1/2 of 2/3 = 1/2 of ____ third(s) = ____ third(s)

Answer:

[tex]a_{n}[/tex] = 6n - 5

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

7 - 1 = 13 - 7 = 19 - 13 = 6

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = 6 , then

[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5

Answer:

y = 2; x = 1/4

Step-by-step explanation:

We can solve for y then x using elimination.  We can multiply the first equation by -4 to cancel out the xs:

[tex]-1(3y=4x+5)\\\\4y=4x+7\\-3y=-4x-5\\\\y=2\\\\[/tex]

Now, we can plug in this 2 for y in any of two equations to find x:

[tex]3(2)=4x+5\\6=4x+5\\1=4x\\1/4=x[/tex]

5 dollars equals 500 pennies, once 5 dollars times 100 equals 500. What's 5 dollars in cents? 5 dollars equals 500 cents, once 5 dollars times 100 equals 500.

The given statement about the intermediate value theorem is false

The given statement is

"Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

But according to Intermediate value theorem "if a continuous function f with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

So if we takes discontinuous function the given statement will be wrong

Therefore, the statement is false

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The mean of this data set is 65.

The average distance between each data item and the mean is known as the mean absolute deviation.

The gap between each data value and the mean in absolute terms is represented by this average.

Let the mean be 'x' and the standard deviation be 'y'

3 standard deviations the mean means that we are taking away 3 standard deviations from the mean

Mathematically, we have that as;

x - 3y = 41...(i)

73 is 1 standard deviation above the mean

Mathematically;

x + y = 73...(ii)

So let us solve both equations simultaneously

Simply multiply equation (ii) by 3 then add to (i)

x - 3y = 41

3x + 3y =219

4x = 41 + 219

4x = 260

x = 260/4

x = 65.

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Answer: 26

Step-by-step explanation:

Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

Explanation:

To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:

y = 1.55x + 110,419

y = 1.55 * 64,000 + 110,419

y = 101,600 + 110,419

y = $212,019

So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.

To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:

Time = (Distance / Average Speed) * 60

Time = (352 km / 220 km/h) * 60

Time = (1.6) * 60

Time = 96 minutes

Time = 1 hour and 36 minutes

Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.

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Jayden needs to purchase 3900 square feet of sod to cover his front and back yards.

The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then multiplying or dividing to find the value of the whole. In this case, the unit we will use is square feet.

To calculate the area of the front yard, we need to multiply its length by its width. So, we have:

Area of front yard = Length x Width = 50 ft x 70 ft = 3500 sq ft

To find the area of the back yard, we use the same formula:

Area of back yard = Length x Width = 10 ft x 40 ft = 400 sq ft

Now, we need to add the two areas to find the total area that requires sod. So, we have:

Total area = Area of front yard + Area of back yard

=> 3500 sq ft + 400 sq ft = 3900 sq ft

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Answer:

Gavin made a Profit of $66.69 that is 93% Profit

Step-by-step explanation:

First, we calculate the Selling Price of Jeans after converting from GBP to USD on the given rate:

Rate: £1 = $1.34

Quantity: 3

Price in USD = Selling Price per pair * Rate in USD

£34.50 * 1.34 = $46.23 per pair of jeans.

Total Selling Price = Price Per Pair * Quantity
= 46.23 * 3
= $138.69

Total Profit = Total Selling Price - Total Cost Price
= $138.69-$72
= $66.69

Percentage of Profit = Total Profit / Total Cost Price
=66.69 / 72
=92.65

Therefore, the Profit Percentage is 92.65 % the nearest whole number would be 93%

To calculate Gavin's percentage profit, find the difference between the selling price and the buying price, and calculate the percentage of the buying price that the profit represents.

To calculate Gavin's percentage profit, we need to find the difference between the selling price and the buying price, and then calculate the percentage of the buying price that the profit represents.

Gavin's percentage profit is approximately 92.6%.

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Answer:

a the answer for angle 1 is also 52

b the answer for angle 3 is 180- 112= 68

Answer:

Step-by-step explanation:

According to question

    [tex]4ax^{2} +9x+c < 0[/tex]

This means that the coefficient of the highest degree term

([tex]4ax^{2}[/tex]) must be positive

And the constant term (c) must be negative

So, the according to condition

   4a must be positive,

    which means a must be positive

And, c must be negative

          [tex]a > 0\\c < 0[/tex]

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The fraction of the group are boys with brown eyes with total group of students who attend the math club is equals to the 2/9.

Let us assume that total number of students who attend the math club be 'x'. Now, according to problem, half of students who attend the math are boys. So, boys students out of total students who attend the math club, B = ( 1/2)x --(1)

Also, 4/9 of them boys have brown eyes. That is the boys students have brown eyes out of boys students who attend the math club, E = 4/9 of B

=> (4/9)B --(2)

We have to determine the relationship between boys with brown eyes (E) and the group of students (x). so, let's replace B in second equation with the expression present in eqution (1).

=> E = (4/9)(x/2)

For simplification, multiply the two fractions, that denominator with denominator and numerator with numerator.

=> E = 4x/18

For further simplification, simply dividing both the numerator and denominator by their common factor, ( 4, 18 ) = 2,

=> E = 2x/9

so, the required relationship between E and x is 2/9. Hence, required value is 2/9.

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Complete question :

a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group are boys with brown eyes.

The distance between the given pair of points (3,-4) and (9,-9) is 7.8 unit.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1 ( 3,-4 )

Point 2 ( 9,-9 )

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 9 - 3 )² + ( -9 - (-4) )² )

D = √( ( 9 - 3 )² + ( -9 + 4 )² )

D = √( ( 6 )² + ( -5 )² )

D = √( 36 + 25 )

D = √( 61 )

D = 7.8 units

Therefore, the distance between the of points is 7.8 units.

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A building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34. 5-foot shadow then the building is approximately 95.2 feet tall.

What is similar triangles ?

Similar triangles are useful in geometry and other fields because they allow us to solve problems involving unknown distances or heights. We can use the known lengths and angles of one triangle to find the lengths and angles of the other triangle, as long as we know that the two triangles are similar. This can be done using the properties of proportional relationships and the rules of similar figures.

Let's use similar triangles to solve this problem. The height of the building and the height of the flagpole are proportional to the lengths of their shadows. We can set up the following equation:

height of building / length of building's shadow = height of flagpole / length of flagpole's shadow

Let x be the height of the building. Then we have:

x / 103 = 32 / 34.5

Simplifying this equation, we get:

x = 103 * (32 / 34.5) ≈ 95.23

Therefore, the building is approximately 95.2 feet tall.

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Answer:

m<20

Step-by-step explanation:

Answer:

14)37

15)16

16)38

17)C

Step-by-step explanation:

14)7*4+9=28+9=37

15)42/7+10=6+10=16

16)-5*(-6)+8=30+8=38

If p and q vary inversely and p = 14 when a = 4, then the work is  q = 8, p = 7.

What is inverse proportionality?

Inverse proportionality occurs when x increases and y decreases, and when x decreases and y increases.

If p and q vary inversely, this means that their product is constant:

p * q = k

where k is a constant. We can use this relationship to solve the problem.

We are given that when a = 4, p = 14. This means that:

p * a = k

14 * 4 = k

56 = k

So we know that the product of p and a is 56.

To find p when q = 8, we can use the fact that p and q vary inversely. This means that:

p * q = k

We know that k = 56, so we can substitute:

p * q = 56

We are given that q = 8, so we can substitute this as well:

p * 8 = 56

Solving for p, we get:

p = 56 / 8 = 7

Therefore, when q = 8, p = 7.

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Answer:

3

Step-by-step explanation:

You multiply the pre-image by 3 to get the image numbers.

Answer:

B.3

Step-by-step explanation:

The scale factor is 3 because all of the images are dilated 3 times larger than the preimage.

The missing sides of right triangles are, respectively:

Case 1: x = 18.910

Case 2: x = 23.584

Case 3: x = 15.890

Case 4: x = 16.659

Case 5: x = 24.111

And the angles of the right triangles are, respectively:

Case 6: 32°

Case 7: 31°

Case 8: 71°

Case 9: 71°

Case 10: 32°

The exact values of trigonometric functions:

Case 11: cos A = 12 / 13

Case 12: tan C = 3 / 4

Case 13: tan A = 3 / 4

And the trigonometric ratios of right triangles are:

Case 14: tan X = 1.3333

Case 15: sin A = 0.6000

Case 16: cos C = 0.3243

In this question we find 16 cases of right triangles that must be analyzed by trigonometric functions. Trigonometric functions is an important tool to determine missing sides and angles and relationships with sides. Most important trigonometric functions are described below:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Where:

Please notice that hypotenuse is the longest side of a right triangle.

The first five cases implies the determination of missing lengths in five right triangles:

Case 1

x = 20 · cos 19°

x = 18.910

Case 2

x = 20 / cos 32°

x = 23.584

Case 3

x = 10 / cos 51°

x = 15.890

Case 4

x = 15 / tan 42°

x = 16.659

Case 5

x = 19 / sin 52°

x = 24.111

The following five cases implies the determination of angles by means of direct and inverse trigonometric functions:

Case 6

tan θ = 16 / 26

tan θ = 8 / 13

θ = 31.608° (32°)

Case 7

tan θ = 6 / 10

θ = 30.964° (31°)

Case 8

tan θ = 76 / 26

θ = 71.114° (71°)

Case 9

tan θ = 67 / 23

θ = 71.053° (71°)

Case 10

tan θ = 26 / 42

θ = 31.759° (32°)

The next three cases implies the computation of the exact values of trigonometric functions:

Case 11

cos A = 24 / 26

cos A = 12 / 13

Case 12

tan C = 24 / 32

tan C = 3 / 4

Case 13

tan A = 27 / 36

tan A = 3 / 4

And the last three triangles implies the values of trigonometric ratios:

Case 14

tan X = 36 / 27

tan X = 4 / 3 (1.3333)

Case 15

sin A = 30 / 50

sin A = 3 / 5 (0.6000)

Case 16

cos C = 12 / 37 (0.3243)

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The lengths of the sides, measures of the angles and the values of the trigonometric ratios are as follows;

1) x ≈ 18.9

2) x ≈ 23.1

3) x ≈ 15.9

4) x ≈ 16.7

5) x ≈ 23.1

6) x ≈ 32°

7) x ≈ 31°

8) x ≈ 71°

9) x ≈ 71°

10) x ≈ 32°

11) cos(A) ≈ 0.9

Trigonometric ratios are expressions that specify the relationships between two sides of a right triangle and an interior angle of the triangle.

1) The opposite side = 20 × sin(19°) ≈ 6.5

The adjacent side = 20 × cos(19°) ≈ 18.91

2) cos(30°) = 20/x

cos(30°) = (√3)/2, therefore;

(√3)/2 = 20/x

x = 20/((√3)/2) = 40·√3/3 ≈ 23.1

x ≈ 23.1

3) cos(51°) = 10/x

Therefore;

x = 10/(cos(51°)) ≈ 15.9

4) tan(42°) = 15/x

Therefore;

x = 15/(tan(42°)) ≈ 16.7

x ≈ 16.7

5) sin(52°) = 19/x

Therefore;

x = 19/(tan(52°))

x = 20/(cos(30°)) ≈ 23.1

x ≈ 23.1

6) tan(x) = 16/26

tan(x) = 16/26 = 8/13

x = arctan(8/13) ≈ 32°

7) tan(x) = 6/10

tan(x) = 6/10 = 3/5

x = arctan(3/5) ≈ 31°

8) tan(x) = 76/26

tan(x) = 76/26 = 38/13

x = arctan(38/13) ≈ 71°

9) tan(x) = 67/23

x = arctan(67/23) ≈ 71°

x ≈ 71°

10) tan(x) = 26/42

tan(x) = 26/42 = 13/21

tan(x) = 13/21

x = arctan(13/21) ≈ 32°

11) The trigonometric ratios for cosine indicates that we get;

cos(A) = 24/26 ≈ 0.9

12) Trigonometric ratio for tangent indicates that we get;

tan(C) = 24/32 = 0.75

13) tan(A) = 27/36

27/36 = 3/4

Therefore; tan(A) = 3/4 = 0.75

14) tan(x) = 36/27 = 4/3

tan(x) = 4/3 = 1 1/3

15) sin(A) = 30/50 = 3/5

sin(A) = 3/5 = 0.6

16) cos(C) = 12/37 ≈ 0.32

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In a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

To calculate the test performance of the screening test in a primary care setting with a 15% baseline cervical cancer prevalence,

we can use the same sensitivity and specificity values obtained in the study, but apply them to a different population.

Given that the prevalence of cervical cancer is 15%, the number of true positives (TP) and false negatives (FN) in the screened population would be:

TP = Prevalence x Sensitivity x Number screened

TP = 0.15 x 0.91 x 3300

TP = 449.19, rounded to 449.

FN = Number with disease - TP

FN = 0.15 x 3300 - 449

FN = 26.5, rounded to 27.

Similarly, the number of true negatives (TN) and false positives (FP) in the screened population would be:

TN = (1 - Prevalence) x Specificity x Number screened

TN = 0.85 x 0.85 x 3300

TN = 2382.75, rounded to 2383.

FP = Number without disease - TN

FP = 0.85 x 3300 - 2383

FP = 396.5, rounded to 397.

Using these values, we can construct the following 2x2 contingency table for the primary care setting:

Actual condition:-

Test outcome       Positive (P)                          Negative (N)

Disease (D)       True positive (TP = 449)         False negative (FN = 27)

No disease (ND) False positive (FP = 397)  True negative (TN = 2383)

Using this contingency table, we can calculate the following test performance measures:

Sensitivity = TP / (TP + FN) = 449 / (449 + 27) = 0.943, or 94.3%.

Specificity = TN / (FP + TN) = 2383 / (397 + 2383) = 0.857, or 85.7%.

Positive predictive value (PPV) = TP / (TP + FP) = 449 / (449 + 397) = 0.531, or 53.1%.

Negative predictive value (NPV) = TN / (FN + TN) = 2383 / (27 + 2383) = 0.988, or 98.8%.

Therefore, in a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

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The surface area of a cuboid is 600 cm².

The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.

Given that, a cuboid whose 6 faces have 10 cm.

We know that, surface area of a cuboid = 2(lb+bh+hl)

= 2(10×10+10×10+10×10)

= 2(100+100+100)

= 2(300)

= 600 cm²

Therefore, the surface area of a cuboid is 600 cm².

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Answer:sry

Step-by-step explanation:i need points

The equation which is true is 6 ÷ 100 = 0.06

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = 6

Let the second number be q = 100

Substituting the values in the equation , we get

A = p/q

A = 6/100

The value of A = 0.06

Hence , the equation is A = 0.06 and is true

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Option b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.

The variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college can provide insights into students' preferences for attending college in their home state. A large proportion of students who attend college in their home state indicates that students prefer to stay close to home for higher education, while a small proportion suggests that they are more likely to attend college in a different state. This information can be useful for policymakers and educators to better understand the higher education preferences of their state's students and to develop policies and programs to encourage more students to attend college within their home state.

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Complete question:

The U.S. Census Bureau collects a large amount of information concerning higher education. For example, the bureau provides a table that includes the following variables: state, number of students from the state who attend college, number of students who attend college in their home state.

Consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. Explain how you would use this variable to describe something about the states.

a. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that less of the state’s population attend college while a small proportion means that more of the state’s population attend college.

b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.

c. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college outside their home state and a small proportion means that students prefer to attend college in their home state.

d. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that more of the state’s population attend college while a small proportion means that less of the state’s population attend college.

The equation of line shown on the coordinate plane is,

⇒ y = - 1/4x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (4, -1).

Now,

Since, The equation of line passes through the points (0, 0) and (4, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 0) / (4 - 0)

m = - 1 / 4

Thus, The equation of line with slope - 1/4 is,

⇒ y - 0 = - 1/4 (x - 0)

⇒ y = - 1/4x

Therefore, The equation of line passes through the points (0, 0) and

(4, -1) will be;

⇒ y = - 1/4x

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The ocean current has a bearing of 19.1°E and travels at a speed of about 16.9 knots.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's use the letters "c" for OC magnitude and "" for the angle between OC and OD (the present bearing). Next, we have:

c² = 28² + 20² - 2(28)(20)cos(106°)

c ≈ 16.9 knots

Using the law of sines, we can find the angle θ:

sin(53°) / c = sin(θ) / 20

sin(θ) = (20/c) sin(53°)

θ ≈ 19.1°

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At 100 machines the unit cost will be minimum and the minimum cost is 11985.

The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.

The formula for the minimum value is given by -b/2a

Here we have

The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.  

Compare given C(x) with the standard equation ax² + bx + c  

=> a = 0.9, b = -180 and c = 20,985  

We can find the x - coordinate where the minimum value occurs using the formula -b/2a    

The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)

= (180)/1.8 = 100

Hence at x = 100, the unit cost will be minimum

The unit cost can be calculated as follows

C(100) = 0.9(100)²-180(100)+20,985

= 0.9(10000) -18000 + 20,985    

= 9000 - 18000 + 20985

= 11985

Therefore,

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

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The point that divides a segment into two congruent segments is called the midpoint. Therefore, the answer is B) midpoint.

In geometry, a midpoint is a point that divides a line segment into two equal parts. It is the point on the line segment that is equidistant from both endpoints. The midpoint is important in geometry as it can be used to construct other geometric figures, such as perpendicular bisectors, which are lines that pass through the midpoint of a line segment and are perpendicular to it. For example, if we have a line segment AB, the midpoint M is the point that is exactly halfway between A and B, such that AM = MB. This can be found by drawing a perpendicular bisector of AB, which is a line that passes through the midpoint M and is perpendicular to AB. The perpendicular bisector will intersect AB at the midpoint M. It is important to note that the midpoint is not a bisector, ray, or point on a line. A bisector is a line, segment, or ray that divides an object into two congruent parts, while a ray is a part of a line that extends infinitely in one direction. The midpoint is simply the point that divides a line segment into two equal parts, and it is denoted by a symbol, such as a small vertical line with a hat on top, or by labeling the midpoint as a letter, such as M in the example above

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Answer The formula df = (c – 1) (r – 1) is used to find the degree of freedom – The degree of freedom of the chi-square test is calculated by the formula df = (c – 1) (r – 1), where c represents the column number of cell and r represents the row number of the cell.