Plz help I’ll mark you

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

Answer:

37 buses and 1 van.

Step-by-step explanation:

The cost to rent a van is $1200 for 50 students and 3 chaperones, while a bus for 10 students and a chaperone is $100 .

The cost of renting buses for 50 students is $500

What we do is rent 37 buses and 1 van

37 buses will take in 370 students with empty 2 spaces in 2 buses for chaperones since the chaperones are 36.

Then rent 1 van to take in 50 students and 1 chaperone.

The total cost here will be

$3700 + $1200 = $ 4900

This will help to safe cost.

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex],  cos A = [tex]\frac{\sqrt{13} }{3}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]2\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex],  cos A = [tex]\frac{\sqrt{13} }{2}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = [tex]\sqrt{1872}[/tex]

⇒ AB = [tex]12\sqrt{13}[/tex] ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]             -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]

sin A = [tex]\frac{2}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex]             -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]

cos A = [tex]\frac{3}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = [tex]\frac{opposite}{adjacent}[/tex]             -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = [tex]\frac{24}{36}[/tex]

tan A = [tex]\frac{2}{3}[/tex]

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

Explanation:

Let's find angle D. Recall that for any triangle, the interior or inside angles always add to 180 degrees.

A+D+C = 180

32+D+41 = 180

D+73 = 180

D = 180-73

D = 107

Now notice that triangle ADC is congruent to triangle ABC. We can use the SSS congruence theorem to prove this.

The identical triangles must have corresponding angles that are the same measure, meaning angle D = angle B = 107 degrees.

Side note: This quadrilateral is a kite because it has two pairs of adjacent congruent sides, but not all four sides are the same length (or else it would be a rhombus).

Answer:

a) y=f(x)-2

b) y=f(-x)

9514 1404 393

Answer:

  Given: Quadrilateral QRST ...

Step-by-step explanation:

The first statement of a proof is always a restatement of the facts that are Given. The "prove" statement is a goal, never stated in the proof. The statement to be proven is the last statement (conclusion) of a proof.

9514 1404 393

Answer:

  2 -i

Step-by-step explanation:

The two diagonals have the same center point. Here, it is ...

  (1 +2) +(-1 -2i) = 0 +0i

The fourth point is found by reflecting the 2nd point across the origin:

  p4 = -p2 = -(-2 +i) = 2 -i . . . . . fourth corner of the square

Answer:

C

Step-by-step explanation:

In ∆DEG, we are given that all the three angles are congruent.

This means that all the three angles have equal measure. Thus,

<D = <E = <F

An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.

Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°

m<D = 60°

Answer:

sensory measurement are lower after hypnotism

Step-by-step explanation:

Given the data :

Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6

After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0

The difference ;

After - Before, d = 0.2, - 4.1, - 1.6, - 1.8, - 3.2, - 2, - 2.9, - 9.6

Hypothesis :

H0 : μd = 0

H0 : μ < 0

The test statistic ;

T = μd / sd/√n

Where, xd = mean of difference

sd = standard deviation of difference

n = sample size

Mean of difference, μd = Σx/n = - 3.13

Standard deviation of difference, sd = 2.91

T = - 3.13 / 2.91/√8

T = - 3.13 / 1.0288403

T = - 3.042

α = 0.01

The Pvalue using a Pvalue calculator ;

Degree of freedom, df = n - 1 ; 8-1 = 7

Pvalue(-3.042, 7) = 0.00939

Pvalue < α ; we reject the null and conclude that sensory measurement are lower after hypnotism

Answer:

[tex]x = \sqrt{-2} = 2i[/tex]

Step-by-step explanation:

[tex]5x^2-2=-12[/tex]

[tex]5x^2 =-10[/tex]

[tex]x^2 =-2[/tex]

[tex]x = \sqrt{-2} = 2i[/tex]

Answer:

Purplemath

Introduces reflections in the x- and y-axes. ... To see how this works, take a look at the graph of h(x) = x2 + 2x – 3. ... The previous reflection was a reflection in the x-axis. ... f (x – b) shifts the function b units to the right.

Answer:

[tex]\frac{-1}{4} x^{2}[/tex]

[tex]\frac{-1}{4} g(x)[/tex]

Step-by-step explanation:

Answer:

w = 5

y = 4

Step-by-step explanation:

w + y = 9

3w - y = 11 ( + )

________

4w + 0 = 20

4w = 20

w = 20 / 4

w = 5

Substitute w = 5 in eq. w + y = 9,

w + y = 9

5 + y = 9

y = 9 - 5

y = 4

Answer:

C. YES

Step-by-step explanation:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Answer:

SAA

Step-by-step explanation:

HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.

Answer:

AB is perpendicular to [GH] and GH is [A]

Step-by-step explanation:

Answer:

90 maybe is a correct answer

Answer:

Y=40°

Step-by-step explanation:

VUW~YXZ

VWU~YZX

YXZ+XYZ+YZX=180°

70°+XYX+70°=180°

140°+XYZ=180°

XYZ=180°-140°

XYZ=40°

Answer:

r is the radius of the base and s is the slant height of the cone. From the options given, We can make s the subject of the formula. Hence: Option a) s equals StartFraction L A Over pi r EndFraction

Two equivalent equations are s = LA/πr and r = LA/πs

A cone is a shape formed using a series of line segments or lines that connect a common point, called a apex or vertex, to all points on the base of a circle that do not contain a vertex. The distance from the apex of the cone to the base is the height of the cone. A circular base has a measured radius value. And the length from the apex of the cone to any point around the base is the height of the slope. Equations for the surface area and volume of a cone can be derived from these quantities

Volume(V) = ⅓ πr²h cubic units

The total surface area of the cone = πrs + πr²

where, r is radius of the base, s is slant height and h is height of the cone

Given,

Lateral area of cone is denoted by LA

Lateral area of cone = πrs

where r is radius and s is slant height

⇒ LA = πrs

⇒ s = LA/πr

⇒ r = LA/πs

Hence, s = LA/πr and r = LA/πs are two equivalent equations in the given options.

Learn more about cone here:

https://brainly.com/question/16394302

#SPJ7

Answer:

- 3.027

Step-by-step explanation:

First price = 10000 ; second price = 700

Number of tickets sold = 11000

Ticket cost = $4

Probability that a ticket wins grand price = 1 / 11000

Probability that a ticket wins second price = 1 / 11000

X ____ 10000 _____ 700

P(x) ___ 1 / 11000 ___ 1/11000

Expected winning for a ticket buyer :

E(X) = Σx*p(x)

E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost

E(X) = 0.9090909 + 0.0636363 - 4

E(X) = - 3.0272728

E(X) = - 3.027

9514 1404 393

Answer:

  $180

Step-by-step explanation:

The relationship between the prices is said to be ...

  (amount you pay) = 2/3 × (original price)

To find the original price, multiply the equation by the reciprocal of the coefficient of the (original price).

  (3/2)×(amount you pay) = (3/2)(2/3)(original price) = (original price)

  (3/2)×$120 = original price = $180

Answer:

3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].

Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:

K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)

L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)

M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)

N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)

Therefore the image of segment KL will be 3 times long.

Answer:

[tex]H_o :[/tex] Satisfaction and Gender are independent of one another

[tex]H_a :[/tex] Satisfaction and Gender are dependent of one another

Step-by-step explanation:

Given

Parameters: Meal satisfaction and Gender

Test: If both parameters are dependent

Required

The appropriate hypotheses

To do this, we set the null hypothesis to independence of both parameters

i.e.

[tex]H_o :[/tex] Satisfaction and Gender are independent of one another

The alternate hypothesis will be the opposite, i.e. dependence of both parameters

i.e.

[tex]H_a :[/tex] Satisfaction and Gender are dependent of one another

Answer:

the answer is 91

Step-by-step explanation:

Answer:

The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).

Step-by-step explanation:

Before building the confidence interval, we have to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{381.3+394.8+396.1+380}{4} = 388.05[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(381.3-388.05)^2+(394.8-388.05)^2+(396.1-388.05)^2+(380-388.05)^2}{3}} = 8.58[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 4 - 1 = 3

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{8.58}{\sqrt{4}} = 13.65[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 388.05 - 13.65 = 374.4

The upper end of the interval is the sample mean added to M. So it is 388.05 + 13.65 = 401.7

The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).

Answer:

Circumference =10 pi yard

Area =25 pi yard squared

Step-by-step explanation:

C=2*pi*r

Circumfrance =10 pi

A=pi r^2

Area =25 pi

For the estimate just sub in pi on the calculator for pi, then round to the hundreth.

Circumfrence= just the unit

Area= squared

Answer:

If you buy per dozen, each buns costs about 91 cents.

You will save $4.11 if you buy per dozen.

Step-by-step explanation:

1.25 * 12= $15

10.89/12= .9075 = .91 cents

15-10.89= $4.11

Answer:

main age = total age/total people

if Main age is = 27

[tex]27 = \frac{ \times }{5} [/tex]

and x = 135

Total age is = 135

then main age is 35

[tex][35 = \frac{y}{6} [/tex]

and y = 210

first main age - second main age = age of the person participating

210 - 135 = 75

HAVE A NİCE DAY

Step-by-step explanation:

GREETINGS FROM TURKEY

Answer:

The price per ounce is $0.16

Step-by-step explanation:

We have:

Price of a 4-pound bag = $10.24

1 pound = 16 ounces

Price per ounce =?

Hence the price per ounce is:

[tex] \frac{\$ 10.24}{4 pound}*\frac{1 pound}{16 ounces} = \frac{\$ 0.16}{ounce} [/tex]

Therefore, the price per ounce is $0.16

I hope it helps you!