Calculate the volume of cuboids with the following dimensions
length= 1.2 m, breadth= 1 m, height= 150 cm​

Answer:

x=50

Step-by-step explanation:

for x = 50, the equation 2x + 50 = 3x holds true

What is an equation?

An equation is a statement indicating that the values of two mathematical expressions are equal (indicated by the sign =). For example -

2x + 3 = 5

ax + c = 9

Given is the following equation to solve -

2x + 50 = 3x

We have -

2x + 50 = 3x

On solving for [x], we can write -

3x - 2x = 50

x = 50

Therefore, for x = 50, the equation 2x + 50 = 3x holds true.

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The circumference is 160 feet for a length of 40 feet. The perimeter is 200 feet for a length of 50 feet. The circumference is 240 feet for a length of 60 feet.

A rectangular region with a 1200 square foot area will have a different perimeter depending on how long it is. The perimeter will be 160 feet if the area is 40 feet long. The length of 40 feet is multiplied by four to get a final measurement of 160 feet. In a similar manner, if the area is 50 feet long, the perimeter will be 200 feet.

The length of 50 feet is multiplied by four to get a final result of 200 feet. Finally, the perimeter will be 240 feet if the area is 60 feet long. The length of 60 feet is multiplied by four to get a final measurement of 240 feet. A rectangular region with an area of 1200 square feet will therefore have a different perimeter depending on its length, with a length of 40 feet resulting in a perimeter of 160 feet, a length of 50 feet resulting in a perimeter of 200 feet, and a length of 60 feet resulting in a perimeter of 240 feet.

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Answer:

y=-2x-1

Step-by-step explanation:

Answer:

  179.3 square units

Step-by-step explanation:

The area of the figure is the sum of the areas of the parts. That is, the area is the sum of the area of the rectangle, and the area of the semicircle.

__

The area of a circle with radius 5 is ...

  A = πr²

  A = π(5²) = 25π

The area of the semicircle is half that:

  semicircle area = (25π)/2 = 12.5π ≈  39.3 . . . . square units

The area of a rectangle with length L and width W is ...

  A = LW

The width of this rectangle is the diameter of the circle, twice the radius, or 10 units.

  A = (14)(10) = 140 . . . . square units

The sum of the areas of the parts is ...

  total area = semicircle area + rectangle area

  total area = 39.3 + 140 = 179.3 . . . . square units

The surface integral of the function f(x, y, z) = x² + y² over the surface of the sphere x² + y² + z² = a² is (2/3) a⁴π.

The surface of the sphere can be parametrized using spherical coordinates as follows:

x = a sin(θ) cos(φ)

y = a sin(θ) sin(φ)

z = a cos(θ)

where θ represents the polar angle (ranging from 0 to π) and φ represents the azimuthal angle (ranging from 0 to 2π).

Now, we need to calculate the surface element ds in terms of the spherical coordinates.

The surface element can be expressed as:

ds = a² sin(θ) dθ dφ

We need to calculate the unit normal vector n to the surface. The unit normal vector to a sphere is given by:

n = (x, y, z) / a

Now, we can calculate the surface integral using the parametrization and the unit normal vector:

∫∫(o) f(x, y, z) ds = ∫∫(o) (x² + y²) a² sin(θ) dθ dφ

Since we are integrating over the entire surface of the sphere, the limits of integration for θ are 0 to π, and for φ, the limits are 0 to 2π.

∫∫(o) f(x, y, z) ds = ∫(0 to 2π) ∫(0 to π) (a² sin(θ) cos²(φ) + a² sin(θ) sin²(φ)) a² sin(θ) dθ dφ

Simplifying the integrand:

∫∫(o) f(x, y, z) ds = ∫(0 to 2π) ∫(0 to π) a⁴ sin³(θ) (cos²(φ) + sin²(φ)) dθ dφ

Since (cos²(φ) + sin²(φ)) = 1, the integrand simplifies to:

∫∫(o) f(x, y, z) ds = ∫(0 to 2π) ∫(0 to π) a⁴ sin³(θ) dθ dφ

Now, we can evaluate the integrals.

The integral with respect to θ is straightforward:

∫(0 to π) sin³(θ) dθ = -cos(θ) + 1/3 cos³(θ) evaluated from 0 to π

= -(-1) + 1/3(-1) - (-cos(0) + 1/3 cos³(0))

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

= 1/3

we substitute the result of the integral with respect to θ into the remaining integral:

∫∫(o) f(x, y, z) ds = ∫(0 to 2π) 1/3 a⁴ dφ

Integrating with respect to φ:

∫(0 to 2π) dφ = φ evaluated from 0 to 2π

= 2π - 0

= 2π

Substituting the result of the integral with respect to φ:

∫∫(o) f(x, y, z) ds = (1/3 a⁴) (2π)

= (2/3) a⁴π

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The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Answer

to solve the equation for t

You have r= t/m

So you need to rearrange the terms

r= t /m ; t = r*m

you pass the m from dividing to multiplying

t = r * m

The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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The standard deviation of the nation's construction wages is approximately $4.22. Null hypothesis is the population variance of the third region's construction wages is greater than or equal to the population variance of the nation's construction wages (σ_3^2 ≥ σ^2). Alternative hypothesis is the population variance of the third region's construction wages is less than the population variance of the nation's construction wages (σ_3^2 < σ^2).

a. To estimate the standard deviation of the nation's construction wages, we can use the given information that the highest-paying region's wages are approximately 29% larger and the lowest-paying region's wages are about 40% lower than the national average.

Let's assume the average wage for construction workers in the nation is represented by μ.

According to the information provided, the highest-paying region's wages are approximately 29% larger than the national average. Therefore, the wage in the highest-paying region can be approximated as 1.29μ. Similarly, the lowest-paying region's wages are about 40% lower than the national average. Thus, the wage in the lowest-paying region can be approximated as 0.60μ.

To estimate the standard deviation of the nation's construction wages, we can consider the range between the highest-paying and lowest-paying regions:

Range = Highest wage - Lowest wage = 1.29μ - 0.60μ = 0.69μ

Since the range is typically equal to 4 times the standard deviation for normally distributed data, we can set up the equation:

Range = 4 * Standard Deviation

0.69μ = 4 * Standard Deviation

Dividing both sides by 4, we get: Standard Deviation = 0.69μ / 4

Given that the average wage for construction workers in the nation is approximately $24.47, we substitute this value into the equation:

Standard Deviation = 0.69 * 24.47 / 4 ≈ 4.219

Therefore, the standard deviation of the nation's construction wages is approximately $4.22.

b. To test whether both the average and the standard deviation of the construction workers' wages in the third region are smaller than those of the nation as a whole, we need to conduct a hypothesis test. Let's start by testing the standard deviation.

Null hypothesis (H0): The population variance of the third region's construction wages is greater than or equal to the population variance of the nation's construction wages (σ_3^2 ≥ σ^2).

Alternative hypothesis (HA): The population variance of the third region's construction wages is less than the population variance of the nation's construction wages (σ_3^2 < σ^2).

The correct choice is A.

H0: σ_3^2 ≥ σ^2

HA: σ_3^2 < σ^2

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The value of x = 11√3 and y = 22

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving angles and distances in various fields such as physics, engineering, and architecture.

We will use Trigonometric Ratios to calculate the value of x and y

tan 30 = 11/x

1/√3 = 11/x

x = 11√3

sin 30 = 11/y

1/2 = 11/y

y = 22

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Answer:

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer:

\(Change = \$36\)

Step-by-step explanation:

Given

See attachment for line plot

\(Amount = \$100\)

Required

Determine the change

First, we calculate the amount represented by the line plot

\(Amount (Plot) =10+12+12+14+16\)

\(Amount (Plot) =64\)

The change from $100 is then calculated as:

\(Change = Amount - Amount (Plot)\)

\(Change = \$100 -\$64\)

\(Change = \$36\)

2x + y = 12 matched with x + 3y = 16

x = 9 - 2y matched with y = 10 + x

y = 11 - 2x matched with 2x - y = 11

4x - 3y = -13 matched with -3x + 3y = 30

x + 2y = 9 matched with x = 5, y = 2

2x + 4y = 20 matched with x = 7, y = 3

To match the systems of equations to their solutions, let's analyze each equation and find the corresponding solution:

System of equations:

2x + y = 12

x = 9 - 2y

y = 11 - 2x

4x - 3y = -13

x + 2y = 9

2x + 4y = 20

Solutions:

A. -3x + 3y = 30

B. x = 2, y = 7

C. x = 5, y = 2

D. x = 3, y = 5

E. y = 10 + x

F. x = 7, y = 3

G. x + 3y = 16

H. 2x - y = 11

I. 2x + y = 11

J. x - 2y = -7

Now, let's match the equations to their solutions:

Equation 2x + y = 12 corresponds to solution G (x + 3y = 16).

Equation x = 9 - 2y corresponds to solution E (y = 10 + x).

Equation y = 11 - 2x corresponds to solution H (2x - y = 11).

Equation 4x - 3y = -13 corresponds to solution A (-3x + 3y = 30).

Equation x + 2y = 9 corresponds to solution C (x = 5, y = 2).

Equation 2x + 4y = 20 corresponds to solution F (x = 7, y = 3).

The remaining equations and solutions are not matched since not all tiles will be used.

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Step-by-step explanation:

Refer to attachment.

Hope it helps.

1. rhombus - figure (f)

2. quadrilateral - figure (h)

3. trapezoid - figure (e)

4. square - figure (c)

5. isosceles trapezoid - figure (a)

6. kite - figure (g)

7. rectangle - figure (b)

8. parallelogram - figure (d)

"It is polygon that has four sides, four vertices and four angles."

"It is a quadrilateral whose opposite sides are parallel and equal in length."

"It is a quadrilateral whose all angles measure 90° and opposite sides are parallel and equal in length."

"It is a quadrilateral whose all angles measure 90° and all sides are equal in length."

"It is a quadrilateral whose all sides are equal in length."

"It is a quadrilateral that has two pairs of adjacent sides that are equal in length."

"It is a quadrilateral whose one pair of opposite sides is parallel."

"It is a trapezoid in which the non-parallel sides are equal in measure."

For given question,

We need to match the quadrilateral to its most precise name.

1. rhombus - figure (f)

2. quadrilateral - figure (h)

3. trapezoid - figure (e)

4. square - figure (c)

5. isosceles trapezoid - figure (a)

6. kite - figure (g)

7. rectangle - figure (b)

8. parallelogram - figure (d)

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Answer:

Step-by-step explanation:

Total is:

Answer: $41.89

Step-by-step explanation:

You first need to find out how much the tip was. Put the percent into decimal form and multiply it by the price of the meal.

0.18 x 35.50 = 6.39

add the tip to the meal price

6.39+35.50=41.89

$41.89

Hope this helps!

Answer:

x=30°

Step-by-step explanation:

53+97+x=180

150+x=180

x=180-150

x=30°

hope this helps

plz mark as brainliest

The graph of the equation -3x+y=6 is linear and is attached with the answer below.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given linear equation is -3x+y=6. When we plot the linear equation -3x+y=6 on the graph it will be a straight line and the x and y-intercepts are -2 and 6 respectively.

The graph of the linear equation is attached with the answer below.

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If two meeps and four bleeps is equal to 22, and two bleeps and twelve meeps is equal to –66, then value of seven meeps and three bleeps is equals to the 198.

We have, meeps and bleeps value. Let the numbers of meep and beep be "x" and "y" .

According to problem, two meeps and four bleeps is equal to 22.

=> 2x + 4y = 22

=> x + 2y = 11 --(1)

Also, two bleeps and twelve meeps is equal to –66.

=> 2x + 12y = - 66

=> x + 6y = - 33 --(2)

We have to determine the value of seven meeps and three bleeps. Equation (1) and (2) form a linear system of equations. Using the Substitution method, from equation (1), x = 11 - 2y

Substitute the value of x in equation (2),

=> x + 6y = - 33

=> 11 - 2y + 6y = - 33

=> 11 + 4y = - 33

=> 4y = -33 - 11

=> 4y = - 44

=> y = -44/4 = - 11

plugging the value of y = - 11 in above equation,

=> x = 11 - 2y = 11 - 2( - 11)

=> x = 11 + 22 = 33

Now, the value of seven meeps and three bleeps = 7x + 3y = 7(33) + 3(-11)

= 231 - 33 = 198

So, required value is 198.

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By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.

In this question we have to prove the trigonometric expression by means of fundamental trigonometric relationships and known values for certain angles. We proceed to prove that one side of the expression is equivalent to the other side:

By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.

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The amount of money which the chef spends on steak as calculated from the data given is found to be $412.50.

Now as we know that ,

for a meal of 12 meals the chef uses 3 pounds.

Therefore , for a meal of 250 meals the chef uses x pounds

Now , we will solve this proportion.

x=(250 meals*3 pounds)/12 meals

= 62.5 pounds

Now , cost of steaks = 6.60 dollars.

Therefore cost of 62.5 pounds of steaks will be ,

62.5 pound x $ 6.60/pound

=  $ 412.50

A comparison between two numbers is called a proportion. If two sets of provided numbers increase or decrease in the same ratio, then the ratios are said to be directly proportional to each other.

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Answer:

B (3,1)

Step-by-step explanation:

Answer:

∆QRS is an obtuse triangle

Step-by-step explanation:

\(x + 2x + 8x - 40 = 180 \\ 11x = 220 \\ x = 20\)

\( < q = 20 \\ < r = 8(20) - 40 = 120 \\ < s = 2(20) = 40\)

<R = 120° > 90° which makes this an obtuse triangle

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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Answer:

Measure C, the Sacramento Community Stabilization and Fair Rent Charter Amendment is on the November ballot for the city of Sacramento after a lengthy court battle. The measure is written to supersede the Sacramento Tenant Protection Act, which was passed in 2019. Here are the results for Measure C as they come in:

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\((3 \times 25 )+ 60 = 75 + 60 = \)

\(135\)

Thus Lisa spent 135 $ .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

$135

Step-by-step explanation:

1. Three gallons of paint that cost 25$ would total 75$, since 25 x 3 is 75$.

2. She also had to pay her friend 60$, so 60$+75$ is 135$. Hope this helps!

Answer:

∠JKP = 35°

Step-by-step explanation:

since P is the incenter, then lines to incenter bisect the corner angles:

7x - 6 = 5x + 4

subtract 5 x from both sides of the equation:

2x - 6 = 4

add 6 to each side:

2x = 10

divide both sides by 2:

x = 5

∠KJP = 7(5) - 6 = 29°

∠LJP = 5(5) + 4 = 29°

then ∠KJL = 29° + 29° = 58°

∠KLJ = 26° + 26° = 52°

∠JKL = 180° - 58° - 52° = 70°

∠JKP = 1/2 ∠JKL = 1/2(70°) = 35°

there might be a more direct way about it but this was the least confusing way I know to explain it.

Answer: y = 5x/4 - 13

Step-by-step explanation:

y=mx+b

7=5/4 *16+b

7=5*16/4 +b

7=80/4+b

7=20+b

b=-13

y = 5x/4 - 13

Answer:

the slope is 8 and the y-int is 1

Step-by-step explanation:

Slope Intercept Form---> y=mx+b

m= slope

b= y-int

Answer:

y=1 hope this help

Step-by-step explanation: