People from two houses 9,000 feet apart are looking up at a plane that is BETWEEN them. House 1 is west of the plane has an angle of elevation of 17.5 degrees and house 2 is east of the plane and has an angle of elevation that is 18.8 degrees. How far is the plane from House 1?

Answer:

3(x + 4)(x - 5) = 3x² - 3x - 60.

Step-by-step explanation:

3(x + 4)(x - 5)

Combine x + 4 and x - 5 using FOIL, or first, outer, inner, last.

F: x * x = x²

O: x * -5 = -5x

I: x * 4 = 4x

L: 4 * -5 = -20

3(x² - 5x + 4x - 20)
Simplify inside the parenthesis.

3(x² - x - 20)

Distribute the 3 into the equation.

3x² - 3x - 60

Answer:

y = -3

Step-by-step explanation:

5(y+2/5) = -13

distributive property ( 5 x y is 5y, 2 divided by 5 is 0.4 x 5 is 2.)

5y + 2 = -13

take away 2 from both sides (2 is currently positive, so doing opposite)

5y + 2 - 2 = -13 - 2

divide by 5 on both sides

5y = -15

y = -3

hope this helps

Answer:

Step-by-step explanation:

Using it's formula, considering the results, it is found that the accuracy of the test is of 0.95 = 95%.

It is given by the number of correct results divided by the number of tests.

In this problem, there were 80 tests, of which 80 - 2 - 2 = 76 had correct results, hence the accuracy is given by:

A = 76/80 = 0.95 = 95%.

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Answer:

[tex]5x-53+\frac{529}{x+10}[/tex]

Step-by-step explanation:

The complete question is

"Segment MP is a diameter of circle O. Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.

Which equation can be used to find mArc M N?

mArc M N + 150 = 180, mArc M N + 150 = 360, mArc M N – 150 = 180, mArc M N – 150 = 360"

The Equation m Arc(MN) + 150  = 180 is used to find mArc MN. Thus, the correct option is A.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

It is Given:

Segment MP is the diameter of circle O. Circle O is shown.

Line segment M P is a diameter.

Line segment N O is a radius.

∠NOP = 150°

We need to Find the Equation for m Arc MN

We already know the Diameter subtends 180° as it is the half of Circle 360°

∠NOP = 150°  

∴ m(Arc NP) = 150°

The measure of an arc is the measure of its central angle

Therefore,

m Arc Diameter = 180°

m Arc(MN) + m Arc(NP)  = 180

m Arc(MN) + 150  = 180

Therefore, the Equation m Arc(MN) + 150  = 180 is used to find mArc MN.

Thus, the correct option is A.

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[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= x^2-2x-4 \qquad \begin{cases} x_1=-1\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-1)}{4 - (-1)} \\\\\\ \cfrac{[(4)^2-2(4)-4]~~ - ~~[(-1)^2-2(-1)-4]}{4+1}\implies \cfrac{4~~ - ~~(-1)}{5} \\\\\\ \cfrac{4+1}{5}\implies \cfrac{5}{5}\implies 1[/tex]

The center of the circle is (0,2) and the radius is 5 units

The equation is given as:

x² + (y-2)² =25

The equation of a circle is given as:

(x - a)² + (y - b)² = r²

Where:

Center = (a,b)

Radius =  r

By comparison, we have:

(a,b) = (0,2)

r² = 25

Evaluate

r = 5

Hence, the center of the circle is (0,2) and the radius is 5 units

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Answer:

retang gular figure of 7 ft and 12 ft

Step-by-step explanation:

i want 100 thx

Answer:

Hi,

Step-by-step explanation:

[tex]\left\{\begin {array} {ccc}x&=&2*cos(t)-1\\y&=&3*sin(t)+4\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}\dfrac{x+1}{2}&=&cos(t\\\dfrac{y-4}{3}&=&sin(t)\\\end{array}\right.\\\\Squaring\\\\\boxed{(\dfrac{x+1}{2})^2+(\dfrac{y-4}{3})^2&=1}\\[/tex]

The curve is an ellipse having (-1,4) as center and half-axis (2 and 6)

Answer:

How?

I don't know

haha

thanks for the points

Answer:

5

Step-by-step explanation:

6 + 4 is 10

Half of 10 is 5

Step-by-step explanation:

A, ×* y = -10 / 9

B, y / x = -8 / 5

C, x / y = -5 / 8

D, x+ y = 1 / 2

E, x- y = - 13 / 6

F, y- x = 13 / 6

Answer:

138.16

Step-by-step explanation:

Answer:

153.86 sq m

Step-by-step explanation:

Area if a circle is:

A = pi•r^2

You have diameter = 14, so the radius (the r in the formula) is HALF the diameter. The radius for your circle is 7.

Area = pi•7^2

The directions said to use 3.14 for pi and do not round.

A = 3.14•7^2

A = 3.14•49

A = 153.86m^2

The units are square meters.

Answer:

total weight in pounds = 22 lb

Step-by-step explanation:

Let's first find out the total weight in kilograms.

total weight = 4 x 2.5 kg = 10 kg

The approximation for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb.

So if 1 kg is 2.2 lb, 10 kg is 10 times more.

10 kg = 10 x 2.2 lb = 22 lb

The time it would take for the bacteria to reach 1119 is 5.83 hours

Given the function:

[tex]Pt= P_0e^k^t[/tex]

To find the exponential growth;

80 = [tex]50e^k^*^3[/tex]

[tex]k= 1.6/3\\k= 0.533[/tex]

If there is a constant growth, then to get to 1119:

1119= [tex]50e^0^.^5^3^3^*t[/tex]

3.8 = 0.533*t

t= 5.83 hours

Therefore, it would take 5.83 hours for the bacteria to increase to 1119.

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

We know that there's a probability of [tex]p=\frac{40}{50}=\frac{4}{5}=0.8[/tex] of choosing an electronic component that is not defective and a probability of [tex]q=\frac{10}{50}=\frac{1}{5}=0.2[/tex] of choosing an electronic component that is defective:

[tex]\displaystyle P(X\geq4)=P(X=4)+P(X=5)+P(X=6)\\\\P(X\geq4)=\binom{6}{4}(0.8)^4(1-0.8)^{6-4}+\binom{6}{5}(0.8)^5(1-0.8)^{6-5}+\binom{6}{6}(0.8)^6(1-0.8)^{6-6}\\\\P(X\geq4)=\frac{6!}{4!(6-4)!}(0.8)^4(0.2)^2+\frac{6!}{5!(6-5)!}(0.8)^5(0.2)^1+\frac{6!}{6!(6-6)!}(0.8)^6(0.2)^0\\ \\P(X\geq4)=0.90112[/tex]

So, if 6 components are drawn at random from the container, the probability that at least 4 are not defective is 0.90112

Problem 2

[tex]\displaystyle P(X=3)=\binom{8}{3}(0.2)^3(1-0.2)^{8-3}\\\\P(X=3)=\frac{8!}{3!(8-3)!}(0.2)^3(0.8)^5\\ \\P(X=3)\approx0.1468[/tex]

So, if 8 components are drawn at random from the container, the probability that exactly 3 are defective is 0.1468

The probability of exactly 3 of the containers being defective is given as 0.1468

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

to solve for the probability

We have to set p as the  probability of container being non- defective

We have p as the  probability of container being defective 50 - 10 = 40

p = 40/50

= 0.8

q = 10/50

= 0.2

P(3) = 8c3 * 0.2² * 0.8⁵

= 0.1468

Hence the probability that the container has exactly 3 defective containers is 0.1468

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Answer:

3x - y = 1

Explanation:

Equation formula:

y - y1 = m(x - x1)

where m is slope, (x1, y1) are coordinates

Find Equation:

⇒ y - 2 = 3(x - 1)

⇒ y = 3x - 3 + 2

⇒ -3x + y = -1

⇒ 3x - y = 1

Equation of line in point slope form

The value of f(-2) in the polynomial is 43

The polynomial function is given as:

f(x) = 10x^2 − 4x − 5;

To calculate f (−2), we substitute -2 for x in f(x).

So, we have:

f(-2) = 10(-2)^2 - 4(-2) - 5

Evaluate the expression

f(-2) = 43

Hence, the value of f(-2) in the polynomial is 43

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By decomposing the figure in simpler shapes, we will see that the total area is:

a = 180 cm²

Remember that the area of a rectangle of width W and length L is:

A = L*W

And the area of a triangle with base B and height H is:

A = B*H/2.

Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.

So the area of that part is:

A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²

Now, the bottom triangle has a base of 12 cm, and a height of:

15cm - 6cm = 9cm

Then its area is:

A' = 12cm*9cm/2 = 54cm²

This means that the total area of the figure is:

total area = 54cm² + 54cm² = 108cm²

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Answer:

Murat can fill 6/13 kg of rice

Step-by-step explanation:

because it has 2/3 kg of rice and 3/10 each and I added 6+2 and 3+10 hope it makes your day

Answer:  Murat can fill 6/13 kg of rice

The degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

The amount of rows of training data used to fit the model equals the degrees of freedom.

Total observation = 10

Number of independent variables = 7

Degree of freedom for regression = 10 – 7 - 1

= 2

Thus, the degrees of freedom in a regression model is 2 if the model that has 10 observations and 7 independent variables.

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Recall that for |x| < 1, we have

[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]

Differentiating both sides gives

[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty n x^{n-1} = \sum_{n=0}^\infty (n+1) x^n[/tex]

so that the Maclaurin expansion of the given function is

[tex]\displaystyle \frac5{1-x} = \boxed{\sum_{n=0}^\infty 5(n+1) x^n} = 5 + 10x + 15x^2 + 20x^3 + \cdots[/tex]

Answer:

d)14

Step-by-step explanation:

use Pythagoras

a² = b² ,+ c²

50² = 48² + c²

2500 - 2304 = c²

196 = c²

√196 = c

c=14

Answer:

3/2

Step-by-step explanation:

Answer:

y = 5sin(6π/7) + 3

Answer:

The answer you selected is correct. Because, [tex]\frac{4}{5} ^{3\\}[/tex]is 4/5, 3 times.

Attached is more explanatory information

Step-by-step explanation:

Answer:

B. [tex]\frac{4}{5}\cdot\frac{4}{5} \cdot\frac{4}{5}=\frac{64}{125}[/tex]

Step-by-step explanation:

(4/5) is raised to a numerical power of 3.

Instead, (4/5) is being multiplied by itself 3 times.

The complete expansion is written as: [tex]\frac{4}{5}\cdot\frac{4}{5} \cdot\frac{4}{5}=\frac{64}{125}[/tex]

You have the correct option selected.

Answer:

1) Scalene

2) Equilateral

3) Isosceles

4) Right

5)Obtuse

Step-by-step explanation:

The requried correct match for the given triangle and its sides and angle has been shown.

Following the given characteristic the match of the the properties of triangle is given as:
Type of Triangle:            Characteristics

Scalene:                 all side lengths and angles are different sizes

Equilateral:            all side lengths are equal and all angles are 60°

Isosceles:              two sides and their base angles are equal

Right:                     one angle is 90°

Obtuse:                 one angle is greater than 90°

Thus, the required match shown above is the correct match.

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Answer:

D

Step-by-step explanation:

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{r}[/tex]

Answer:

AC = BC = 5

AB = 5√2

∠A = ∠B = 45

∠A = 90

Step-by-step explanation:

AC = 5 ( Reason : 5 squares are present in between A and C )

Similarly,

BC = 5

By Pythagoras theorem,

(AB)² = (AC)² + (BC)²

        = 5² + 5²

        = 2 * 5²

(AB)² = 2 * 5²

AB = 5√2

Since, sides AC and BC are equal,

∠A = ∠B = 45

Since, AC is perpendicular to BC,

∠A = 90