8. A rectangle is inch longer
than it is wide.
Let w = width.
Let = length.
Graph=w+
1
l=w+ 2

Therefore, the distance between the 90 degree angle and the hypotenuse is approximately 0.829 units.

A triangle is a two-dimensional geometric shape that is formed by three straight line segments that connect to form three angles. It is one of the most basic shapes in geometry and has a wide range of applications in mathematics, science, engineering, and everyday life. Triangles can be classified by the length of their sides (equilateral, isosceles, or scalene) and by the size of their angles (acute, right, or obtuse). The study of triangles is an important part of geometry, and their properties and relationships are used in many areas of mathematics and science.

Here,

1. To find HF, we can use the angle bisector theorem, which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides. Let's denote the length of HF as x. Then, by the angle bisector theorem, we have:

JF/FH = JG/HG

Substituting the given values, we get:

15/x = 18/21

Simplifying and solving for x, we get:

x = 15 * 21 / 18

x = 17.5

Therefore, HF is 17.5 cm.

2. Let's denote the length of the hypotenuse as h and the length of the leg opposite the 18-unit perpendicular as a. We can then use the Pythagorean theorem to write:

h² = a²  + 18²

We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:

h = x + 6

Substituting this expression into the first equation, we get:

(x + 6)² = a² + 18²

We are also told that the leg adjacent to the angle opposite the 4-unit segment is divided into segments of length 4 and (a - 4), so we can write:

a = 4 + (a - 4)

Simplifying this equation, we get:

a = a

Now we can substitute this expression for a into the previous equation and solve for x:

(x + 6)² = (4 + (a - 4))² + 18²

Expanding and simplifying, we get:

x² + 12x - 36 = 0

Using the quadratic formula, we get:

x = (-12 ± √(12² - 4(1)(-36))) / (2(1))

x = (-12 ± √(288)) / 2

x = -6 ± 6√(2)

Since the length of a segment cannot be negative, we take the positive root:

x = -6 + 6sqrt(2)

x ≈ 1.46

Therefore, the value of x is approximately 1.46 units.

3. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the 9-unit perpendicular as b. We can then use the Pythagorean theorem to write:

h² = b² + 9²

We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:

h = x + 6

Substituting this expression into the first equation, we get:

(x + 6)² = b² + 9²

Expanding and simplifying, we get:

x² + 12x - b² = 27

We also know that the length of the leg opposite the 9-unit perpendicular is:

a = √(h² - 9²)

= √((x + 6)² - 9²)

= √(x² + 12x + 27)

Now we can use the fact that the tangent of the angle opposite the 9-unit perpendicular is equal to the ratio of the lengths of the opposite and adjacent sides:

tan(θ) = a / b

Substituting the expressions for a and b, we get:

tan(θ) = √(x² + 12x + 27) / (x + 6)

We also know that the tangent of the angle theta is equal to the ratio of the length of the opposite side to the length of the adjacent side:

tan(θ) = 9 / b

Substituting the expression for b, we get:

tan(θ) = 9 / √(h² - 9²)

Substituting the expression for h, we get:

tan(θ) = 9 / √((x + 6)² - 9²)

Since the tangent function is the same for equal angles, we can set these two expressions for the tangent equal to each other:

√(x² + 12x + 27) / (x + 6) = 9 / √((x + 6)² - 9²)

Squaring both sides, we get:

(x² + 12x + 27) / (x + 6)² = 81 / ((x + 6)² - 81)

Cross-multiplying and simplifying, we get:

x⁴ + 36x³ + 297x² - 1458x - 2916 = 0

Using a numerical method such as the Newton-Raphson method or the bisection method, we can find the approximate solution to this equation:

x ≈ 9.449

Therefore, the value of x is approximately 9.449 units.

4. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the distance we want to find as b. We can use the Pythagorean theorem to write:

h² = b² + d²

We are told that the hypotenuse is divided into segments of length 9 and 4 units, so we can write:

h = 9 + 4 = 13

Substituting this expression into the first equation, we get:

13² = b² + d²

Simplifying and solving for d, we get:

d = √(13² - b²)

Now, we need to find the value of b. We know that the hypotenuse is divided into segments of length 9 and 4 units, so we can use similar triangles to write:

b / 4 = 9 / 13

Simplifying and solving for b, we get:

b = 36 / 13

Substituting this expression for b into the equation we found earlier for d, we get:

d = √(13² - (36/13)²)

Simplifying and finding a common denominator, we get:

d =√ (169*13 - 36²) / 13²

Simplifying further, we get:

d = √(169169 - 3636) / 169

Calculating this expression, we get:

d ≈ 0.829

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

Answer:The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius (or Kelvin).

To find the specific heat of the unknown substance, we can use the following equation:

Q = m x c x ΔT

where Q is the heat gained or lost, m is the mass of the substance, c is its specific heat, and ΔT is the change in temperature.

In this problem, we know the mass and initial and final temperatures of both the unknown substance and the water, as well as the specific heat of water. We can use this information to calculate the heat gained by the water, which must be equal to the heat lost by the unknown substance:

Heat gained by water = Heat lost by unknown substance

m(water) x c(water) x ΔT(water) = m(substance) x c(substance) x ΔT(substance)

We can plug in the values we know and solve for the specific heat of the unknown substance:

m(water) = 75.0 g

c(water) = 4.18 J/g°C

ΔT(water) = 27.1 °C - 20.00 °C = 7.1 °C

m(substance) = 100.0 g

ΔT(substance) = 200.0 °C - 27.1 °C = 172.9 °C

75.0 g x 4.18 J/g°C x 7.1 °C = 100.0 g x c(substance) x 172.9 °C

Simplifying this equation, we get:

c(substance) = (75.0 g x 4.18 J/g°C x 7.1 °C) / (100.0 g x 172.9 °C)

c(substance) = 0.197 J/g°C

Therefore, the specific heat of the unknown substance is 0.197 J/g°C.

Step-by-step explanation:

Answer:

The specific heat of the unknown substance is 0.39 J/g°C.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of energy, which states that the heat lost by the unknown substance is equal to the heat gained by the water and the calorimeter. We can express this principle mathematically as:

Q_lost = Q_gained

where Q_lost is the heat lost by the unknown substance, and Q_gained is the heat gained by the water and calorimeter.

We can calculate Q_lost using the formula:

Q_lost = m × c × ΔT

where m is the mass of the unknown substance, c is its specific heat, and ΔT is the change in temperature it undergoes.

We can calculate Q_gained using the formula:

Q_gained = (m_water + m_calorimeter) × c_water × ΔT

where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat of water, and ΔT is the change in temperature of the water and calorimeter.

Since the system reaches an equilibrium temperature, we can set Q_lost equal to Q_gained and solve for the specific heat of the unknown substance (c).

Here's the calculation:

Q_lost = Q_gained

m × c × ΔT = (m_water + m_calorimeter) × c_water × ΔT

100.0 g × c × (200.0 °C - 27.1 °C) = (75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)

Simplifying:

c = [(75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)] / (100.0 g × (200.0 °C - 27.1 °C))

c = 0.39 J/g°C

Therefore, the specific heat of the unknown substance is 0.39 J/g°C.

Step-by-step explanation:

Might be a little easier to visualize if yo re-arrange it into y = mx + b form:

4x+ 5y = 20

5y = -4x + 20

y = - 4/5 x + 4         y-axis intercept at y = 4

                                x axis intercept is found by:

                                     0 = -4/5 x + 4

                                             - 4 = -4/5 x

                                                 x = 5

So===> plot the two intercept points ( 0,4)  and  ( 5,0)  and connect the dots

Answer:

z=3.75

Step-by-step explanation:

The value stored in 0x10000004 on a big-endian machine is given by 0x00000011.

The word "endianness" refers to the arrangement of bytes as they are stored in computer memory. Endianness is classified as big or little depending on which value is stored first.

The "big end" (the most important item in the sequence) is put first and at the lowest storage address in a big-endian order. The "small end" (the least important item in the sequence) is put first in a little-endian order.

(1)In Big-endian Machine, first byte of multi-byte data will be stored first(at lower memory address)

Address                 Data

0x10000000            0x11

0x10000001            0x22

0x10000002            0x33

0x10000003            0x44

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

lbu $t0, 0($t1)

Load unsigned byte in Register $t0 at address 0x10000000

Here byte at address 0x10000000 is 0x11

$t0 = 0x00000011

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

sw $t0, 0($t2)

Store a word(4 bytes) from Register $t0 to memory address 0x10000004

value stored in 0x10000004 is 0x00000011

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

(2)In Little-endian Machine, last byte of multi-byte data will be stored first(at lower memory address)

Address                 Data

0x10000000            0x44

0x10000001            0x33

0x10000002            0x22

0x10000003            0x11

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

lbu $t0, 0($t1)

Load unsigned byte in Register $t0 at address 0x10000000

Here byte at address 0x10000000 is 0x44

$t0 = 0x00000044

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

sw $t0, 0($t2)

Store a word(4 bytes) from Register $t0 to memory address 0x10000004

value stored in 0x10000004 is 0x00000044.

Learn more about Big-endian machine:

https://brainly.com/question/30848621

#SPJ4

Answer:

Step-by-step explanation:

To find the total length of both pieces of fabric in centimeters, we need to add the length of the first piece of fabric (142 cm) and the length of the second piece of fabric (2 meters).

However, we need to make sure that the units are consistent before we add the lengths. We can convert the length of the second piece of fabric from meters to centimeters by multiplying by 100. Therefore, the total length in centimeters is:

142 cm + 2 meters * 100 cm/meter = 142 cm + 200 cm = 342 cm

The option that correctly gives the answer is "Multiply 2 by 100, then add 142" (Option C).

(a) θ is a biased estimator for θ.

(b) (α+1)Y/α is an unbiased estimator of θ.

(c) MSE(θ) = αθ^2/[(α+1)^2(α+2)]

(a) To show that θ is a biased estimator for θ, we need to show that E(θ) ≠ θ.

Using the definition of the maximum function, we have

P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n

where F(y) is the cumulative distribution function of Y.

Differentiating both sides with respect to y, we get:

f(θ) = n(F(θ))^(n-1)f(θ)

Simplifying, we get

F(θ) = (1/n)^(1/(n-1))

Using this result, we can find the expected value of θ

E(θ) = ∫₀^∞ θf(θ)dθ = ∫₀^θ θαθ^α-1dθ = αθ/(α+1)

Thus, E(θ) ≠ θ, which means that θ is a biased estimator for θ.

(b) To find a multiple of θ that is an unbiased estimator of θ, we can use the method of moments.

We know that the population mean of Y is

μ = ∫₀^θ yf(y)dy = αθ/(α+1)

The sample mean is

Y = (Y1+Y2+...+Yn)/n

Equating these two expressions and solving for θ, we get

θ = (α+1)Y/α

Thus, (α+1)Y/α is an unbiased estimator of θ.

(c) The mean squared error (MSE) of θ can be written as

MSE(θ) = E[(θ - θ)^2]

Expanding the square and using the linearity of expectation, we have

MSE(θ) = E[θ^2] - 2θE[θ] + E[θ]^2

We already know that E[θ] = αθ/(α+1).

To find E[θ^2], we can use the fact that θ = max(Y1,Y2,...Yn)

P(θ ≤ y) = P(Y1 ≤ y, Y2 ≤ y, ..., Yn ≤ y) = (F(y))^n

Differentiating both sides with respect to y, we get

f(θ) = n(F(θ))^(n-1)f(θ)

Using this result, we can find E[θ^2]

E[θ^2] = ∫₀^∞ θ^2f(θ)dθ = ∫₀^θ θ^2αθ^α-1dθ = αθ^2/(α+2)

Substituting these expressions into the MSE formula, we get

MSE(θ) = αθ^2/(α+2) - 2θ(αθ/(α+1)) + (αθ/(α+1))^2

Simplifying, we get

MSE(θ) = αθ^2/[(α+1)^2(α+2)]

Learn more about biased estimator here

brainly.com/question/30982574

#SPJ4

Answer:

j = - 9/14

Step-by-step explanation:

-4(7j+2) = 10

Distributing First

-28j - 8 = 10

Try to get the variable on one side.

-28j = 18

Divide both sides by -28

j = -18/28 = - 9/14

Answer:

Step-by-step explanation:

1. Rounded to 0.56

2. Rounded

Answer:

1. a square plus b square is c square where c is the hypotenuse.

so 1. 7^2 + 6^2 = c^2

49+36=c^2

85=c^2

the square root of 85 is c

9.22 is c

all the other questions are blurry :OO

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability of a baby being a boy or a girl is 1/2 or 50% each. Since the couple has already had three boys, the probability of the fourth child being a boy or a girl is still 1/2 or 50%, as the gender of each child is independent of the others. Therefore, the probability of the couple's last child being a baby boy is 50%.

The required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

Assuming boys and girls are equally​ likely.

The first two children were both boys

According to given question we have

The probability of having a baby girl is an independent probability.

The first two children were both boys

So, it is not related to the previous child.

So required probability = 1/2 / 50%

Therefore, the required probability of a couple having a baby boy when their third child is​ born is 1/2 / 50%.

Learn more details about probability here:

https://brainly.com/question/11234923

The cost to rent one shed of the rectangular prism shaped shed is $2772.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.

Volume of prism= BH

where B= area of base and H= height

B= 11*7 = 77 feet²

H= 12 feet

Volume= 77*12=924 cubic feet

Cost =$3 per cubic foot

Total cost= 3*924= $2772

To know more about area, visit

https://brainly.com/question/27683633

#SPJ1

Answer:

  6 cm

Step-by-step explanation:

You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².

The formula for the are of a trapezium is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  156 = 1/2(17 +35)h = 26h

  6 = h . . . . . . . . . . divide by 26

The height of the trapezium is 6 cm.

Answer:

6cm

Step-by-step explanation:

To find:-

Answer:-

We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.

The area of the trapezium is given by the formula,

[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]

where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.

Now on substituting the respective values in the given formula, we have;

[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]

[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]

[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]

[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]

Hence the height of the trapezium is 6cm .

By linear equality , g >1.5 is must be true.

What are equality and inequality along a line?

Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.

                          x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).

If h> 3 and h - 2g= 0

H=2g

2g>3

g >1.5

Learn more about linear equality

brainly.com/question/11874554

#SPJ1

Answer: 6,160

Step-by-step explanation:

Immediately, without even doing any math, the only logical answer would be 6160. This is because the current tuition is 5,500 and it is increasing so the answer cannot be lower.

However, mathematically you can prove this by turning 12% into a decimal and multiplying it by 5,500. 12% could be converted to .12 and because it is increasing you must add 1, or 100%, since that is what it started with. 5,500 x 1.12 = 6,160.

Answer:

410 Black and Green shirts

Step-by-step explanation:

150 shirts were pink

135 shirts were green

so knowing this we can set up the equation 2x+85=465

there were 275 black shirts in the box

and 190 yellow shirts

therefore there were 410 Black and Green shirts in the box

Answer:1+1=3

Step-by-step explanation: if 1 doesn't use protection the 1 and the other 1 are going to make 3

Answer:

Multiplicative

Step-by-step explanation:

If the area of the first rectangle is l*w, the area of the second would be 2w*w. The area is multiplied by 2 and the relationship is therefore multiplicative.

Answer:

y = 0.8x

Step-by-step explanation:

machine fills 24 jars in 30 seconds , then

fills 1 jar in [tex]\frac{24}{30}[/tex] = 0.8 seconds

thus number of jars filled in x seconds is

y = 0.8x

The perimeter of the garden in the drawing is 22 inches and the perimeter of the actual garden is 770 inches

The perimeter of the garden in the drawing is calculated as

Perimeter of garden in drawing = 2(length + width)

So, we have

Perimeter of garden in drawing = 2(7 inches + 4 inches)

Evaluate

Perimeter of garden in drawing = 22 inches

So the perimeter of the garden in the drawing is 22 inches.

For the perimeter of the actual garden, we have

Perimeter of actual garden = 22 inches * 35

Perimeter of actual garden = 770 inches

We can see that the perimeter of the actual garden is 35 times larger than the perimeter of the garden in the drawing.

This makes sense since the length and width of the actual garden are 35 times larger than the length and width in the drawing, so the perimeter (which is the sum of the lengths of all four sides) would also be 35 times larger.

Read more about scale drawing at

https://brainly.com/question/29229124

#SPJ1

The function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.

(a) The function f(n) = n - 3 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a - 3 = b - 3, which implies a = b. Therefore, the function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.

(b) The function f(n) = n^2 - 1 is not one-to-one (not injective). To see this, note that f(1) = f(-1) = 0, so different inputs map to the same output. In general, for any positive integer k, we have f(k) = f(-k), since (k^2 - 1) = ((-k)^2 - 1). Therefore, the function f(n) = n^2 - 1 is not injective.

(c) The function f(n) = n^5 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a^5 = b^5, which implies a = b (since the fifth root of a non-zero real number is unique). Therefore, the function f(n) = n^5 maps distinct integers to distinct integers, and thus is injective.

Find out more about functionsat  

brainly.com/question/13262879

#SPJ4

Answer:

If you add all the numbers together and divide the number of females by the total number of people. It is a 5% chance that out of all the people, the group of 37 females, one would be selected.

If you add up all the numbers of people and divide by the number of pescatarians, there is an 89.5% chance of a pescatarian being selected.

all numbers added together, 72 meat eaters, and 616 pescatarians = 688

females = 37

37/688 = 0.0537 = 5.37 = rounded to hundredths place = 5%

all numbers added together = 688

number of pescatarians = 616

616/688 = .0895 = 89.5%

Step-by-step explanation:

The value of the angles in the triangle are:

∠A = 60°, ∠B = 80° and ∠C = 40°

We  are given that BD = DC

Thus, ∠DBC = ∠BCD ---- 1  (angle in isosceles triangle)

We also have ∠BDC = 100°

In ΔBDC

∠BDC + ∠DBC + ∠BCD = 180°  (sum of angles of triangle is 180°)

Using 1:

∠BDC + 2∠DBC = 180°  

100° + 2∠DBC = 180°  

2∠DBC = 180 - 100

2∠DBC = 80

∠DBC = 80/2

∠DBC = 40°

∠DBC = ∠BCD = ∠2 = 40°

Thus, ∠C = 40°

We are given that  m∠1 = m∠2

Thus, ∠1 = ∠2 = 40°

Now,  ∠BDC +  ∠BDA = 180° (Linear pair)

100° + ∠BDA = 180°

∠BDA = 180 - 100

∠BDA = 80°

In ΔABD

∠ABD + ∠BDA +  ∠BAD = 180° (sum of angles of triangle is 180°)

∠1 + ∠BDA +  ∠BAD = 180°

40° +  80° +  ∠BAD = 180°

120° +  ∠BAD = 180°

∠BAD = 60°

So,  ∠A = 60°

∠B =  ∠1  + ∠2 = 40° + 40° = 80°

Therefore,  ∠A = 60°, ∠B = 80° and ∠C = 40°

Learn more about triangle on:

brainly.com/question/9132922

#SPJ1

Complete Question

m∠1=m∠2

D∈

AC

, BD = DC

m∠BDC = 100°

Find: m∠A, m∠B, m∠C

if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.

The first step in solving this problem is to calculate the amount of each quarterly deposit. We know that the first deposit is $400, and each subsequent deposit decreases by 1% from the previous deposit. This means that each deposit is 99% of the previous deposit. To calculate the size of each deposit, we can use the following formula:

deposit_ n = deposit_(n-1) * 0.99

Using this formula, we can calculate the size of each quarterly deposit as follows:

deposit_1 = $400

deposit_2 = deposit_1 * 0.99 = $396.00

deposit_3 = deposit_2 * 0.99 = $392.04

deposit_4 = deposit_3 * 0.99 = $388.12

...

We can continue this pattern for 40 years (160 quarters) to find the size of each quarterly deposit.

Next, we need to calculate the future value of these deposits using an nominal annual interest rate of 8% compounded quarterly. We can use the formula for compound interest to calculate the future value:

[tex]FV = PV * (1 + r/n)^(n*t)[/tex]

where FV is the future value, PV is the present value (which is zero since we are starting with deposits), r is the nominal annual interest rate (8%), n is the number of times the interest is compounded per year (4 since we are compounding quarterly), and t is the number of years (40).

We can substitute the values into the formula and solve for FV:

[tex]FV = $400 * (1 + 0.08/4)^(440) + $396.00 * (1 + 0.08/4)^(439) + $392.04 * (1 + 0.08/4)^(4*38) + ... + $1.64 * (1 + 0.08/4)^4[/tex]

After solving this equation, we get a future value of $143,004.54, rounded to two decimal places. This means that if we make quarterly deposits and invest them at an nominal annual interest rate of 8% compounded quarterly for 40 years, we will have $143,004.54 at the end of the 40 years.

This calculation highlights the power of compound interest over long periods of time. By making regular contributions and earning interest on those contributions, our investment grows exponentially over time. It also shows the importance of starting early and consistently contributing to an investment over time in order to achieve long-term financial goals.

To know more about quarterly deposit.  click here:

brainly.com/question/17218467

#SPJ4

The system described above is nonlinear because it contains a term with y(t) multiplied by t. The Laplace transform of f(t) is (6/s²)+(1/s).

If we substitute y1(t) and y2(t) into the equation and add them together, we get:

dy1/dt + 3 + 3ty1(t) = 1² f(t) dt dy2/dt + 3 + 3ty2(t) = 1² f(t) dt

Then we can add these two equations together to get:

d(y1+y2)/dt + 3 + 3t*(y1+y2)(t) = 2*1² f(t) dt

This is not equal to the original equation with y(t), which means that the system is nonlinear.

To find the Laplace transform of f(t), we can use the formula:

L{f(at+b)} = (1/a) ×F(s-b/a)

where F(s) is the Laplace transform of f(t). In this case, we have:

f(t) = (1+6t)

So we can rewrite this as:

f(t) = (6×t+1)

Now we can use the formula to find the Laplace transform:

L{(6×t+1)} = (6/s²)+(1/s)

Therefore, the Laplace transform of f(t) is (6/s²)+(1/s).

To know more about Laplace transform, refer:

https://brainly.com/question/17062586

#SPJ4

d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

what is a geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed constant called the common ratio. The common ratio is denoted by the letter r.

The general formula for a geometric sequence is:a₁, a₁r, a₁r², a₁r³, ...

a. False. The sum of a 20° angle and a 70° angle is 90°, so they can compose a 90° angle.

b. False. The sum of three 50° angles is 150°, so they cannot compose an angle that measures 350⁰.

c. False. The sum of a 15° angle and a 60° angle is 75°, so they can compose an angle that measures 75°.

Therefore, d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

To learn more geometric sequence from the given link:

https://brainly.com/question/16274868

#SPJ1

Answer:

27.78%

Step-by-step explanation:

We know

Total of 18 students 5 students prefer country.

What is the probability?

5/18 = 27.78%

So, the answer is 27.78%

Answer:

In this scenario, we have:

n = 3 (since we are watching 3 cars)

x = 1 (since we are interested in the probability of exactly one car being red)

p = 0.1 (since the probability of a car being red is 10%, or 0.1)

The binomial formula for calculating the probability of exactly x successes in n independent trials with a probability of success p is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient, which can be calculated as:

nCx = n! / (x! * (n-x)!)

Using these values and the binomial formula, we can calculate the probability of exactly one of the three cars being red as:

P(1) = (3C1) * 0.1^1 * (1-0.1)^(3-1)

= (3) * 0.1 * 0.81

= 0.243

Therefore, the probability of exactly one of the three cars being red is 0.243.

The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).

A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.

We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.

a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).

b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).

To know more about probability visit:

https://brainly.com/question/30719832

#SPJ1

The area of the right triangle given in this problem is given as follows:

21 units squared -> Option A.

To calculate the area of a triangle, you can use the formula presented as follows:

Area = (1/2) x base x height

In which the parameters are given as follows:

For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5 x 7 x 6 = 21 units squared.

The complete problem is defined as follows:

"Calculate the area of the given triangle".

More can be learned about the area of a triangle at brainly.com/question/21735282

#SPJ1