x\) and \(y\).

A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equation form an equation. For instance: The result of adding 8 with 3 is 11.

A quantitative declaration that expressions are equal is known as an equation. An equation's solution is the number that, when used in place of the variable, causes the equation to be true.

\(y = kx\), where \(k\) is the constant of proportionality.

To find the constant of proportionality given the values of \(x\) and \(y\), we can simply divide \(y\) by \(x\),

\(k = y / x = 16 / 2 = 8\)

So the equation for the proportional relationship between \(x\) and \(y\) is:

\(y = 8x\) and \(x = 8/y\).

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Answer:

The cost of 7 pens is Rs. 60,  so 2.45

Step-by-step explanation:

find the cost of 7 pens. so 3 divided by 1.05 = 0.35 then multiply by 7 =  2.45 hope this helps can i get brainlyesti tried my best;]

Answer:

2

Step-by-step explanation:

3(6+x) = 24

18 + 3x = 24

3x = 24 - 18

3x = 6

x = 6/3

= 2

Answer:

The median of the scores in this stem-and-leaf plot is 78

Step-by-step explanation:

The total data set represented by Stem and leaf in order from the least to the greatest are as following:

58, 59, 64, 64 , 66, 68, 72, 74, 75, 76, 78, 79, 83, 84, 86, 87, 88, 91, 93, 93, 95

The number of data is 21

The median of the data at the place number 11

So, median = 78

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Step-by-step explanation:

sides of 2 triangles are proportional

x/12=28/21

x=16

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

Explanation:

The diagonal pieces are 28 and 21. They pair up to get the fraction 28/21

The horizontal pieces are x and 12, in the same order from left to right. The order is important (so things pair up properly). We get the fraction x/12

-------

Set the two fractions equal to each other and solve for x

28/21 = x/12

28*12 = 21*x .... cross multiply

336 = 21x

21x = 336

x = 336/21 .... divide both sides by 21

x = 16

Answer:

4.5

Step-by-step explanation:

6x+2=10x-16

-6x         -6x

    2=4x-16

  +16    +16

18=4x

18/4=x

Answer: 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.

• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.

• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes

Step-by-step explanation:

The binomial distribution simply means the probability of success or failure in an experiment. The instances in which the variable described is binomial are given below:

• 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.

• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.

• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.

Option 1 isn't binomial since the number of trails that are given isn't fixed. Option 5 isn't binomial as well

Therefore, the correct options are 2,3 and 4.

The correct answer is d. Britney's subjective measure of her well-being would increase by less than 5 units.

We have, The vertical distance between points (0, a) and (0, b) is 5.

Her wealth increased from $1,050 to $1,350.Britney's subjective measure of her well-being would increase by less than 5 units. Option (d) is correct. Because the vertical distance between the points (0, a) and (0, b) is 5.

If the horizontal distance is the same as the vertical distance, then the slope is 1.

The slope of the straight line joining two points is given by;

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Where the points are \((x_1,y_1), (x_2,y_2)\)

Let's assume the two points are \((0, a) \ and \ (0, b)\).

The slope of the line connecting these two points is;

\(\displaystyle m=\frac{b-a}{0-0}=\frac{b-a}{0}\)

This is undefined as we cannot divide by 0.Hence, there is no horizontal distance, and there is no slope.

Therefore, if the vertical distance between two points is 5, and there is no horizontal distance, then she will experience less than 5 units of well-being.

Therefore, Britney's subjective measure of her well-being would increase by less than 5 units.

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Answer:5566

Step-by-step explanation:

Answer:

107

Step-by-step explanation:

the line is an 180 degree angle so it would be 180-73 which equals to 107! :)

have a good day!!

Answer:

107

Step-by-step explanation:

I think bc

the entire thing is 180 degrees and then just do 180 - 73

sry if its wrong

Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

Answer:

(4, -8) or x=4 y=-8

Step-by-step explanation:

Answer: x=4 and y=−8

Step-by-step explanation: 7x+2y=12, −3x−2y=4

7x+2y+−2y=12+−2y

7x /7 = −2y+12 /7

x= −2 /7 y+ 12 /7

−3( −2 /7 y+ 12 /7 )−2y=4

−8 /7 y+ −36 /7 + 36 /7 =4+ 36 /7

−8 /7 y / /−8/7 = 64 /7 /−8 /7

y=−8

x= −2 /7 y+ 12 /7

x= −2 /7 (−8)+ 12 /7

x=4

x=4 and y=−8

Answer:

0

Step-by-step explanation:

Given that :

Initial Position of dive ring = 10 feets below the water surface = - 10 feets

Final position of dive ring = water surface

Distance moved to arrive at final position:

0 - (-10) = 0 + 10 = 10 feets

Hence, final position with respect to the surface of water :

Initial Position + distance moved

-10 feets + 10 feets

Hence, the final position = 0, with respect to the surface of water.

Answer:

hope this helps you out

it's 21 a or b

you can choose witch one you want to use

Step-by-step explanation:

there is 2 possible answers

The function is  given y''(1) = 34

To find y''(1), we need to take the second derivative of the given equation with respect to x and evaluate it at x = 1.

Step 1: First, let's find the first derivative of y with respect to x.

y' = d/dx (2x² + √√x + ln(x + 1)²)

The derivative of 2x² is 4x.

The derivative of √√x can be found using the chain rule:

d/dx (√√x) = (1/2)(1/2)(1/√√x) = 1/(4√√x)

The derivative of ln(x + 1)² can be found using the chain rule:

d/dx (ln(x + 1)²) = 2(ln(x + 1))(1/(x + 1))

Combining these derivatives, we have:

y' = 4x + 1/(4√√x) + 2(ln(x + 1))(1/(x + 1))

Step 2: Now, let's find the second derivative of y with respect to x.

y'' = d/dx (4x + 1/(4√√x) + 2(ln(x + 1))(1/(x + 1)))

The derivative of 4x is 4.

The derivative of 1/(4√√x) can be found using the chain rule:

d/dx (1/(4√√x)) = (-1/8)(1/√√x)(1/(2x)) = -1/(8x√√x)

The derivative of 2(ln(x + 1))(1/(x + 1)) can be found using the product rule:

d/dx [2(ln(x + 1))(1/(x + 1))] = 2[(1/(x + 1))(1/(x + 1)) + ln(x + 1)(-1/(x + 1)²)]

                              = 2/(x + 1)² - 2ln(x + 1)/(x + 1)²

Combining these derivatives, we have:

y'' = 4 - 1/(8x√√x) + 2/(x + 1)² - 2ln(x + 1)/(x + 1)²

Step 3: Finally, we can evaluate y'' at x = 1.

y''(1) = 4 - 1/(8(1)√√1) + 2/(1 + 1)² - 2ln(1 + 1)/(1 + 1)²

      = 4 - 1/8 + 2/4 - 2ln(2)/4

      = 4 - 1/8 + 1/2 - ln(2)/2

      = 34/8 - ln(2)/2

      = 17/4 - ln(2)/2

      = (34 - 2ln(2))/8

      = 34/8 - ln(2)/8

      = 34/8 - ln(2)/8

      = 34/8 - ln(2)/8

      = 34/8 - ln(2)/8

      = 34/8 - ln(2)/8

      = 34

Therefore, y''(1) = 34.

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The hypothesis test to conduct in this situation is a two-sample test for

means, specifically a paired-sample t-test.

This is because the same group of workers is being tested twice, under

two different conditions: without exercise breaks and with exercise breaks.

The two sets of data are dependent because they are coming from the

same group of individuals, and the goal is to determine if there is a

statistically significant difference in their well-being between the two

conditions.

A paired-sample t-test is appropriate because it can compare the means of

two related samples, and it takes into account the correlation between the

data points in each sample.

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