Find the slope of the line that passes through (-10, -52) and (56, -37).

Answer:

[tex]Pr = 0.4286[/tex]

Step-by-step explanation:

Given

Let

[tex]U \to\\[/tex] Undergraduates

[tex]G \to[/tex] Graduates

So, we have:

[tex]U = 3; G =5[/tex] -- Total students

[tex]r = 4[/tex] --- students to select

Required

[tex]P(U =2)[/tex]

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

So, we have:

[tex]Total = ^{U + G}C_r[/tex]

[tex]Total = ^{3 + 5}C_4[/tex]

[tex]Total = ^8C_4[/tex]

[tex]Total = \frac{8!}{(8-4)!4!}[/tex]

[tex]Total = \frac{8!}{4!4!}[/tex]

Using a calculator, we have:

[tex]Total = 70[/tex]

The number of ways of selecting 2 from 3 undergraduates is:

[tex]U = ^3C_2[/tex]

[tex]U = \frac{3!}{(3-2)!2!}[/tex]

[tex]U = \frac{3!}{1!2!}[/tex]

[tex]U = 3[/tex]

The number of ways of selecting 2 from 5 graduates is:

[tex]G = ^5C_2[/tex]

[tex]G = \frac{5!}{(5-2)!2!}[/tex]

[tex]G = \frac{5!}{3!2!}[/tex]

[tex]G =10[/tex]

So, the probability is:

[tex]Pr = \frac{G * U}{Total}[/tex]

[tex]Pr = \frac{10*3}{70}[/tex]

[tex]Pr = \frac{30}{70}[/tex]

[tex]Pr = 0.4286[/tex]

Answer:

what is the question

Step-by-step explanation:

Answer:

18. 28 cm*2

19. 24 m

Step-by-step explanation:

18. length × l = 16

l*2= 16

l = 4

RQ = 4 cm

PR =7cm

Area of parallelogram = b×h

= 7×4

=28cm*2

19. 8 +8 + (6-2) +( 6- 2)

=24 m

Answer:

5

Step-by-step explanation:

We know that we can use the Pythagorean theorem

a^2 + b^2 =c^2

where a and b are the legs and c is the hypotenuse

one of the legs is 12 and the hypotenuse (diagonal) is 15

a^2 + 12^2 = 15^2

a^2 +144 = 169

a^2 +144-144 =169-144

a^2 = 25

Taking the square root of each side

sqrt(a^2) = sqrt(25)

a = 5

Answer:

l = 9 cm

Step-by-step explanation:

Using Pythagoras' identity in one of the right triangles with legs width w, length l and hypotenuse h , then

l² + w² = h²

l² + 12² = 15²

l² + 144 = 225 ( subtract 144 from both sides )

l² = 81 ( take the square root of both sides )

l = [tex]\sqrt{81}[/tex] = 9

2x+8 = 22

2x+8-8 = 22-8

2x = 14

2x/2 = 14/2

x=7

Hope this helps :)

Answer:

[tex]2x+8=22[/tex]

[tex](2x+8)+(-8)=22+(-8)[/tex]

[tex]2x+8-8=22-8[/tex]

[tex]x=7[/tex]

OAmalOHopeO

Answer:

when you have items outside a parentheses that needs to be multiplied by the items inside

a(b+c) = ab + ac

Step-by-step explanation:

C 72°

Answer:

we have

f(c)=9/5C+32

now

22°C to °F

°C=22°

we have

f(c)=9/5C+32

f(c)=9/5*22+32=71.6≈72

answer is

22°C=72°F

Answer:  [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}[/tex]

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F[/tex]

Answer:

The answer is 1

Step-by-step explanation:

Answer:

The fourth option.

x + b/2a = +- sqrt((b^2 - 4ac)/(4a^2))

Step-by-step explanation:

Answer:

GH = 8.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan J = opp side / adj side

tan J = HG / HJ

tan 40 = GH / 10

10 tan 40 = GH

8.39099=GH

Rounding to the nearest tenth

GH = 8.4

124

4×23 =92(for cats)

4×8=32(for dogs)

then 92+32=124

Answer:

f(x)=2(x-3)-2

Step-by-step explanation:

when you hear if it translate to the right, it mean subtract " - "

so translate 3 unit right, it mean minus 3.

and same if translate left, it mean add, "+"

But if it mean shift down, it mean minus -

and if it mean shift up, it mean add +

so shift down 2 unit, mean -2

stretch factor of 2, mean multiply by 2

I hope this help! Im gonna explain further more if you have any question☺

The transformation of a function involves changing the features of the original function to another.

The new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]

The function is given as:

[tex]f(x) = (x + 2)^2 - 5[/tex]

When translated right, the rule is:

[tex](x,y) \to (x - h, y)[/tex]

In this case;

[tex]h= 3[/tex] --- i.e. 3 units right

So, the function becomes

[tex]f'(x) = (x + 2 - 3)^2 - 5[/tex]

[tex]f'(x) = (x - 1)^2 - 5[/tex]

When shifted down, the rule is:

[tex](x,y) \to (x, y - b)[/tex]

In this case;

[tex]b =2[/tex]  --- i.e. 2 units down

So, the function becomes

[tex]f'(x) = (x- 1)^2 - 5-2[/tex]

[tex]f'(x) = (x- 1)^2 - 7[/tex]

When vertically stretched, the rule is:

[tex](x,y) \to (x, ay)[/tex]

In this case;

[tex]a =2[/tex]  --- i.e. factor of 2

So, the function becomes

[tex]f"(x) = 2*[(x- 1)^2 - 7][/tex]

[tex]f"(x) = 2(x- 1)^2 - 14[/tex]

Hence, the new function is: [tex]f"(x) = 2(x- 1)^2 - 14[/tex]

Read more about function transformations at:

brainly.com/question/24326503

Answer:

Step-by-step explanation:

The greatest common factor of 5 and -20 is 5

x: the greatest common factor is x

y: the greatest common factor is y^3

Answer: 5xy^3(y - 4x)

Answer:

the school band

Step-by-step explanation:

the band, the band has a percentage of 53.85...,which is (14/26)x100, and the choir has 35.71% which is (5/14)x100

Answer:

120°

Step-by-step explanation:

<U + <T = 180

or, 6x-6+9x+21=180

or, 15x=165

or, x=11

so, <T = 9×11+21 = 120

Answer and Step-by-step explanation:

1.

Since we known how much money Jane and Mark have in total, we can subtract the amount Jane has to find the amount Mark has.

750 - 175 = $575

Mark has $575.

2.

We know how many cards Jamal sold, so if we add it to the amount he still has left, we can find the original amount of cards Jamal had.

17 + 83 = 100

Jamal had 100 cards.

#teamtrees #PAW (Plant And Water)

Answer:

Mark will have $575.

Step-by-step explanation:

Take the total amount ($750) and subtract Jane's contribution ($175) to get Mark's contribution($575).

$750-$175=$575

Step-by-step explanation:

the missing side is the adjacent side of the angle 66..which also has an opposite side of 19, therefore you use tan

tan66=19/x

tan66x/tan66=19/tan66

x=8.5

I hope this helps

Measure of base of the triangle, value of x is 8.46 unit.

Trigonometric ratios can be calculated by taking the ratio of any two sides of a right triangle. Given the scale of the other two sides, we can evaluate the third side using the Pythagorean theorem. We can compare the length of any two sides and the angle of the base using trigonometric ratio. The angle θ is an acute angle (θ < 90°) and  is usually measured counterclockwise with respect to the positive x-axis. The basic formula for trigonometric ratios is:

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

Given,

In right triangle,

Base of the triangle is x

Measure of angle = 66°

Perpendicular = 19 unit

tanθ = Perpendicular/base

tan66° = 19/x

2.246 = 19/x

x = 19/2.246

x = 8.46 unit

Hence, 8.46 unit is measure of base of the triangle, that is value of x.

Learn more about trigonometric ratio here:

https://brainly.com/question/25122825

#SPJ7

x = number of hours

want to find probability (P) x >= 13

x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.

P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

To convert that to percentage, multiply 100, to get 84.13%

Please mark me brainliest

Answer:

The second one

Step-by-step explanation:

This is because when you do the vertical line test none of the lines should intersect more then one point. Remember in a function every x-value (input) has only one y-value (output).

Answer:

-8x² - 106x + 175 = 0

Step-by-step explanation:

Given:

(2x - 7)²- 6(2x - 7)(x-3) = 0

Find:

Solution of the following explanation

Computation:

(2x - 7)²- 6(2x - 7)(x-3) = 0

[(2x)² + (7)² - (2)(2x)(7)] - (12x - 42)(x-3) = 0

[4x² + 49 - 28x] - [12x² - 36x - 42x + 126] = 0

[4x² + 49 - 28x] - [12x² - 78x + 126] = 0

-8x² - 106x + 175 = 0

Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = [tex]3^{x + 2}[/tex]

The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = [tex]3^{0 + 2}[/tex] = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = [tex]5^{1 - x}[/tex]

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = [tex]2^{x + 3}[/tex] - 1

The asymptote is [tex]2^{x + 3}[/tex]  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  [tex]2^{0 + 3}[/tex] - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0

[tex]2^{x + 3}[/tex] = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]

The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]

The y-intercept is (0, 6)

Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:

[tex]6=a(6-4)^2+5[/tex] and

[tex]6=a(2)^2+5[/tex] and

6 = 4a + 5 and

1 = 4a so

[tex]a=\frac{1}{4}[/tex] and the equation is

[tex]y=\frac{1}{4}(x-4)^2+5[/tex]

Answer:

First, find the function of the line:

Therefore, the function is [tex]y=\frac{3}{4} x[/tex].

Since it's the area under the graph that's shaded(not ≥ or >) and the graphed line is dotted(not ≤ or ≥), then the inequality would be [tex]y<\frac{3}{4} x[/tex].

Answer:

56 + 77 + 88 + 99 = 320km²

Step-by-step explanation:

A triangular prism has 5 sides. We can start with the top and bottom, which have a base of 7 km and a height of 8km, making each of their areas equal to 7 * 8/2 = 28. Adding those up, we get 28+28 = 56 km² as the surface area of the top and bottom portions.

Next, we have the face that has 7 as the base and 11 as the height. The area of that is 7 * 11 = 77km²

After that, we have the face with 8 as the base and 11 as the height, making the area of that 8 * 11 = 88km²

Finally, we have the face with 9 as the base and 11 as the height, making that area 9 * 11 = 99km²

Adding these all up, the total surface area is

56 + 77 + 88 + 99 = 320km²

9514 1404 393

Answer:

  53°

Step-by-step explanation:

The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.

  m∠Y = 53°

Answer: 53

Step-by-step explanation:

______________________________

[tex]\sf\bold{The\:above\:graph\:says:}[/tex]

$\space$

$\sf\bold{here:}$

$\space$

$\sf\bold{Find\:acceleration\:by\:v-t\:graph:}$

$\mapsto$ $\sf\small{TanØ =}$ $\sf\dfrac{slope\:of\:y}{slope\:of\:x}$= $\sf\dfrac{20}{8}$ $\sf{m/s^2}$

$\space$

$\space$

$\sf\bold{Now,calculate\:the\:distance:}$

$\space$

$\sf\bold{Given\:parameters:}$

$\space$

$\sf\bold{Substituting \: the\:values:}$

$\mapsto$ $\sf\small{s=0+}$ $\sf\dfrac{1}{2}$ $\times$ $\sf\dfrac{5}{8}$ $\sf\small{8^2}$

$\space$

$\longmapsto$ $\sf\underline\bold\purple{S=80m}$

$\space$

❍Therefore , the acceleration is $\sf\bold{2.5m/s^2}$ and the distance traveled by car is $\sf\bold{80m.}$

_______________________________

80 m is distance ! Please mark as brainliest

Answer:

x = 4

139.2

Step-by-step explanation:

Given the Cost function :

C(x) = 1.7x² - 13.6x + 166.4

To achieve minimum cost ;

dc/dx = 0

dc/dx = 2(1.7)x - 13.6

3.4x - 13.6 = 0

3.4x = 13.6

x = 13.6 / 3.4

x = 4

To achieve minimum cost, speed = 4 ;

Minimum cost will be :

C(x) = 1.7x² - 13.6x + 166.4

Put x = 4

C(4) = 1.7(4)² - 13.6(4) + 166.4

C(4) = 27.2 - 54.4 + 166.4 = 139.2

Minimum cost = 139.2

Answer:

[tex]x=32768.000[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]log_2(x)+log_4(x)=5[/tex]

Use the logarithm base change rule, which states the following:

[tex]log_b(y)=\frac{log(y)}{log(b)}[/tex]

Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:

[tex]log_2(x)+log_4(x)=5[/tex]

[tex]\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5[/tex]

Factor out (log(x)),

[tex](log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5[/tex]

Inverse operations:

[tex]log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}[/tex]

Simplify,

[tex]log(x)=5(log(2)+log(4))[/tex]

[tex]log(x)=4.51545[/tex]

Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:

[tex]b^x=y\ \ -> log_b(y)=x[/tex]

[tex]log(x)=4.51545[/tex]

[tex]10^4^.^5^1^5^4^5=x[/tex]

[tex]32768.000=x[/tex]

Answer:

100 ft

Step-by-step explanation:

We need to find the diagonal ( or hypotenuse)

We can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

80^2 + 60^2 = c^2

6400+3600 = c^2

10000 = c^2

Taking the square root of each side

sqrt(10000) = sqrt(c^2)

100 = c