1, In a class of 80 students in Debreberhan University, 45 are good in mathematics, 15 are good in both mathematics and in English, 13 are good in both mathematics and psychology, 16 are good in both English and psychology only, 20 are good in psychology and 9 are good in both of the three courses.

a) How many students are good in mathematics only? b) How many students are not good in any of the three course?​

Answer:

Yes. It is a rational number.

When both quantities in a rate are fractions, the strategy to write the rate as a unit rate is to divide both the numerator and denominator of the rate by their greatest common factor (GCF) to simplify the fraction.

To write the rate as a unit rate:

1. Identify the rate, which is a fraction with a numerator and a denominator.

2. Find the greatest common factor (GCF) of the numerator and denominator.

3. Divide both the numerator and denominator by the GCF to simplify the fraction.

4. The resulting simplified fraction is the unit rate.

For example, if the rate is 3/6, the GCF of 3 and 6 is 3. Divide both the numerator and denominator by 3:

3/6 ÷ 3/3 = 1/2

So, the unit rate of 3/6 is 1/2.

By converting the rate to a unit rate, we make it easier to compare the rate for a single unit of one quantity to a single unit of the other quantity, making it more convenient for comparison and analysis.

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Answer:

if both the electron and proton have the same number then the charge of an atom is neutral because each proton executes each neutron

Answer:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

Or, their exact solutions:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle 2\sec^2 \theta = 4\tan \theta + 1[/tex]

For 0° ≤ θ ≤ 360°.

Recall that tan²(θ) + 1 = sec²(θ). Substitute:

[tex]\displaystyle 2\left(\tan^2 \theta + 1\right) = 4\tan \theta + 1[/tex]

Distribute:

[tex]\displaystyle 2\tan^2\theta + 2 = 4\tan\theta + 1[/tex]

Isolate:

[tex]\displaystyle 2\tan^2\theta - 4\tan\theta + 1 = 0[/tex]

This is in quadratic form. Thus, we can solve it like a quadratic. Let u = tan(θ). Hence:

[tex]\displaystyle 2u^2 - 4u + 1=0[/tex]

The equation is not factorable. Therefore, we can consider using the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]

In this case, a = 2, b = -4, and c = 1. Substitute and evaluate:

[tex]\displaytstyle \begin{aligned} u &= \frac{-(-4)\pm\sqrt{(-4)^2 - 4(2)(1)}}{2(2)} \\ \\ &= \frac{4\pm\sqrt{8}}{4} \\ \\ &= \frac{4\pm2\sqrt{2}}{4} \\ \\ &= \frac{2\pm\sqrt{2}}{2}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle u = \frac{2+\sqrt{2}}{2} \approx 1.7071\text{ or } u = \frac{2-\sqrt{2}}{2}\approx 0.2929[/tex]

Back-substitute:

[tex]\displaystyle \tan\theta = \frac{2+\sqrt{2}}{2} \text{ or } \tan \theta = \frac{2-\sqrt{2}}{2}[/tex]

Take the inverse tangent of both equations. Hence:

[tex]\displaystyle \theta = \arctan\frac{2+\sqrt{2}}{2} \approx 59.6388^\circ\text{ or } \theta = \arctan\frac{2-\sqrt{2}}{2}\approx 16.3249^\circ[/tex]

The same value of tangent occurs twice in every full rotation. Hence, by reference angles, the other two solutions are:

[tex]\displaystyle \theta = 180^\circ + \arctan\frac{2+\sqrt{2}}{2} \approx 239.6388^\circ \\ \\ \theta = 180^\circ + \arctan\frac{2-\sqrt{2}}{2} \approx 196.3249^\circ[/tex]

In conclusion, the four solutions are:

[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]Or, approximately:

[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]

Answer:

60

Step-by-step explanation:

5(x + 7)

when x is equal to 5, then

Answer:

1.60934 per hour

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Answer:

1.60934 per hour

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Answer:d

Step-by-step explanation:

Answer:

0.48

Step-by-step explanation:

[tex]0.6*0.8 = 0.48[/tex]

9514 1404 393

Answer:

  a2 = 12

  a3 = 36

Step-by-step explanation:

Terms of a geometric sequence have a common ratio. If we call that ratio r, then we have ...

  a2 = 4r

  a3 = (a2)r = 4r^2

  108 = (a3)r = 4r^3

  27 = r^3 . . . . . . . . . . . divide by 4

  3 = r . . . . . . . . . . cube root

__

  a2 = 4(3) = 12

  a3 = 12(3) = 36

Answer:

first question: reflection on the y axis

second question: reflection on the x axis

Step-by-step explanation:

Answer:

Area = 80

Step-by-step explanation:

area = a^2 = 4^2 = 16 = square

area = wl = 12*8 = 96 = rectangle

rectangle - square

96 - 16 = 80

The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.

To find the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.

First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:

d = √(h² + p²)

d = √(179² + 16.5²)

d = 180.14 ft

Next, we can use the tangent function to find the angle of deviation (θ):

tan(θ) = p/h

tan(θ) = 16.5/179

θ = tan⁻¹(16.5/179)

θ ≈ 5.31 degrees

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Answer:

-2

Step-by-step explanation:

Simply plug 3 into the equation and follow the order of operations.

2(3 - 4) + (3(3)) - (3^2)

2(-1) + (9) - (9)

= -2

9514 1404 393

Answer:

  3 in

Step-by-step explanation:

Ratios of corresponding sides are equal, so we have the proportion ...

  x/(5 in) = (6 in)/(10 in)

  x = (5 in)(6/10) = 3 in

The missing side (x) is 3 in.

Answer:

n | 0 | 0 1

| y 2 | 2 y 3 | 3 años

Step-by-step explanation:

Answer:

The choose B) -9/8

Step-by-step explanation:

[tex] \frac{ - 2a ^{ - 3 } {b}^{2} }{a} \\ \frac{ - 2( - 2)^{ - 3} {3}^{2} }{ - 2} \\ \frac{ - 2(9)}{ - 2( - 8)} = - \frac{9}{8} [/tex]

I hope I helped you^_^

Answer:

d= 3h-6

Step-by-step explanation:

h= d/3+2

h-2= d/3

d= 3(h-2)= 3h-6

Answer:

d = 3h - 6

Step-by-step explanation:

[tex]h = \frac{d}{3} + 2[/tex]

subtract 2 on all sides :

[tex](h) - 2 = (\frac{d}{3} + 2) - 2 \\ \\ h - 2 = \frac{d}{3} [/tex]

multiply 3 on all sides:

[tex](h - 2) \times 3= \frac{d}{3} \times 3 \\ \\ 3(h - 2) = d[/tex]

open bracket:

[tex]d = 3h - 6[/tex]

Answer:

11

Step-by-step explanation:

(y+5)-(y-6)

y+5-y+6(opening the bracket)

5+6

11

Answer:

11

Step-by-step explanation:

(y+5) - (y-6) = y + 5 - y + 6 =

0y + 11 = 11

Remember, y - y = 1y - 1y = 0y or 0,  and - (y-6) = -1 (y-6) = -y + 6

Step-by-step explanation:

Given line y=1/3x-4

slope of given line m=1/3

Slope of required line :

m=1/3

As lines are parallel then slope of lines are equal.

Using point slope form:

y-y1=m(x-x1)

p(x1,y1)=(9,8)

y-8=1/3(x-9)

3y-24=x-9

x-3y-9+24=0

x-3y+15=0

Note:if you need to ask any question please let me know.

Answer:

B

Step-by-step explanation:

it simplifies to [tex]x^{4}[/tex]

Step-by-step explanation:

3(2-x)=9

this is the answer to the statement

The expression three times the quantity two decreased by x is nine is - 1

A quantity two decreased by x can be expressed thus :

Multiplying the quantity by 3 :

The expression can be written Mathematically as thus : 3(2 - x) = 9

The expression can be expanded further as :

3(2 - x) = 9

6 - 3x = 9

Collect like terms

-3x = 9 - 6

-3x = 3

x = (3 ÷ -3)

x = - 1

Therefore, the expression equates to - 1

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Answer:

15 is the middle number

Step-by-step explanation:

BECAUSE IF YOU COUNT FROM THE LEFT AND RIGHT AND WHICH NUMBER APPEARS IN THE MIDDLE IS YOUR MEDIAN

Answer:

15

Step-by-step explanation:

this asks for the median, and not the mean value.

please notice that these 2 values are often if not mostly different from each other.

the median just defines the middle of the value interval, so that half of the different values are left, and half are right of that median value.

here we have 7 values. do we find one, so that 3 other values are smaller, and 3 other values are bigger than that ?

that is 15.

10, 12, 13 are smaller.

16, 19 and 25 are bigger.

so, 15 is the median.

Step-by-step explanation:

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Answer:

d is the answer

Step-by-step explanation:

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Answer:

20

Step-by-step explanation:

For the area of a rectangle we use A = L* W

We know area or A = 420

and we know length or L = 21

Now we need to find the width or W

(420) = (21) * W

Divide both sides of the equation by 21 to isolate the variable.

That leaves us with:

W = 20

Here, we want to solve for the number of servings 10 pounds of egg whites can make

Number of servings 10 pounds of egg whites can make is approximately 27 servings

1 pound = 16 ounce

10 pounds = 160 ounce

Quantity of egg whites available = 10 pounds

Quantity of egg whites per serving = 6 oz

Number of servings 10 pounds can make = Quantity of egg whites available / Quantity of egg whites per serving

Recall,

10 pounds = 160 oz

= 160 oz / 6 oz

= 26.67

Approximately,

27 servings

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Step-by-step explanation:

500 divided by 3 __

__ + 3645 = __

__ - 240 = __

9514 1404 393

Answer:

  70

Step-by-step explanation:

If we consider the terms to have decreasing powers of x, then the middle term is the one with x^4y^4 as its variables. The full value of that term is ...

  (8C4)(2x)^4(3y)^4 = 70(6xy)^4

Substituting for x and y, this is ...

  70(6(1/3)(1/2))^4 = 70(1^4) = 70

The middle term is 70 when (x, y) = (1/3, 1/2).

_____

The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.

Answer:

46 hours and 5 minutes she worked

Answer is 15.60

we can say 4h and 15 min is 4.15

4.15 + 5.00 + 6.45 =

15.60

so the answer would be B

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