Due to covid-19 pandemic, the number of available seats in a hall was reduced from 125 to 93. Calculate the percentage decrease in the number of available seats.​

Answer:

the solution set is { - 7, - 3 }

Step-by-step explanation:

(x + 3)(x + 7) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x + 7 = 0 ( subtract 7 from both sides )

x = - 7

solution set is { - 7, - 3 }

a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

Learn more about the equations here:

brainly.com/question/10413253

#SPJ1

The measure of the arc of the circle is mST = 122°

Given data ,

Let the circle be represented as C

where the two chords of the circle are RT and PS

And the chords RT and PS intersect at the point U

Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.

On simplifying , we get

m∠SUT = ( 1/2 ) ( mPR + mST )

123° = ( 1/2 ) ( 124° + mST )

On solving for mST , we get

( 124° + mST ) = 246°

Subtracting 124° on both sides , we get

mST = 122°

Hence , the measure of arc mST = 122°

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ1

To solve the equation |7x - 20| = |2x + 20|, we need to consider two cases based on the absolute values.

Case 1: (7x - 20) = (2x + 20)

Simplifying this equation, we get:

7x - 20 = 2x + 20

Subtracting 2x from both sides:

5x - 20 = 20

Adding 20 to both sides:

5x = 40

Dividing both sides by 5:

x = 8

Case 2: (7x - 20) = -(2x + 20)

Simplifying this equation, we get:

7x - 20 = -2x - 20

Adding 2x to both sides:

9x - 20 = -20

Adding 20 to both sides:

9x = 0

Dividing both sides by 9:

x = 0

Therefore, the solutions to the equation |7x - 20| = |2x + 20| are x = 8 and x = 0.

Para resolver este problema, podemos utilizar el Teorema de los Cosenos para calcular los ángulos interiores del triángulo.

Sea A, B y C los vértices del triángulo correspondientes a los centros de los engranajes. Sea a, b y c las longitudes de los lados opuestos a los ángulos A, B y C respectivamente.

Dado que los radios de los engranajes miden 15 cm, 16 cm y 17 cm, podemos considerar que los lados del triángulo son a = 15 cm, b = 16 cm y c = 17 cm.

El Teorema de los Cosenos establece que en un triángulo con lados a, b y c, y ángulos opuestos A, B y C respectivamente, se cumple la siguiente fórmula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Podemos aplicar esta fórmula para cada uno de los ángulos del triángulo.

Para el ángulo A, tenemos:

c^2 = b^2 + a^2 - 2ab * cos(A)

17^2 = 16^2 + 15^2 - 2 * 16 * 15 * cos(A)

Resolviendo la ecuación, encontramos que cos(A) = -1/8. Tomando el coseno inverso (arcocoseno), encontramos que el ángulo A es aproximadamente 135.2 grados en el sistema de medición radial.

Para el ángulo B, tenemos:

a^2 = c^2 + b^2 - 2cb * cos(B)

15^2 = 17^2 + 16^2 - 2 * 17 * 16 * cos(B)

Resolviendo la ecuación, encontramos que cos(B) = -7/17. Tomando el coseno inverso, encontramos que el ángulo B es aproximadamente 120.6 grados en el sistema de medición radial.

Para el ángulo C, tenemos:

b^2 = a^2 + c^2 - 2ac * cos(C)

16^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)

Resolviendo la ecuación, encontramos que cos(C) = -1/2. Tomando el coseno inverso, encontramos que el ángulo C es aproximadamente 120 grados en el sistema de medición radial.

Entonces, los ángulos interiores del triángulo son:

A ≈ 135.2 grados

B ≈ 120.6 grados

C ≈ 120 grados

Estos valores están expresados en el sistema de medición radial.

The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For the mileages, we have that:

Hence the functions are given as follows:

Cost B is the better plan when:

A(x) > B(x)

Hence:

30 + 0.14x > 50

0.14x > 20

x > 20/0.14

x > 142.9 miles -> rounded to 143.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

The statement that best describes the solution to the inequality in this problem is given as follows:

all real numbers except x = 1.

The inequality in the context of this problem is defined as follows:

2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7

The solution to the first inequality is given as follows:

2(x + 7) – 1 > 15

2x + 14 > 16

2x > 2

x > 1.

The solution to the second inequality is given as follows:

3(x + 2) < 2x + 7

3x + 6 < 2x + 7

x < 1.

The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:

all real numbers except x = 1.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

Answer:

The Pythagorean Theorem describes the relationship among the three sides of a right triangle

[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle

Answer:1/1875

Step-by-step explanation:

the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.

The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:

(1/5) * (1/5) * (1/5) * (4/5) = 4/3125

Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.

1) The three figure bearing of B from A when B is due East of A is 090°

2) Note that Kenzi drives 60km further than Jafar.

A) A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.

Hence in the above case of option A,  The three figure bearing of B from A when B is due East of A is 090°

B) To find or compute how much further Kenzi drives than Jafar, we need to convert the distances on the map to their real-world distances using the given scale of 1cm to 200km.

So  A to B for Jafar -

Distance from A to B = 2.4cm x 200km/ cm = 480km

Then for  B to C for Kenzi  -

Distance from B to C = (1.2cm + 1.5cm) x 200km/cm

= 2.7cm x 200km/cm

= 540km

So to  determine how much further Kenzi drives compared to Jafar

Kenzi drives 540km - Distance from A to B

= 540km - 480 km = 60km

Therefore, Kenzi drives 60km further than Jafar.

Learn more about bearing at:

https://brainly.com/question/24340249

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:

D'E' = 1/2 × DE

In conclusion, line segment D'E' is equal to one half line segment DE.

Read more on dilation and scale factor here: brainly.com/question/4421026

#SPJ1

Step-by-step explanation:

Using rules of logs :

9 loga x =  loga x^9

Then using another rule:

loga x^9 + loga y =   loga (x^9 * y )

Answer:

Step-by-step explanation:

A brokerage account is an investment account that allows you to buy and sell a variety of investments, such as stocks, bonds, mutual funds, and ETFs.

Therefore the answer is D

Answer:

(d) 18 in.

Step-by-step explanation:

When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:

P = s1 + s2 + s3, where

P = 2 + 6 + 10

P = 8 + 10

P = 18

Thus, the perimeter of the triangle is 18 in.

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.

If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.

The possible outcomes when two coins are flipped are;

head - head = HH

tail - tail = TT

Head and tail = HT

Tail and head = TH

The probability of getting two heads = 1/4

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;

Expected value = (68 flips) x (1/4 probability of getting HH) = 17

The probability of getting two tails = 1/4

Expected value = 68 x 1/4 = 17

Learn more about probability here: https://brainly.com/question/24756209

#SPJ1

The length x in the triangle below is 16 m.

Length is the distance between two points.

To calculate the length of the triangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for x

Learn more about length here: https://brainly.com/question/28108430

#SPJ1

Answer:

[tex]d < 20[/tex]

Step-by-step explanation:

The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.

Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

Answer:

just start scamming

Step-by-step explanation:

Answer: 14,5,15 is correct

Step-by-step explanation:

The equation is an identity is discussed below.

An identity is a mathematical equation that holds true for all values of the variables involved.

In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.

For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.

When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.

Learn more about Equation Identity here:

https://brainly.com/question/29125576

#SPJ1

Answer:

The answer is 64°

Step-by-step explanation:

opposite angles are equal

x=64°

Answer:

X is 64 degrees.

Step-by-step explanation:

X is directly across from 64 degrees. These angles are equal. So are angle y and 18, and angle z and the blank angle at the bottom.

The probability of getting Blue then Green while spinning the wheel is

3 / 32

Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.

From the given figure we can find out the following information

The probability of getting Blue While spinning the wheel = 3/8

The probability of getting Green While spinning the Wheel = 2 / 8

The probability of getting Blue then Green while spinning the wheel

= 3/8 * 2/8

= 6/64

= 3/32

Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32

To know more Probability about  here

https://brainly.com/question/11234923

#SPJ1

Eight fourths is proportional to the value of 2/1

Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.

A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.

Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1

Learn more about ratios here:

https://brainly.com/question/25927869

#SPJ1

The requried solution of the given derivative has been given below.

If F(t) is an antiderivative of t⁵, then we have:

F'(t) = d/dt(F(t)) = t⁵

According to the Second Fundamental Theorem of Calculus, we have:

[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]

Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:

[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]

Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]

Learn more about derivatives here:

https://brainly.com/question/25324584

#SPJ1