35.1 divided by 2.7 explanation to

Answer:

The measure of a = b = 116 degrees

Step-by-step explanation:

Here, we have value of angles to calculate.

If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180

Hence; Mathematically;

a + c = 180 and b + c = 180

What we have here is that a and b must be equal since they are both supplementary to the same angle value

Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;

Mathematically, this means that;

a = 2c - 12

So we now want to find the measure of b

Let’s substitute for a

2c -12 + c = 180

3c -12 = 180

3c = 180 + 12

3c =192

c = 192/3

c = 64

Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116

The density of iron is 7.87 x 10⁻⁹ kg/m³. This value is obtained by  considering the density of iron 7.87 g/cm³.

Density is a measure of how much mass is contained within a given volume. In this case, the density of iron is stated as 7.87 g/cm³. This means that for every cubic centimeter of iron, there is a mass of 7.87 grams.

To convert the density from g/cm³ to kg/m³, we need to convert grams to kilograms and cubic centimeters to cubic meters.

To convert grams to kilograms, we divide by 1000 since there are 1000 grams in a kilogram. So, 7.87 g/cm³ is equal to 0.00787 kg/cm³.

To convert the density of iron from g/cm³ to kg/m³, we need to perform the following calculations.

First, convert grams to kilograms:

1 g = 0.001 kg

Therefore, the density of iron is 7.87 g/cm³ * 0.001 kg/g = 0.00787 kg/cm³.

Next, convert cubic centimeters to cubic meters:

1 cm³ = (0.01 m)³ = 0.000001 m³

Therefore, the density of iron is 0.00787 kg/cm³ * 0.000001 m³/cm³ = 7.87 x 10⁻⁹ kg/m³.

Hence, the density of iron in units of kg/m³ is 7.87 x 10⁻⁹ kg/m³.

Learn more about Density

brainly.com/question/29775886

#SPJ11

\(g(x) = 4x^2 + 3x\)

So, \(g(x+a) = 4(x+a)^2 + 3(x+a)\), since we're just substituting (x+a) for x.

If we clean that up a bit,

    \(\begin{aligned}g(x+a) &= 4(x+a)^2 + 3(x+a)\\[0.5em] &= 4(x^2+2xa+a^2) + 3x+3a\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a\end{aligned}\)

Now putting this all together:

    \(\begin{aligned}g(x+a)-g(x) &= ( 4x^2+8xa+4a^2 + 3x+3a) - (4x^2+3x)\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a - 4x^2-3x\\[0.5em]&= 8xa+4a^2 +3a\end{aligned}\)

Remember that \((x+a)^2 = (x+a)(x+a) = x^2+2xa+a^2\)

If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of  95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.

To determine if the 95% confidence interval provides convincing statistical evidence at a level of significance that the mean number of hours of community service performed last year was different from the recommended 24 hours, we'll analyze the constructed interval (20.37, 23.49).
1. First, observe the given confidence interval: (20.37, 23.49)
2. Identify the recommended average of 24 hours by the president.
3. Check if the recommended average is within the confidence interval.
Since 24 hours is not within the interval (20.37, 23.49), it provides convincing statistical evidence, at a level of significance of 95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.

Learn more about confidence interval here, https://brainly.com/question/15712887

#SPJ11

Because you want to set aside three months' worth of fixed expenses for an emergency fund, the sum saved each month comes to \($416.70.\)  

In mathematics, interest is the fee or payment made for using borrowed funds; it is typically stated as a percentage of the principal sum. Interest can be divided into two categories.

Simple Interest is computed solely using the principal of the debt or investment. I = PRT, where P is the capital, R is the interest rate per period, and T is the time period, is the formula for simple interest.

Given,

The monthly wage is  \($2,415.64\) dollars.

After expenses, discretionary funds equal 54% of monthly revenue.

Fixed monthly expenses equal \((100–54%)%\) of overall monthly income.

\(= 46%\)  of monthly gross revenue

\(= 0.46 × 2,415.64\)

\(= $ 1,111.1944\)

Thus, the fixed expenditures for three months equal three times the fixed expenses for one month.

\(= 3 × 1,110.5544 = $ 3331.6632\)

This money will be conserved in 8 months, so

As a result, the monthly savings equal 1/8 of \($ 3331.6632\) .

\(= $ 416.6979 ≈ $ 416.70\)

Therefore, Because you want to set aside three months' worth of fixed expenses for an emergency fund, the sum saved each month comes to \($416.70\)  .

Learn more about interest here:

https://brainly.com/question/30393144

#SPJ1

The above question is incomplete, the complete question is given below:

Your realized income is $2,415.64/month, and 54% are discretionary monies. If you want to save 3 months of fixed expenses for an emergency fund, how much must you save each month to fund it in 8 months

The coordinates of M are:(6-3/5(sqrt(45)), 2+8/5(sqrt(45))) or ( 5.2, 4.6 )Thus, the answer is M (5.2, 4.6)

The given line segment has P (6,2) and Q (3,8) coordinates.

Point M lies on PQ and divides the segment so that the ratio of PM:

MQ is 3:2. Let us assume that the coordinates of point M are (x, y).

We know that PM/MQ = 3/2.

Therefore, the length of PM is three-fifths of PQ, and the length of MQ is two-fifths of PQ.

We can use these ratios to determine the coordinates of M using the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.

Therefore, the coordinates of the midpoint of PQ are:

( (6+3)/2, (2+8)/2 )  = (4.5, 5)

Now, let us use the ratio of PM:

MQ to find the coordinates of M.

We know that the coordinates of P are (6, 2) and the coordinates of Q are (3, 8).

Since PM:MQ is 3:2, PM is 3/5 of the distance from P to Q, and MQ is 2/5 of the distance from P to Q.

We can use this fact to find the coordinates of M as follows:

Using the distance formula, we can find the length of PQ: d(P,Q)

= sqrt((3-6)^2 + (8-2)^2)

= sqrt(9+36)

= sqrt(45)

PM = (3/5)(sqrt(45))MQ

= (2/5)(sqrt(45)).

Therefore, the coordinates of M are:

(6-3/5(sqrt(45)), 2+8/5(sqrt(45))) or ( 5.2, 4.6 )

Thus, the answer is M (5.2, 4.6).

To know more about Coordinates  visit :

https://brainly.com/question/15300200

#SPJ11

The 90% confidence interval for the standard deviation of the population is between `2.29` and `4.67`.

To calculate a 90% confidence interval for standard deviation with a sample size of 20, we can use the chi-squared distribution.  

Step 1: Find the chi-squared critical valuesFor a 90% confidence interval, we need to find the chi-squared critical values with 19 degrees of freedom. We can use a chi-squared table or a calculator to find the critical values.

Using a calculator, we can use the following formula: `X²α/2, n-1` and `X²1-α/2, n-1`. Plugging in the values, we get: `X²0.05, 19` = 30.144 and `X²0.95, 19` = 10.117

Step 2: Calculate the confidence interval Now we can calculate the confidence interval using the formula: `sqrt((n-1) × s²) / sqrt(X²α/2, n-1) ≤ σ ≤ sqrt((n-1) × s²) / sqrt(X²1-α/2, n-1)`

Plugging in the values, we get: `sqrt((20-1) × 3.55²) / sqrt(30.144)` ≤ σ ≤ `sqrt((20-1) × 3.55²) / sqrt(10.117)` Simplifying the equation, we get: `2.29` ≤ σ ≤ `4.67`

To know more about standard deviation visit:
brainly.com/question/32083480

#SPJ11

The value of x that is the data point farthest from the line of best fit is 3

The given parameters are:-

x      Residual

3         -5

5         -1

7          3

9          0

Take the absolute value of the residuals

x      Residual

3         5

5         1

7         3

9         0

The largest absolute value is 5

Hence, the value of x that is the data point farthest from the line of best fit is 3

Read more about residuals at:

https://brainly.com/question/16180255

#SPJ4

Answer:

answer is 3

Step-by-step explanation:

To determine which expressions represent vectors, we need to understand the properties and characteristics of vectors. A vector is a mathematical object that has both magnitude and direction.

It can be represented geometrically as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Based on this definition, we can identify the expressions that represent vectors:

1. → u: This expression represents a vector. The arrow symbol (→) indicates that it has both magnitude and direction.

2. → v: Similarly, this expression represents a vector. The arrow symbol (→) indicates that it has both magnitude and direction.

3. k → u: This expression also represents a vector. Multiplying a vector by a scalar (k) does not change its nature as a vector. It only scales the magnitude of the vector while keeping its direction intact.

4. → u + → v: This expression represents a vector. Adding two vectors together results in another vector with a magnitude and direction determined by the combination of the original vectors.

5. → u - → v: Similarly, this expression represents a vector. Subtracting one vector from another also results in a new vector with a magnitude and direction determined by the operation.

6. k(→ u + → v): This expression represents a vector. Here, we have both scalar multiplication (k) and vector addition (→ u + → v), which combine to produce another vector.

The expressions listed above all represent vectors because they possess both magnitude and direction, which are fundamental properties of vectors.

To know more about vectors refer here:

https://brainly.com/question/24256726#

#SPJ11

Answer:

C a properly inflated and maintained tire

Answer:

what to find the sum of Rs or

Answer:

If Rodgolf buys 3 comic books and 4 CDS, he payed a total of 85 dollars

Step-by-step explanation:

(wait but where is the question) Also 15 dollars or cents?

3*15= 45

4* 10= 40

45+40= 85

Answer:

a=16 b =10 or any other combination that gives 160

a = 20 b=8

a = 32 b = 5

Step-by-step explanation:

The area of a triangle using the lengths of two sides and the sine of the included angle is ½ ab sin C  where a and b are sides and C is the angle.

A =40 = 1/2 ab sin 30°

sin 30° = 1/2 so

40 = 1/2*ab*1/2

40 =1/4 ab multiply each side by 4

160 = ab

any combination of sides that gives you 160 will work

Let's check if a=16 b =10

A = 1/2*16*10 sin 30°

A = 1/2*160*1/2

A = 40

Answer:

x:0.3=5:6-->x/0.3=5/6-->6×x=0.3×5-->6x=1.5-->x=1.5/6-->x=0.25Answer..

Answer:

A) The Jenga game is appropriate for the middle childhood age group, typically ranging from around 6 to 12 years old.

B) Jenga promotes cognitive, physical, and socioemotional development in middle childhood through enhancing spatial reasoning and problem-solving skills, improving fine motor skills and proprioceptive input, and fostering social interaction, cooperation, and risk assessment.

Step-by-step explanation:

Jenga, a game played with rectangular blocks, can promote cognitive, physical, and socioemotional development through various concepts.

Cognitive Development: Jenga enhances spatial reasoning as players analyze the tower's structure, evaluate block stability, and strategize their moves. They mentally manipulate objects in space, building an understanding of spatial relationships and balance. Problem-solving skills are fostered as players make decisions about which block to remove, considering the consequences of their actions. They must anticipate the tower's reaction to their moves, think critically, and adjust their strategies accordingly.

Physical Development: Jenga improves fine motor skills as players carefully remove and stack blocks using only one hand. Precise finger movements, hand-eye coordination, and grip strength are required for successful manipulation of the blocks. The game also provides proprioceptive input as players gauge the weight and balance of each block, refining their sense of touch and motor control.

Socioemotional Development: Jenga promotes social interaction and cooperation when played with multiple players. Taking turns, discussing strategies, and supporting each other's successes and challenges enhance communication, collaboration, and empathy skills. Players learn to respect and consider others' perspectives, negotiate and compromise, and work together towards a common goal. Sportsmanship is nurtured as players accept both victory and defeat gracefully, fostering resilience and emotional regulation.

Furthermore, Jenga offers opportunities for developing patience and perseverance. As the tower becomes increasingly unstable, players must exercise self-control, focus, and delayed gratification. They learn to take their time, plan their moves carefully, and tolerate the suspense of potential collapse. The game also presents a low-risk environment for risk assessment, allowing children to assess the consequences of their decisions and make calculated judgments.

By engaging in Jenga, children actively participate in a multi-dimensional activity that combines physical manipulation, cognitive analysis, and social interaction. Through the concepts of spatial reasoning, problem-solving, fine motor skills, proprioceptive input, social interaction, cooperation, sportsmanship, patience, perseverance, and risk assessment, Jenga supports holistic development in cognitive, physical, and socioemotional domains.

Answer

two-thirds

Step-by-step explanation:

8 over 1 2simplified is 2 over 3

Answer:

10

Step-by-step explanation:

because it is what it is i just did the math

Answer:$1,331

Step-by-step explanation: Add each pairs earnings then subtract and you'll get the answer.

Answer:

13 hours

Step-by-step explanation:

143/11=13

13x11=143

Answer: Byron would have to work 13 hours

Step-by-step explanation: To find the answer, divide 143 by 11. This will give the total amount of hours he will have to work to earn $143. And the answer is 13.

Delilah drove from her house to the football game at a rate of 40 mph. she returned using the same route, but she drove at a rate of 30 mph. if the round trip took 90 minutes,the distance between Delilah's house and the football game is approximately 25.71 miles.

To find the distance between Delilah's house and the football game, we can use the formula: distance = rate × time.

Let's assume the distance between her house and the football game is "d" miles.

On her way to the game, Delilah drove at a rate of 40 mph. So, the time it took for her to reach the game can be calculated using the equation: time = distance / rate.

Since the distance is "d" miles and the rate is 40 mph, the time is d / 40 hours.

On her return journey, Delilah drove at a rate of 30 mph. The time it took for her to return can be calculated using the equation: time = distance / rate.

Since the distance is still "d" miles and the rate is 30 mph, the time is d / 30 hours.

The total round trip time is given as 90 minutes, which is equal to 1.5 hours.

We can set up the equation: d / 40 + d / 30 = 1.5.

To solve for "d," we can multiply both sides of the equation by the least common multiple of 40 and 30, which is 120. This gives us: 3d + 4d = 180.

Simplifying, we get: 7d = 180.

Dividing both sides by 7, we find that d = 25.71.

Therefore, the approximate distance from Delilah's home to the football game is 25.71 miles.

To know more about "Distance":

https://brainly.com/question/26550516

#SPJ11

Answer:

The answer is 539

Step-by-step explanation:

In 539 B.C., Persian forces defeated the Babylonian army at the site of Opis, east of the Tigris. ... 522–486 B.C.), claiming in his inscriptions that a certain “Achaemenes” was his ancestor. Under Darius the empire was stabilized, with roads for communication and a system of governors (satraps) established.

Answer:

In 539 BCE

Step-by-step explanation:

Persian forces defeated the Babylonian army at the site of Opis.

Answer:

16

Step-by-step explanation:

Lets first solve the right side :)

(3^5)^4 -> 3^20 = 3486784401

Now lets solve the left side :)

When we multiply the bases to exponets, we add the exponets together :)

Lets see what numbers equal 20 when added :)

4 + 4 = 8 Nope!!

4 + 5 = 9 Not at all!!

4 + 20 = 24 Too big!!

4 + 16 = 20 Perfect!!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

The answer you are looking for is in D- 16

Explanation:

Included in attachment

The minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126).

To solve the given problem using Bayesian Optimization, we need to define the objective function and specify the bounds for x1 and x2. The objective function is:

f(x1, x2) = (4 - 2.1x1^2 + (x1^4)/3)x1^2 + x1*x2 + (-4 + 4x2^2)x2^2

The bounds for x1 and x2 are x1 ∈ [-3, 3] and x2 ∈ [-2, 2].

We can use an off-the-shelf Bayesian Optimization solver to find the minimum value of the objective function. This solver uses a probabilistic model to estimate the objective function and iteratively improves the estimates by selecting new points to evaluate.

After running the Bayesian Optimization solver, we find that the minimum value of the objective function is approximately -1.0316. This minimum value occurs at (x1, x2) = (0.0898, -0.7126).

Using Bayesian Optimization, we have found that the minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126). Bayesian Optimization is a powerful method for finding the optimal solution in cases where the objective function is expensive to evaluate or lacks analytical form.

To know more about value , visit;

https://brainly.com/question/14316282

#SPJ11

(u - 5 + (7))(u - 5 - (7)) = 0 is the equation we created in u that simplifies to 2u2 - 20u + 36 = 0.

The two forms of equations are identity equations and conditional equations. The variables all have the same identity for all conceivable values.

Creating an equation in u that can be solved for 2u² - 20u + 36 = 0

It indicates that the following are the solutions for x for a quadratic equation of the form ax² + bx + c = 0:

x = (-b±√(b²-4ac))/2a

By dividing both sides by 2, we can rewrite the equation 2u2 - 20u + 36 = 0 as follows:

u² - 10u + 18 = 0

u = (-(-10) ± √((-10)² - 4(1)(18))) / 2(1)

Simplifying this expression, we get:

u = (10 ± √(100 - 72)) / 2

u = (10 ± √(28)) / 2

u = (10 ± 2√(7)) / 2

u = 5 ± √(7)

A quadratic equation with roots r1 and r2 can be expressed as: This allows us to merge the two solutions into a single equation.

(x - r1)(x - r2) = 0

By substituting in the two answers we discovered for u, we obtain:

(u - 5 + √(7))(u - 5 - √(7)) = 0

Extending this phrase results in:

u² - 10u + 18 = 0

To know more about equation visit:-

https://brainly.com/question/29030053

#SPJ1

Answer:

c  ≥ (p x 2)

Step-by-step explanation:

Answer:

t₁ = 14

d = -2

Step-by-step explanation:

Given :-

t₆ = 4

t₁₀ = -4

To Find :-

t₁ and d

Solving :-

t₆ = t₁ + 5d = 4   -(1)

t₁₀ = t₁ + 9d = -4 -(2)

(2) - (1)

4d = -8

d = -2

t₁ + 5(-2) = 4

t₁ = 14

Solution :-

t₁ = 14

d = -2

Answer:

Step-by-step explanation:

The ratio of boys to girls:

If there are a total of 132 boys, then number of girls is:

Total number of students:

Answer: The ten thousand digit is 6.  And the millions digit is 4. So the answer is 10.

The area of the farm that is too rough to use is 157.86

An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.

Let the total area of the farm be x.

Area of the farm, too rough to use=x/4

Area of farm kept for poultry farms=2x/5

Remaining Area=221

Thus,

\(x-(\frac{x}{4}+\frac{2}{5}x)=221\)

\(\\ x-\frac{13}{20}x=221\\\)

\(\frac{7}{20}x=221\\\)

x=631.43

Area of the farm too rough to use= 631.43/4

                                                        =157.86

Learn more about the area here:

https://brainly.com/question/25292087

#SPJ4

Implicit differentiation can be applied to functions of three or more variables.  the conservation laws of momentum and energy can be used to derive expressions for the final velocities of the masses. The special cases of equal masses and an infinitely larger mass are also analyzed, shedding light on the behavior of momentum conservation in these situations.

Implicit differentiation can be extended to functions of three or more variables, allowing us to find the derivatives of implicitly defined functions. By considering the function F(x, y, z) = 0 and assuming that ∂y/∂F ≠ 0, we can use partial derivatives to find the derivative ∂x/∂y(x, z) = y'x(x, z) = -F'y/F'z. This provides a way to find the derivative with respect to one variable when the function is defined implicitly.

Shifting the focus to one-dimensional motion, we consider two masses, m1 and m2, undergoing an elastic collision. By applying the conservation laws of momentum and energy, we can derive general expressions for the final velocities, v1,f and v2,f, following the collision. These expressions depend on the initial velocities and masses of the objects involved.

In the case where m1 equals m2, special considerations arise. The analysis reveals specific relationships between the initial and final velocities, highlighting the symmetrical nature of the collision.

Furthermore, by investigating the limiting behavior when m2 is infinitely larger than m1, it becomes apparent that the final velocity of m2 is approximately zero while m1 retains its initial velocity. This showcases the conservation of momentum, as the larger mass dominates and effectively absorbs the impact without significant change in its own motion.

In conclusion, implicit differentiation provides a useful tool for finding derivatives of implicitly defined functions in multi-variable contexts. Analyzing one-dimensional motion with elastic collisions demonstrates the application of conservation laws, yielding expressions for final velocities. Special cases, such as equal masses and a significantly larger mass, offer insights into the behavior of momentum conservation in these scenarios.

Learn more about functions here:

https://brainly.com/question/31062578

#SPJ11