Find the size of angle x.

The probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

Then:

[tex]P(E) = \dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for event E, and similar for A(S).

For this case, we're given that:

The favorable space is the blue shaded region.

The total sample space is the area of the considered square.

Let we take:

E = event of choosing point in the blue shaded region

Now, we have:

Area of blue region = Area of triangle with base = height = 8 inches + Area of right sided triangle which has base of 4 inch (look it upside down), and height of 8 inches

Area of blue region = [tex]\dfrac{1}{2} \times (8 \times 8 + 4 \times 8) = 48 \: \rm in^2[/tex]

Area of the square of sized 8 inches = 64 sq. inches.

Thus, we get:

[tex]P(E) = \dfrac{A(E)}{A(S)} = \dfrac{48}{64} = \dfrac{3}{4} = 0.75[/tex]

Thus, the probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

Learn more about geometric probability here:

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What is it?

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

How do you find IQR?

Step 1: Put the numbers in order. ...

Step 2: Find the median. ...

Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically, but it makes Q1 and Q3 easier to spot. ...

Step 4: Find Q1 and Q3. ...

Step 5: Subtract Q1 from Q3 to find the interquartile range.

Answer:

The answer to this quesion is a measure of statistical dispersion, the spread of data or observations, first you need to get the data find the median calculate the median from both lower and upper half of the data and the iqr is the diffrence between the lower and upper.

Step-by-step explanation:

I Hope This Helps You!

-Justin:)

Answer:

c. 141 eighth-grade band students

Part B:

y = 3x

1/3y = x

Answer:

5a - 4b

Step-by-step explanation:

= 8a - 6b - 3a +2b

= 8a - 3a - 6b + 2b

= 5a - 4b

Hope it helps :)

Answer:

5a - 4b

Step-by-step explanation:

The function [tex]y = -5t^2 + 125[/tex] of the nickel is quadratic function

It will take 5 seconds for the coin to hit the ground

The function is given as:

[tex]y = -5t^2 + 125[/tex]

When the nickel hits the ground, the value of the function is:

y = 0

So, we have:

[tex]-5t^2 + 125 = 0[/tex]

Subtract 125 from both sides

[tex]-5t^2 =- 125[/tex]

Divide both sides by -5

[tex]t^2 =25[/tex]

Take the square root of both sides

[tex]t = 5[/tex]

Hence, it will take 5 seconds for the coin to hit the ground

Read more about quadratic functions at:

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Answer:

below

Step-by-step explanation:

the law of indices:

a) x⁵

b) x¹⁷

c) -18s⁹

d) -60x²

Answer:

(a) Kaylee earns $19.50 per hour.

(b) Kaylee earns more per hour.

Step-by-step explanation:

a)

[tex]m[/tex] = $ per hour

[tex]y = mx[/tex]

[tex](39) = m(2)[/tex]

[tex](39 = m(2)) = 19.50 = m[/tex]

b) Kaylee earns more per hour

Kaylee earns $19.50 per hour and Joey earns $16.50 per hour.

Answer:

yes she can

Step-by-step explanation:

yes she can because $20 is great than $18.50

Answer:

Part A: [tex]x^2-30x+224\geq 0[/tex]

Part B: Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Since there are 2 question-

Let,

How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:

Let,

The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.

Be Part B:

Hint:

J=Jessica

30-J=Martha

(J-6)*((30-J)-6)<=80

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve:

Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has

Let,

"x" be the number of cookies when Jessica started

"30-x" be the number of cookies when Martha started

Given us that:

Each of them ate 6 cookies from their bag

Therefore,  

Cookie left in each bag are:

(x-6) which is - Jessica

30 - x - 6 = (24 - x) - Martha

Solution - (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

Thus,

[tex](x-6)(24-x\leq 80[/tex]

[tex]24x-x^2-144+6x\leq 80[/tex]

[tex]-x^2+30x-144-80\leq 0[/tex]

[tex]-x^2+30x-244\leq 0[/tex]

[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]

[tex]x^2-30x+224\leq 0[/tex]

Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve:

Part B: Solve the quadratic equation:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]

[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]

[tex]14\le \:x\le \:16[/tex]

The solution is x=16 cookies

Thus, (30-x)=30-16=14 cookies

Now we know that;

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

So,

The number of cookies left in each bag  is equal to

Jessica:

16-6=10 cookies

Martha:

14-6=8 cookies

10 > 8

As a result, Jessica has at least 2 cookies more than Martha.

Fill in blank for:

The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.

Jessica has at least __2__ cookies more than Martha.​

~Lenvy~

Answer:

Third option

Step-by-step explanation:

Since our leading coeffeicent has a leading even degree, and a positive number,

The end behavior will as

as x approaches oo, and -oo, f(x) approaches oo.

The area of Square 4 is a2+2ab+b2

The area of Square 5 is 2ab+c2

Setting them equal to one another (a2+2ab+b2=2ab+c2) and simplifying yields that a2+b2=c2 (note that 2ab is what they have in common), which is Pythagoras' theorem.

Answer:

Step 1 : First, solve one linear equation for y in terms of x .

Step 2 : Then substitute that expression for y in the other linear equation. ...

Step 3 : Solve this, and you have the x -coordinate of the intersection.

Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.

Step-by-step explanation:

These are all of the steps

The expression of [tex]\sqrt{[/tex](16a^4x^6) is an algebraic expression

The equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3

The expression is given as:

[tex]\sqrt{[/tex](16a^4x^6)

Expresss 16 as the square of 4

[tex]\sqrt{[/tex](16a^4x^6) = [tex]\sqrt{[/tex](4^2a^4x^6)

Evaluate the square root of each factor in the expression

[tex]\sqrt{[/tex](16a^4x^6) = 4a^2x^3

Hence, the equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3

Read more about equivalent expressions at:

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Answer:

[tex]10.67\pi[/tex] OR [tex]33.49[/tex]

Step-by-step explanation:

Volume of a Sphere: [tex]\frac{4}{3} *\pi*r^3[/tex]

Radius = 2

[tex]\frac{4}{3} *\pi*r^3[/tex]

[tex]\frac{4}{3} *\pi*2^3[/tex]

[tex]\frac{4}{3} *\pi*8[/tex]

[tex]10.67\pi[/tex]

OR

[tex]\frac{4}{3} *\pi*r^3[/tex]

[tex]\frac{4}{3} *3.14*2^3[/tex]

[tex]\frac{4}{3} *3.14*8[/tex]

[tex]\frac{4}{3} *25.12[/tex]

[tex]33.49[/tex]

Hope this helps!

Answer:

$464

Step-by-step explanation:

Answer:

10 feet

Step-by-step explanation:

Drawing obviously not to scale but... Red segment is the ruler, at least the part between 5 and 6 inches, 1 inch long. Brown segment is the pole, ground to the top. Leftmost point is the eye, green line is the horizontal. The triangles are similar (AAA, the vertical lines are parallel), the ratio of the side is the same as the ratio of the heights. The height of the larger triangle (measured across the green line is

[tex]40 yd \times 3\frac{ft}{yd} \times 12\frac{in}{ft}= 1440''[/tex].

Ratio of the height is then [tex]1440\div24 = 60[/tex].

At this point the height of the pole is 60 times the length of the measure on the ruler, or 60 inches, that is 5 feet. Add the 5 feet the pole was starting from, it's 10 feet.

Answer:

the answer is 56

Step-by-step explanation:

first off you need to add every number up which adds to be 336,

then you divide by the number of pieces in the data which in this case is 6,

366 divided by 6 is 56

I HOPE THIS HELPED!

Answer:

hannah 54

raoul 9

Step-by-step explanation:

hannah _ 6x

raoul _ x

6x+x=63

7x=63

x=9

hannah _ 6×9=54

raoul _ 9

Answer: 578

Step-by-step explanation:

12 x 7 = 84

13 + 8 + 4 + 10 = 25

25 x 14 = 350

4 x 10 = 40

8 x 13 = 104

84 + 350 + 40 + 104 = 578

Problem 1 (on the left)

It appears we have an exponential function curve through the points (0,4) and (1,7)

The general exponential function is of the form

y = a*b^x

The value of 'a' is the y intercept or initial value. So a = 4

Plug in (x,y) = (1,7) to help solve for b

y = a*b^x

y = 4*b^x

7 = 4*b^1

7 = 4b

b = 7/4 = 1.75

Therefore, the function is y = 4*(1.75)^x

These two facts help confirm we have the correct exponential equation.

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

Problem 2 (on the right)

The steps will follow the same idea as the previous question.

The exponential curve goes through (-1, 120) and (0,40)

We have a = 40 this time due to the y intercept (0,40)

Plug in the coordinates of the other point to find b

y = a*b^x

y = 40*b^x

120 = 40*b^(-1)

120 = 40/b

120b = 40

b = 40/120

b = 1/3

Answer: (1) and (4)

Step-by-step explanation:

The parts listed in the ciongruence statements don't correspond, so they aren't necessarily congruent.

Answer:

3:4

Step-by-step explanation:

18inches : 2feet

18 inches: 2x12 =24 inches

18:24 - 3:4(divide by 6)

Answer:

16

Step-by-step explanation:

You're doing a subtraction problem between (x+5) and (2x+3)

(x+5) - (2x+3) =

**You need to solve for x first then plug it in to find the answer.***

(I had to break the parentheses because that is the only way to solve)

-x +8

x= -8

-8 + 5 - (-16+3)

-3 + 16 + 3

13 + 3 = 16

Answer:

-x+2

Step-by-step explanation:

(x+5)-(2x+3)
distribute
x+5-2x-3
combine like terms
x-2x+5-3
-x+2

Using an exponential function, it is found that the equation that represents the value of the car after 5 years is:

[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the car is purchased for 21,800 dollars, and it's value deprecites 9.5% per year, hence the equation for it's value after t years is given by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 21800(1 - 0.095)^t[/tex]

[tex]A(t) = 21800(0.905)^t[/tex]

After 5 years, the value is given by:

[tex]A(5) = 21800(0.905)^5 = 13234.25[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, flop it over, and change its sign.

In this case, we take [tex]\boxed{-3}[/tex], change its sign:

[tex]\boxed{3}[/tex]

3 can also be written as

[tex]\boxed{\frac{3}{1} }[/tex]

Now the numerator & denominator switch places:

[tex]\boxed{\frac{1}{3}}[/tex]

So that's the slope of the new line.

Now, let's write the equation in point-slope form:-

[tex]\bigstar{\underline{\boxed{\pmb{y-y_1=m(x-1)}}}[/tex]

Where

y₁  is the y-coordinate of the point (in this case, y₁ = 3)

m = slope (1/3)

x₁= the x-coordinate of the point (in this case, it's -2)

Plug in the values:-

[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x-(-2)}}[/tex]

[tex]\bigstar{\boxed{\pmb{y-3=\frac{1}{3}(x+2)} }\longleftarrow\sf{Point-Slope~Formula:)}}[/tex]

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

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Third option: An infinite geometric series converges if −1<r<1 is true.

Step-by-step explanation:

An infinite geometric series contains an infinite number of terms. A convergent infinite geometric series can go to infinity on a graph. An infinite geometric series can converge if the ratio "r" is true in the equation " –1 < r < 1".

Answer:

[tex] {3}^{2} = 9 \\ \\ 81 = 9[/tex]

Answers:

Choice A) 0

Choice B) 0.5

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

Explanation:

Matia claims that [tex]x^2 > x[/tex]

However, the claim isn't true when 0 ≤ x ≤ 1.

For example, x = 0 leads to [tex]x^2 = 0^2 = 0[/tex]

Meaning that [tex]x^2 > x[/tex] would update to [tex]0 > 0[/tex] which is false.

------------------

Similarly, if x = 0.5, then

[tex]x^2 > x\\\\0.5^2 > 0.5\\\\0.25 > 0.5 \ \text{which is also false}\\\\[/tex]

Because the last inequality is false, the first inequality must also be false for x = 0.5

-------------------

Those last two previous sections showed that x = 0 and x = 0.5 are counter-examples to Matia's claim to thereby prove it false.

Answer:

[tex]\sf x =15.5[/tex]

Step-by-step explanation:

[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]

[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]

[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]

[tex]\sf 2x+1 =32[/tex]

[tex]\sf 2x+1 -1=32-1[/tex]

[tex]\sf 2x =31[/tex]

[tex]\sf x =15.5[/tex]

Answer:

Step-by-step explanation:

[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]

[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x

~~~~~~~~~~~~~~

[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5

[tex]log_{2} \frac{10x+5}{5}[/tex] = 5

[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]

10x + 5 = 32 × 5

2x + 1 = 32

x = 15.5