Juliet's monthly entertainment expenses are $275.00 and account for 12% of her income. She would like to reduce her entertainment spending to 8% of her income.

Therefore, the bumblebee bat is 0.5 centimeters shorter than the Etruscan pygmy shrew.

Inequalities are used in many areas of mathematics, including algebra, calculus, and geometry. They are also used in other fields such as economics, physics, and engineering to model real-world situations where values can vary within certain bounds. Solving inequalities involves finding the set of values that satisfy the inequality. This can be done using algebraic techniques such as adding or subtracting the same quantity from both sides of the inequality, multiplying or dividing both sides of the inequality by a positive number, or using the properties of absolute value. The solution to an inequality is often expressed as an interval or a set of numbers that satisfy the inequality.

Here,

According to the Guinness World Records, the bumblebee bat is the smallest mammal in the world, measuring only about 3 centimeters in length, while the Etruscan pygmy shrew measures about 3.5 centimeters in length.

To find out how much shorter the bat is than the shrew, we can subtract the length of the bat from the length of the shrew:

3.5 cm - 3 cm = 0.5 cm

The bumblebee bat and the Etruscan pygmy shrew are both very small mammals, but the bumblebee bat is actually shorter than the Etruscan pygmy shrew.

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Answer:

Step-by-step explanation:

have the triangles written in the same order to se the corresponding angles

C      A .   T

⇵ .  ⇵ .   ⇵

D      O .   G

∠D ≅∠C

∠O ≅∠A

GD ≅TC

10.

you have an isosceles triangle with vertex angle 48 so the base angle is

(180-48)/2 = 66

32+ x = 66 because is an exterior angle

x= 66-32 = 34

Answer:

3:2

Step-by-step explanation:

For every 3 girls : there is 2 boys, so it's 3:2

3:6 in simplest form=1:2

Answer:

Step-by-step explanation:

Set this up as a proportion

20/8 = 15/vx           Cross multiply

20*vx = 8 * 15

20 * vx = 120          Divide by 20

vx = 6

The missing numbers in the sequence given above are determined as: 3, 2, 20, 13, 12.

The missing numbers in the sequence given as, 8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, ?, ?, ?, ?, ?, can be found as explained bellow:

First, we need to identify the pattern of the sequence. Not that a pattern in the sequence given is that the numbers are arranged in ascending order from left to right, and also in descending order from the right to the left.

Applying the above this pattern, we would determine the missing numbers in the sequence as follows:

The two smallest numbers that are missing from the left side of the sequence = 2 and 3.

The three largest numbers that are missing from the right side of the sequence = 20, 13, and 12.

The complete sequence would therefore be:

8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 3, 2, 20, 13, 12.

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The value of the Boyce’s home in 2020 can be calculated using the given information. The initial value of the house in 2007 was $196,000. The average annual rate of appreciation is 1.3%. We need to calculate the value of the house in 2020.

Therefore, we need to calculate the number of years from 2007 to 2020 which is 13 years.The formula for the future value of an investment or property with a fixed annual interest rate is given by;FV = PV x (1 + r)n whereFV = future valuePV = present value or initial value of the propertyr = annual interest raten = number of years.

So, using the formula above, the future value of the house in 2020 can be calculated as;FV = $196,000 x (1 + 0.013)13FV = $196,000 x (1.013)13FV = $ 249,389.29 Therefore, the value of the Boyce’s home in 2020 was $249,389.29.

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Answer: -36

Step-by-step explanation:

13, 6, -1

to get from 13 to 6 and 6 to -1, you would subtract by 7 so keep subtracting by 7 until you get 8 different terms

13, 6, -1, -8, -15, -22, -29, -36

the eighth term would be -36

i hope that makes sense

It's important to follow the order of operations to ensure accurate calculations. the correct answer to the calculation 5.25 + 41.8 + 34.1 is 81.15.

To perform the calculation using the correct order of operations, we need to follow the rules of precedence, also known as the PEMDAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the given expression step by step:

5.25 + 41.8 + 34.1

According to the PEMDAS rule, we need to start with any calculations inside parentheses, but there are no parentheses in this expression. Next, we move to addition and subtraction from left to right.

5.25 + 41.8 equals 47.05.

Now we add 34.1 to the result:

47.05 + 34.1 equals 81.15.

Therefore, the correct answer to the calculation 5.25 + 41.8 + 34.1 is 81.15.It's important to follow the order of operations to ensure accurate calculations.

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Answer

i think the answer is 46 because

10+9x4=46

Answer:

option D is correct answer. ( 2, 2)

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

given that

volume = 4,000\(cm^{3}\)

let height = h

    width = w

    length = l

width and length are equal

height = length = h

volume of box = height × width × height

             4000  = h × w × h

             4000 = \(h^{2}\)w

                  w = 4000/\(h^{2}\)

surface area(SA) = area of base + sum of area of each side

                           =  \(h^{2}\) + hw + hw + hw + hw

                           =  \(h^{2}\) + 4hw

substitute y = 4000/\(h^{2}\)

SA =  \(h^{2}\)  + 4x(4000/ \(h^{2}\) )

SA =  \(h^{2}\)  + 16000/h

Taking the derivative:

SA' = 2h - 16000/ \(h^{2}\)

making SA' = 0:

0 = 2h - 16000/ \(h^{2}\)

2h = 16000/ \(h^{2}\)

2\(h^{3}\) = 16000

\(h^{3}\) = 8000

h = 20 cm

w = 4000 /  \(h^{2}\)  = 4000 / 20² = 10 cm

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

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We start by using the chain rule to find the derivative of w with respect to t: dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

dw/dt = 320 when t = 1.

To find ∂w/∂x, we treat y and t as constants and differentiate w = x^2 y^2 t with respect to x:

∂w/∂x = 2xy^2 t

To find ∂w/∂y, we treat x and t as constants and differentiate w = x^2 y^2 t with respect to y

∂w/∂y = 2x^2 yt

To find ∂w/∂t, we treat x and y as constants and differentiate w = x^2 y^2 t with respect to t:

∂w/∂t = x^2 y^2

Substituting the given values x = 4t and y = 2t, we get:

∂w/∂x = 2(4t)(2t)^2 t = 32t^4

∂w/∂y = 2(4t)^2 (2t) t = 64t^4

∂w/∂t = (4t)^2 (2t)^2 = 64t^4

Using these values, we can write:

dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

= (32t^4)(4) + (64t^4)(2) + (64t^4)

= 320t^4

Finally, substituting t = 1, we get:

dw/dt = 320(1)^4 = 320

Therefore, dw/dt = 320 when t = 1.

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The ball will be 80 feet above the ground after 3 seconds of flight time.

The solution to the problem of writing a Java program that computes how high the ball .

As provided in the problem statement, the height of the object as a function of time can be modeled by the function h(t) = -16t² + vt + h, where h(t) is the height of the object (in feet) t seconds after it is thrown, and h is the starting height, i.e. the height of the building. In this case, h = 128 and v = 32 feet per second (ft/sec).

If the time of flight of the ball is represented as x, then the height of the ball as a function of time can be modeled by the equation h(x) = -16x² + 32x + 128.

Therefore, to determine how high the ball will be above the ground after x seconds of flight time, the program needs to evaluate h(x) by substituting the value of x provided by the user.

For example, if the user provides the value x = 3, the program will evaluate h(3) = -16(3)² + 32(3) + 128 = 80 feet.

Hence, the ball will be 80 feet above the ground after 3 seconds of flight time. The Java program for this can be written using the Scanner class to get user input and the Math class to perform the necessary calculations.

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b)The marginal PDF fx(x) is given by: fx(x) = (\(2\sqrt{(r^2 - x^2))/(\pi r^2}\)), for -r < x <r

c) the marginal PDF fy(y) is given by: fy(y) = (\(2\sqrt{(r^2 - y^2))/(\pi r^2}\)), for -r < y < r

To find the marginal probability density functions (PDFs) fx(x) and fy(y) from the joint PDF fX,Y(x, y), we need to integrate the joint PDF over the appropriate range.

b) To find the marginal PDF fx(x), we integrate fX,Y(x, y) with respect to y while considering the range of x:

fx(x) = ∫fX,Y(x, y) dy

Since the joint PDF is defined over the circle \(x^2 + y^2 < r^2\), the integration limits for y will be -\(\sqrt{r^2 - x^2)}\) to \(\sqrt{r^2 - x^2)}\)

fx(x) = ∫\([-\sqrt{(r^2 - x^2)}\), \(\sqrt{(r^2 - x^2}\))] (1/(πr^2)) dy

Integrating, we get:

fx(x) = (\(1/(\pi r^2)\)) * 2\(\sqrt{(r^2 - x^2}\)

Therefore, the marginal PDF fx(x) is given by:

fx(x) = (2\(\sqrt{(r^2 - x^2}\)/(\(\pi r^2\)), for -r < x < r

c) Similarly, to find the marginal PDF fy(y), we integrate fX,Y(x, y) with respect to x while considering the range of y:

fy(y) = ∫fX,Y(x, y) dx

Since the joint PDF is defined over the circle\(x^2 + y^2 < r^2\), the integration limits for x will be -\(\sqrt{r^2 - y^2}\)) to \(\sqrt{(r^2 - y^2}\)).

fy(y) = ∫[-\(\sqrt{r^2 - y^2}\), √\(\sqrt{r^2 - y^2}\)] (\(1/(\pi r^2\))) dx

Integrating, we get:

fy(y) = (1/\((\pi r^2\))) * 2\(\sqrt{r^2 - y^2}\))

Therefore, the marginal PDF fy(y) is given by:

fy(y) = \(2\sqrt{(r^2 - y^2))/(\pi r^2}\) for -r < y < r

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The length of the base of the triangle is 17.4 yards.

We have,

The area of a triangle.

A = (1/2) x b x h

where A is the area, b is the base, and h is the height.

We are given that the area is 139.2 square yards and the height is 16 yards.

Substituting,

A = (1/2)bh

139.2 = (1/2)(b)(16)

139.2 = 8b

b = 139.2/8

b = 17.4

Therefore,

The length of the base of the triangle is 17.4 yards.

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The largest number that satisfies the given inequality is x = 4.04, based on the graph of the linear function f(x) = 5x + 5.

To find the largest number that satisfies the given inequality, let's analyze the conditions:

Given: |x − 4| < δ and |5x + 5 − 5| < 0.2

We know that |5x + 5 − 5| is equivalent to |5x|. Therefore, we can rewrite the second inequality as:

|5x| < 0.2

Since the coefficient of x is positive, we can ignore the absolute value signs. Thus, we have:

5x < 0.2

Dividing both sides of the inequality by 5, we get:

x < 0.2/5

x < 0.04

Now, let's consider the first inequality, |x − 4| < δ. The absolute value represents the distance between x and 4, so we want to find the largest value of δ such that x falls within a distance of δ from 4.

By analyzing the graph of f(x) = 5x + 5, we can see that the slope of the line is positive, indicating that the line increases as x increases. Therefore, for any value of x, the function f(x) = 5x + 5 will be larger than f(4) = 5(4) + 5 = 25. Hence, we need to find the largest value of δ such that f(x) > 25.

Substituting f(x) = 5x + 5 > 25, we have:

5x + 5 > 25

Subtracting 5 from both sides:

5x > 20

Dividing both sides by 5:

x > 4

Therefore, for the inequality |x − 4| < δ to hold, we need x to be greater than 4.

Now, let's combine the two conditions:

x > 4 and x < 0.04

The largest number that satisfies both conditions is x = 0.04.

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The rate οf change f(x) in relatiοn tο x is -3.

A pοlynοmial functiοn οf degree 0 οr 1 that has a straight line as its graph is said tο be linear. One independent variable and οne dependent variable make up a linear functiοn. X and Y are the independent and dependent variables, respectively.

Here, we have

Given: Each change οf 6 in the linear functiοn f (x) results frοm a change οf-2 in x.

We have tο find the rate οf change f(x) in relatiοn tο x.

Rate οf change = 6/(-2) = -3

Hence, the rate οf change f(x) in relatiοn tο x is -3.

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Answer:

there are 400 meters in a track

400 times 12 = 4800

4800 divided by 1600 =3

Joyce ran 3 miles

Step-by-step explanation:

Answer:

x= 52

y= 25

z= 90

pls mark me as BRAINLIAST

Answer:

r=6

Step-by-step explanation:

(r-(-3))/(2-(-1)) = (r+3)/3

r+3/3 = 3/1

cross-multiply:

r+3 = 9

r = 6

Check:

6-(-3)/2-(-1) should equal 3

9/3 = 3

checks out correctly

Answer:

r = 6

Step-by-step explanation:

Formula

m = (y2 - y1)/(x2 - x1)

Givens

x1 = - 1

x2 = 2

y1 = - 3

y2 = r

m = 3

Solution

3 = (r - -3) / (2 - - 1)         Combine

3 = (r + 3) / 3                 Multiply both sides by 3

9 = r + 3                       Subtract 3 from both sides

6 = r + 3 - 3

6 = r

By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.

In the given statements, thus the similar triangle are:

ΔWYZ ≈ Δ WZX ≈ ΔZYX

A,

∠Y is common

∠x = ∠z = 90°

Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

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Answer:

x=2

Step-by-step explanation:

Since rectangles have 90* angles at each corner, we can say the two equations in the corner equal to 90*

so,

13x+34+10x+10=90

23x+44=90

23x=46

x=2

The angle of elevation from the ground where the man is standing to the top of the tower is 67°.

According to the question,

We have the following information:

A man is standing 85 meters from the base of a tower. And the tower is 200 meters tall.

Now, we will use the trigonometric function of tan to find the value of angle of elevation.

Let's take the angle of elevation to be x°.

Tan x = Height of the tower/distance of the man from the base of the tower

Tan x = 200/85

Tan x = 2.35

Tan 67 = 2.35

Hence, the angle of elevation from the ground where the man is standing to the top of the tower is 67°.

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Answer:

Solve the rational equation by combining expressions and isolating the variable.

x=47.04630109.

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

11x + 2 is an exterior angle of the triangle, then

11x + 2 = 5x + 10 + 58

11x + 2 = 5x + 68 ( subtract 5x from both sides )

6x + 2 = 68 ( subtract 2 from both sides )

6x = 66 ( divide both sides by 6 )

x = 11

Answer:

50.7

Step-by-step explanation:

For the sequence 818, the divergence test applies because the sequence does not approach a finite limit. Therefore, we can state that lim an does not exist.

For the sequence an = (Inn)², the divergence test does not apply because the divergence test is used to determine the divergence or convergence of a sequence by checking if the limit of the sequence exists and is non-zero. In this case, we cannot directly apply the divergence test because the limit of the sequence is not obvious.

To determine the convergence or divergence of this sequence, we need to use other convergence tests such as the ratio test, comparison test, or root test. Without further information or applying one of these convergence tests, we cannot determine the limit of the sequence an.

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