Determine the slope of the linear relationship

The number of teachers who teach:

(a) science but not humanities = 45

(b) Humanities but not science = 10  

(c) Humanities or science = 70

To find the number of teachers that teach only Science we can subtract the number of teachers who teach both subjects from the number of teachers that teach science.

Similarly, to find the number of teachers that teach only Humanities we can subtract the number of teachers who teach both subjects from the number of teachers that teach Humanities.

To find the number of teachers who teach Humanities or science we use the elementary set formula,

Here we have

Total number of teachers = 100

No of teachers who teach Humanities, n(H)= 25

No of teachers who teach Science, n(S) = 60

No of teachers who teach both Science and Humanities, n(H ∩ S) = 15  

The number of teachers who teach science but not humanities

= No of teachers who teach Science - No of teachers who teach both

= 60 - 15 = 45  

The number of teachers who teach Humanities but not science

= No of teachers who teach Humanities - No of teachers who teach both

= 25 - 15 = 10

The number of teachers who teach Humanities or Science  

As we know n(A ∪ B) = n(A) + n(B) - n(A ∩ B)  

The number of teachers who teach Humanities or Science

= n(S) + n(H) - n(S ∩ H)    

= 60 + 25 - 15

= 70

Therefore,

The number of teachers who teach:

(a) science but not humanities = 45

(b) Humanities but not science = 10  

(c) Humanities or science = 70

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Answer:this is so ez

Step-by-step explanation: 2/5

Answer:

5 tickets for $12.50

Step-by-step explanation:

because in that deal the ticket only costs $2.05

and in the second deal which is 8 tickets for $20.60 the ticket costs 2.57

By Linear Function f(x) = -4 + 2 and g(x) = x - 3 this we get the Value -2.

The slope-intercept form or the point-slope form are used to find a linear function.

With the aid of an example, the procedure for determining a linear function is the same as determining a line's equation.

When "m" and "b" are real numbers, then a function has the form f(x) = mx + b.

Examples :

f(x) = -4 + 2,g(x) = x - 3: -2

Steps

Find  f ° g given f(x) = -4 + 2, g(x) = x - 3

f ° g = f(g (x))

Constant function results in a constant

f (x )  = -4 + 2

-4 + 2 = -2

Answer = -2.

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Answer:

Step-by-step explanation:

5

Answer: 3

Step-by-step explanation:

2/3 4/6

a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.

b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.

c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.

We know that  a mathematical statement is nothing but a sentence which is either true or false.

We need to translate these statements into English.

The meaning of some mathematical symbols:

∀ : for all

∃ : there exists exactly one

∧ : and

Here, x, y, z are real numbers.

Consider given mathematical statements.

a) ∀x∃y(x < y)

For all values of x there exist number y such that all x are less than y.

b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))

For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.

c) ∀x∀y∃z(xy = z)

For any numbers x and y there exist number z such that the product of x and y is equal to z.

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Answer:

(f-g)x is the same as f(x)-g(x)

(f-g)x= 4x^3+7x^2+8x-(7x^2-7x)

= 4x^3+7x^2-7x^2+8x+7x

=4x^3+0+15

=4x^3+15

(f-g)0= 4(0)^3+15

=0+15

=15

Answer:

Step-by-step explanation:

it is simply factorized.

as we have 2x³-x²-2x+1

we will take common number and variable from it

So as we can see that in this polynomial we can take x-1 common

we will take x-1 common and write the rest polynomial

As we will multiply x-1 with 2x²+x-1    

it will give the previous answer or nmber

The inequality that is graphed on the number line is:

x > -2

Here we can see the graph of an inequality on a number line, on it, we can see a blue line that starts with a open circle (which means that we need to use the symbols < or >) at x = -2

Then the line extends to the right of that number, so the allowed values of x are larger than -2, then the inequality graphed is:

x > -2

Thus the correct option is the fourt one.

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Expressed the answers to the given operations with the proper number of significant figures:

(a) (1.600 × 10-¹)(2.1 × 10³) = 336

(b) (1.33)³ = 2.352637

(c) 1.93.x 2.651 = 5.11643

(d) 4.4/2.200 = 2

In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.

A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.

When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.

They're unfit to begin with zero since it'll also be regarded as a single- number .

Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.

a) (1.600 × 10-¹)(2.1 × 10³)

= 1.6 × 2.1 × 10⁻¹⁺³

= 3.36 × 10²

= 336

b) (1.33)³

= 2.352637

c) 1.93 × 2.651

= 5.11643

d) 4.4/2.200

= 2.0

= 2

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Note that in the above problem where a marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore, note that the width of the oil spill is 20m. See the proof below.

In ΔABC and ΔDEC, Note that since

DC = BC; and

EC = AC

It means that ∠DCE = ∠ACB (Diagonal Equality)

⇒ ΔABC ≅ ΔDEC

Therefore:

DE = AB

Since AB = 20m,

DE is also = 20m.

Thus, it is correct to state that the width of the oil spill is 20m.

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Answer: To find the number of balls Ivan makes each day, we need to divide the total volume of lead used each day by the volume of one ball.

The formula for the volume of a sphere is:

V = (4/3) * π * r^3

Where V is the volume, π is pi and r is the radius of the sphere.

We know the radius of the sphere is 3 inches so we can use this information to find the volume of one ball.

V = (4/3) * π * 3^3

V = (4/3) * π * 27

V = 36 * π

Now we know the volume of one ball is 36π cubic inches, we can divide the total volume of lead used per day by the volume of one ball to find the number of balls made per day.

28,260 in^3 / 36π in^3/ball = 785.833 balls/day

Rounding to the nearest hundredth, Ivan on average makes 785.83 balls/day.

Step-by-step explanation:

Answer: Based on the information provided, we can use the proportion of blue m&ms found in the sample (82 out of some larger total number of m&ms) to estimate the total number of m&ms in the entire bag.

If we let x be the total number of m&ms in the bag, we can set up the proportion:

82/x = blue m&ms / total m&ms

To solve for x, we can cross-multiply and divide by 82:

x = 82 * total m&ms / blue m&ms

x = 82 * 1

x ≈ 82

Therefore, based on the sample, we expect there to be approximately 82 m&ms in the entire bag, rounded to the nearest whole m&m.

It's worth noting that this is an estimation, and the actual number of m&ms in the bag may be different.

Step-by-step explanation:

The dominant K allele is necessary for hearing, and the dominant M allele causes deafness regardless of the other genes present. What fraction of the offspring of parents with the genotypes KkMm and Kkmm will most likely be deafi is 1/2 so c option is correct

The percentage that the offspring will be deaf is 75%. Two punnet squares are needed each for km and Kkmm individuals. In punnet square 1, half of the genotypes are Km and km while half are Mm and kk in punnet square 2. The two punnet squares are then combined to form a final one where a quarter of the offspring is deaf.

What does genotype mean?

In a wide sense, the word"genotype" refers to the genetic makeup of an organism;  it defines an organism's complete set of genes. In a more thin sense, the term can be used to guide the alleles, or variant forms of a gene, that are carried by an organism.

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Applying the Midsegment Theorem, the length of BC is: 10.

The Triangle Midsegment Theorem states that in a triangle, a line segment connecting the midpoints of two sides is parallel to the third side and is half as long.

From the information given we know that:

E is the midpoint of BC and D is the midpoint of AC.

Thus, applying the Midsegment Theorem, we have:

ED = 1/2(BA)

Substituting the values not expressive, we would get:

x + 2 = 1/2(4x - 6)

2(x + 2) = 4x - 6

2x + 4 = 4x - 6

2x - 4x = -4 - 6

-2x = -10

x = 5

BE = x = 5

Therefore, BC = 2(5) = 10.

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Answer:

Shortest = 10ft

Middle = 18 ft

Longest = 26ft

Step-by-step explanation:

(btw u can make a diagram to make it easier to visualise)

Let shortest side of triangle be x

So:

1st side = 2x+6

2nd side = x

3rd side = x+8

These sides all equal to 54 ft (perimeter)

2x+6 + x + x+8 = 54

4x + 14 = 54

4x = 40

x = 10

Now that we know the shortest side just sub it back into the equations!

Answer:

0.2142857143

Step-by-step explanation:

4/7 × 3/8

=12/56

=0.2142857143.

Regression toward the mean is most likely to account for the higher scores. So the option 2 is correct.

The answer to this query is based on a long-term investigation. An observational study that tracks the same people across time, sometimes from birth to death, is called a longitudinal study.

The right response is regression to the mean. When a sample point for a random variable is extreme, regression toward the mean is the phenomena that results, with subsequent measurements, in a point that is closer to the mean or average.

This is your response with justification. You can find me in the comments section if you have any questions or doubts about the question or the answer, though.

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The complete question is:

In a flight simulation test, a particular pilot among a group of pilots receives a very low score. However, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. Which of the following is most likely to account for the higher scores?

1. instrument decay

2. regression toward the mean

3. carryover effects

4. fatigue effects

If you look at this rationally I believe it will be 7.0 with the odd number.

When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

Division is the process of splitting a number or an amount into equal parts.

Given is an expression, 3x³+x-200 which is divided by x-4,

Therefore,

(3x³+x-200) / (x-4)

Divide the leading term of the dividend by the leading term of the divisor:

3x³/x = 3x²

Multiply it by the divisor: 3x²(x−4)=3x³−12x²

Subtract the dividend from the obtained result:

(3x³+x−200)−(3x³−12x2) = 12x²+x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x

Multiply it by the divisor: 12x(x−4) = 12x²−48x

Subtract the remainder from the obtained result:

(12x²+x−200)−(12x²−48x) = 49x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49

Multiply it by the divisor: 49(x−4) = 49x−196

Subtract the remainder from the obtained result:

(49x−200)−(49x−196) = −4

Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

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Each cut piece measures 6.25 meters in length.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.

Given

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

The thread was divided into 4 equal pieces after being cut at 25 meters.

= 25/4 \s = 6.25.

Each cut piece measures 6.25 meters in length.

The complete question is,

A 25 meter distance. Cindy cut the string into four equal pieces. each component's quality.

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Number of shingles in the 6th row is 110.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given;

Each row has 7 fewer shingles than the row below it

First row has 75 shingles

Now,

a=75

D=7

n=6

a_{n}=a_{1}+(n-1)d

a6=75+(6-1)7

a6=75+35

a6=110

Therefore, the answer of arithmetic sequence will be 110.

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Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. (75 -7)  On the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

Answer: The set {x|−7 < x} can be written in interval notation as (-infinity, -7) < x.

This set represents all real numbers greater than -7. The interval notation uses the less-than symbol (<) to represent that all values of x greater than -7 are included in the set. The interval notation uses the infinity symbol to represent the fact that there are no limits on the lower end of the interval.

It's important to note that the interval notation includes the endpoint values when it is in the form of (a,b) or [a,b) but it does not include endpoint values when it is in the form of (a,b] or [a,b].

Step-by-step explanation:

No, she does not have enough soil as she needs 4 pounds of soil.

What is meant by soil?

she as = 2 1/8 + 1 3/4

            = 17/8 + 7/4

            = 17+ 7 × 2 / 8

            = 17 + 14 / 8

           = 31/8

           = 3 7/8 pounds

           ≤ 4 pounds.

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After 2 minutes of leaving home, Abby meet Betty.

Given is that Abby's distance from home is given with the function :

S{t} = 100t² + 400t, where {t} is time in minutes.

The given function is -

S{t} = 100t² + 400t

dS{t}/dt = 0

200t = 400

t = 2

Therefore, after 2 minutes of leaving home, Abby meet Betty.

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Answer:

4/5 < 2/6

Step-by-step explanation:

Hope it helps! =D

Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

The area a of the window as a function of the width x of the window 12x -(4 + π)x2/8

Let y be the height of the window's rectangular part, and let P represent the window's perimeter.

P then equals x plus 2y plus the length of the semicircular part. The radius of the semicircular part is x/2.

So, P = x + 2y + (1/2)(circumference)

     P = x + 2y  + (1/2)(2)π(x/2)

     P = x + 2y +πx/2 = 24

2y = 24 - x - πx/2

y = 12 - x/2 - πx/4 = 12 - (2 + π)x/4

A = xy + (1/2)π(x/2)2

   = x(12 - (2 + π)x/4) + πx2/8

   = 12x -(2 + π)x2/4 + πx2/8

    = 12x - (4 + 2π)x2/8 + πx2/8

   = 12x - 4x2/8 - πx2/8

   = 12x -(4 + π)x2/8

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Considering the figure, the value of x is calculated using adjacent angles concept and it is solved to be

The angle at PSR is 90 degrees

Also, angle PSQ and angle QSR are adjacent angles hence

angle PSQ + angle QSR = angle PSR = 90

90 = (5x − 12)∘ + (10x − 3)

opening the parenthesis

90 = 5x − 12 + 10x − 3

collecting like terms

90 + 12 + 3 = 5x + 10x

105 = 15x

isolating x by dividing through by 15

15x / 15 = 105 / 15

x = 7

hence the value of x is 7

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