40 meters in 16 seconds

Answer:

x ≈ 14.4 cm

Step-by-step explanation:

the third angle of the triangle = 180° - 40° - 46° = 94°

Using the Sine rule in the triangle

\(\frac{x}{sin46}\) = \(\frac{20}{sin94}\) ( cross- multiply )

x × sin94° = 20 × sin46° ( divide both sides by sin94° )

x = \(\frac{20sin46}{sin94}\) ≈ 14.4 cm ( to the nearest tenth )

Answer:

14 cm (rounded to nearest whole number)

Step-by-step explanation:

Law of Sine:

\(\displaystyle \large{\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}\)

Given angles are:

Definition of Euclidean Triangle:

Find another angle:

So another angle is 94°.

To find:

Determine:

Therefore:

\(\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} = \dfrac{\sin 94^{\circ}}{20}}\)

Multiply both sides by 20x:

\(\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} \cdot 20x = \dfrac{\sin 94^{\circ}}{20} \cdot 20x}\\\displaystyle \large{20\sin 46^{\circ}= x\sin 94^{\circ}}\)

Divide both sides by \(\displaystyle \large{\sin 94^{\circ}}\):

\(\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = \dfrac{x\sin 94^{\circ}}{\sin 94^{\circ}}}\\\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = x}\)

Evaluate the expression, hence:

\(\displaystyle \large{x = 14.42...}\)

Round to nearest whole number:

\(\displaystyle \large{x = 14}\)

Therefore, the value of x is 14 cm.

The first offer is better from the perspective of a customer but the second one is better from the perspective of a seller.

Here we have different 2 cases, and to find the answer we have to follow a few steps.

First of all, we should simplify these two cases and will try to give them a proper equation format.

Let's assume the price of each yogurt is $x.

Therefore the total price of 2 pots is (2× x) = $2x.

But the condition is if we buy 2 pots, get the 3rd one for free. So, we can purchase a total of 3 pots at the same cost.

∵ If 3 pots cost $2x, then the average cost for each pot is 2x/3 =$0.67x

( average value of each unit = Total value / total unit )

In the second case, if we buy 1 pot we can get the second one at half price.

Therefore, the total price of two pots is, ( x + 0.5x ) = $1.50x

∵ If 2 pots cost $1.50x, then the average cost for each pot is 1.50x/2 = $0.75x

( average value of each unit = Total value / total unit ).

The price of yogurt per pot in the first case <  The price of yogurt per pot in the second case.

As $0.67 <  $0.75.

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The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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Answer: 2

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

Answer:

B) 3x-6y

Step-by-step explanation:

2x+x=3x

5y+y=6y

3x-6y

Answer:

A) 3x - 4y

(2x - 5y) + (x + y)

=> 2x - 5y + x + y

=> 2x + x - 5y + y ------(arranging the like terms together)

=> 3x - 4y

Queremos encontrar la escala que se ha utilizado para la elaboración de la maqueta.

Veremos que la escala utilizada es 1cm = 0.5m

Para encontrar la escala, tenemos que ver la relación entre la medida de la maqueta y la medida real.

Sabemos que:

Lo que tenemos que ver es cuanto representa cada centimetro en la maqueta.

Asi, tenemos la relación:

90cm = 45m

90cm/90 = 45m/90

1cm = 0.5m

Es decir, cada centimetro en la maqueta representa 0.5 metros en la realidad, es decir, la escala utilizada es:

1cm = 0.5m

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The null and the alternative hypothesis are:

H0 : µ = 444

Ha : µ < 444 (Left tail test)

We have the following data to solve the problem with

level of significance is given as 0.1

standard deviation = 10

Sample Size , n = 20

Sample Mean, x = 447.0000

solve for the degree of freedom

degree of freedom

DF

20-1= 19

find the  Standard Error

= s/√n

= 10 / √ 20 = 2.2371

find the test statistic

t-test statistic= (x - µ )/SE =

( 447 - 444 ) / 2.2371 = 1.341

find the p value using df = 19

p value = .097866.

0.1 > .097866.we have to reject the null hypothesis

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Answer:

5 weeks

Step-by-step explanation:

because my teacher told me

Answer:actually it’s 10.3

Step-by-step explanation:delta math gave me the right answer once I got it wrong

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Rate of change of the angle of elevation = 96/845 radians / sec

To solve this related rate (of change) problem:

Attached is the solution picture.

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The ratio of the area of circle A to the area of circle B expressed in the common fraction is 4/9.

An arc is a portion of the circumference of a circle. The length of an arc is proportional to the radius of the circle and the measure of the angle formed by the arc and the center of the circle. The formula for the length of an arc is:

Arc Length = (Angle Measure / 360) x (Circumference)

In this problem, we are given that the arc of 55 degrees on circle A has the same length as the arc of 40 degrees on circle B. So we can set up the following equation:

(55/360) x (Circumference of A) = (40/360) x (Circumference of B)

We can simplify this equation by canceling out the common factor of 360:

(5/12) x (Circumference of A) = (2/9) x (Circumference of B)

Now we can use the fact that the circumference of a circle is equal to 2π times the radius:

(5/12) x (2π x radius of A) = (2/9) x (2π x radius of B)

We can cross-multiply and divide by 2π to find the ratio of the radii of the two circles:

(5/12) x (radius of A) = (2/9) x (radius of B)

radius of A / radius of B = (2/9) / (5/12) = 12/18 = 2/3

Since the ratio of the areas of two circles is equal to the square of the ratio of their radii, the ratio of the area of circle A to the area of circle B is:

Area of A / Area of B = (radius of A / radius of B)^2 = (2/3)^2 = 4/9

So the ratio of the area of circle A to the area of circle B is 4/9.

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Answer:

Step-by-step explanation:

hello : given z =  (-6-10i)/(4+7i)

the complex conjugate of the denominator is : 4-7i

1. Multiply the numerator and the denominator by the complex conjugate of the denominator:  z =  (-6-10i)(4-7i)/(4+7i)(4-7i)

use identity : (a + b)(a - b) = a² - b² calculate the product : (4+7i)(4-7i)

(4+7i)(4-7i) = 4² -(7i)² =16 -49i² =16+49 = 65..... ( i² = -1)

2) Simplify the results calculate the numerator :  (-6-10i)(4-7i)

(-6-10i)(4-7i)  = -24+42i -40i+70i²   = -24+42i -40i-70 .....( i² = -1)

(-6-10i)(4-7i) = -94+2i

now :  z =  (-94+2i )/65  = (-94/65) +(2/65) i

   the real part is :   ( -94/65) and the imaginary part is : 2/65

Answer:

45.67r evalutae

Step-by-step explanation:

45

40

35

30

25

20

0

Fuel Efficiency

2 2.5 3 3.5 4 4.5 5 5.5 6

Car Weight (Thousands of Pounds)

Which of the following is a reasonable value for r, given

the relationship shown in the scatterplot?

O-0.197

O-0.898

O 0.528

O 0.902

Answer:

it's going to be

-8x^2+14x^2+4y+y-5-1=

6x^2+5y-6

Step-by-step explanation:

hope this is what u are looking for

have a nice day

The population in this scenario consists of all employees in the firm, which totals 4,500 individuals. The sample is a subset of the population, specifically 60 randomly selected employees who are part of a committee evaluating the implementation of sensitivity training.

the population refers to the entire group of employees in the firm, which consists of 4,500 individuals. The sample, on the other hand, is a smaller group of 60 employees who have been randomly selected to form a committee. This committee's purpose is to evaluate the proposal of implementing sensitivity training online instead of the current in-person format.

The sample of 60 employees is chosen in a random manner to ensure representativeness and minimize potential bias. By selecting a subset of the population, the committee can provide insights and perspectives that are representative of the larger employee base. Each committee member will have the opportunity to vote "yes" or "no" on the proposal, and their votes will be used to determine the overall sentiment of the committee regarding the implementation of online sensitivity training.

It's important to note that the sample of 60 employees is being used as a representative group to make inferences about the entire population.

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The force Sophia is exerting on the shopping cart can be resolved into two components: one perpendicular to the direction of motion (the normal force), and one parallel to the direction of motion (the force doing work). The force doing work is given by:

F_parallel = F * sin(theta)

where F is the force Sophia is exerting (125 N) and theta is the angle of depression (52 degrees).

F_parallel = 125 N * sin(52 deg) ≈ 95.6 N

The work done by Sophia is given by:

W = F_parallel * d

where d is the distance Sophia pushes the shopping cart (200 m).

W = 95.6 N * 200 m = 19120 J

Therefore, Sophia does 19120 joules of work pushing the shopping cart 200 meters.

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Answer:

Anna's wand can cast 70 spells

Step-by-step explanation:

Elsa's wand can cast 53 spells

her wand casts 17 fewer cells than her sister Anna's

Amount of spells cast by Anna's wand = ?

We write the question down in the form of an equation

\(x - 17 = 53\)

where \(x\) is the amount of spells Anna's wand can cast.

we then proceed to solve by collecting like terms to different sides of the equation. We'll have

\(x = 53 + 17\)

which leaves us with

\(x = 70\)

This means that Anna's wand can cast 70 spells.

A variable is a letter that represents another number or thing.

Steps to solve:

3x + 6 - x + 82 = 44

~Combine like terms

2x + 88 = 44

~Subtract 88 to both sides

2x = -44

~Divide 2 to both sides

x = -22

Best of Luck!

The first car traveled 100 kilometers in 2 hours, the second car covered 150 kilometers in 3 hours, the third car journeyed 200 kilometers in 4 hours, and the fourth car drove 250 kilometers in 5 hours.

The given information provides the distance traveled and the time taken by four different cars. The first car traveled 100 kilometers in 2 hours, indicating an average speed of 50 kilometers per hour. The second car covered a distance of 150 kilometers in 3 hours, resulting in an average speed of 50 kilometers per hour as well. Similarly, the third car journeyed 200 kilometers in 4 hours, with an average speed of 50 kilometers per hour. Lastly, the fourth car drove 250 kilometers in 5 hours, maintaining the same average speed of 50 kilometers per hour.

It is interesting to note that all four cars maintained a consistent average speed of 50 kilometers per hour, despite covering different distances and taking varying amounts of time. This implies that the cars were traveling at a constant speed throughout their respective journeys. The information provided does not indicate any changes in speed or fluctuations in the driving conditions. This consistency in speed suggests that the cars were likely traveling on a straight and uncongested road, allowing them to maintain a steady pace.

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Answer:

Is it -2,3

Step-by-step explanation:

Answer:

2 laranjas

Step-by-step explanation:

3 - 1 = 2

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3,-12) and (3,-8)

The distance between them is

\( |EF| = \sqrt{( {3 - 3})^{2} + ({ - 12 + 8})^{2} } \\ = \sqrt{ {0}^{2} + ({ - 4})^{2} } \\ = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Answer: 4

Step-by-step explanation: 8-12=4

Answer:

Step-by-step explanation:

Answer:

so,the area of the rectangle=length ×width

area of rectangle=10×5

area of rectangle=50in²

Answer:

7 large boxes an 2 small boxes

Step-by-step explaination

its obligatory to be 5 large boxes so i first did 350 * 5 =1750

then i just added a small box with a large until it gave the result

It will take 50 grams of a substance 4.7 years to decay to 10 grams, given that the rate of decay is k = -0. 345.

To find the time it takes for the substance to decay from 50 grams to 10 grams, we can use the equation for exponential decay:

A = A₀e^(kt)

where A is the final amount, A₀ is the initial amount, k is the rate of decay, and t is the time.

We can rearrange the equation to solve for t:

A/A₀ = e^(kt)
ln(A/A₀) = kt
t = ln(A/A₀)/k

Plugging in the given values, we get:
t = ln(10/50)/(-0.345)
t = ln(0.2)/(-0.345)
t = 4.7

So, it will take approximately 4.7 years for the substance to decay from 50 grams to 10 grams at a rate of decay of k = -0.345.

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Answer:

They are not equivalent

Step-by-step explanation:

2(x+4)+4

First you distribute the 2.

2x+8+4

Then combine like terms

2x+12

Therefore they are not equivalent