the diagram below, not drawn to scale, shows right angled triangles EDC and ABC. Angle ABC = 30°, BD = 20° cm, AC = 9cm and DE = 8cm.


Calculate, giving your answer correct to 1 dp.

The length of BC, in cm.


The size of angle EDC in degrees.

The gallons of milk were in each container originally is 2.4 and 4.8 gallons respectively.

Let us say that:

V₁ = initial gallons in the first container

V₂ = initial gallons in the second container.

From the problem statement, we can create the expression:

V₁ = 2 V₂

V₁ – 3 = 45 (V₂ – 2)

Combining the two expressions:

2 V₂ – 3 = 45 (V₂ – 2)

2 V₂ – 3 = 45 V₂ – 9

2.5 V₂ = 6

Divide

V₂ = 6 / 2.5

V₂ = 2.4 gallons

V₁ = 2 V₂:

= 2 × 2.4

= 4.8 gallons

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Complete question

The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 4.5 times as much milk as the second, How many gallons of milk were in each container originally?

The required age from the equation is 12 years old

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the age to be calculated be = a

The age of the brother be b = ( 1 / 3 ) a

Multiply by 3 on both sides , we get

a = 3b

So , Age to be calculated a = 3b

The age of sister c = 6 years elder than brother

So ,

The age of sister c = b + 6

The age of sister c = 10

From the equations , we can simplify that

c = b + 6

Substituting the value for c , we get

10 = b + 6

Subtracting 6 on both sides , we get

b = 4

Now , from the equation , we get

Age to be calculated a = 3b

                                      = 3 x 4

                                      = 12 years old

Hence , the age to be calculated a is 12 years old

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Answer:

the answer is 19: 4

Step-by-step explanation:

19:4

Theoretical flow time = 58 minutes

The complete question is

Mamossa Assaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (15 minutes per roof) and then formed in a roof forming press (8 minutes per roof). Bases are punched in a base punching press (3 minutes per base) and then formed in a base forming press (10 minutes per base), and the formed base is welded in a base welding machine (12 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per https://brainly.com/question/27786618garage) on an assembly welding machine to complete the garage. Assume one operator at each station.

Roof → Roof - punch(15 min) → Roof-form(8 min) →→→→→→→→↓

                                                                                      (10)Assembly→ Door

Base → Base - punch(3 min) → Base - form(10 min) → weld(12 min)↑

Roof path = 15 + 8 = 23

Base path = 3 + 10 + 12 =25

Theoretical flow time = Roof path + base path + assembly = 23 + 25 +10 = 58 mins

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The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.

if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?

The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.

The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".

in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.

in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .

then it will be

b = 12

c = 13

a² = c² - b²

a² = 13² - 12²

a² = 169 - 144

a² = 25

a = 5

you need to plug the coordinates into the slope formula, which is m=(y2-y1)/(x2-x1).

m=(9-6)/(5-4)

m=(3)/(1)

m=3

Answer:

The effective tax rate for a taxable income of $63,425 is 15.18%.

Step-by-step explanation:

Answer:

1.38461538462

Step-by-step explanation:

A quadratic equation in one unknown;

has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.

If we apply discriminant for the above equation, we obtain the following expression;

If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.

Now let's remember our formula for finding the roots and solve the problem using the discriminant value.

Therefore;

Other root is;

The average rate of change of the function is 0.2 inches per day

A rate of change describes how one quantity changes in relation to another quantity. Mathematically, it is defined as the change in one divided by the change in the other quantity.

In this case, the average rate of change of the function g(n) from n=1 to n=5 will be:

Given the function, g(n) = 10(1.02)ⁿ

average rate of change  = g(5)-g(1) / n₅-n₁

g(5) = 10(1.02)⁵ = 11.0

g(1) = 10(1.02)¹ = 10.2

average rate of change  = 11.0-10.2 / 5-1

                                        = 0.8/4

                                        = 0.2 inches per day

Therefore,  the average rate of change from n=1 to n=5 is 0.2 inches per day

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The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

Given,

Number of social networking sites being surveyed = 6

Sample mean = 9.05 million visitors per month

Standard deviation = 5 million

We have to find the 98% confidence interval of the true mean;

Here,

Sample mean, x = 9.05 million

Standard deviation, σ = 5 million

Sample size, n = 6

z score of 98% is 2.326

Now,

9.05 million - 2.326 × (5 million / √6) < true mean < 9.05 million + 2.326 × (5 million / √6)

43.02 million < true mean < 13.80

Therefore,

The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80

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If W(-10, 4), X(-2, 71), and Y(-5, 10), triangle WXY is an isosceles triangle.

What is an obtuse scalene triangle?

An obtuse scalene triangle is a triangle in which one of the angles is greater than 90 degrees but less than 180 degrees and the other two angles are less than 90 degrees. The measurements of all three sides and angles

Distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

The given points are W(-10, 4), X(-2, 71), and Y(-5, 10) .

Let's find the length of WX.

                         [tex]WX = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\\\WX = \sqrt{(-2 -(-10))^2 + (71-4)^2}\\\\WX = \sqrt{(8)^2 + (67)^2}\\\\WX = \sqrt{64 + 4489}\\\\WX = \sqrt{64 + 4489}\\\\WX=67.47[/tex]

Now find the length of XY.

                        [tex]XY = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\\\XY = \sqrt{(-5-(-2))^2 + (10-71)^2}\\\\XY = \sqrt{(-3)^2 + (-61)^2}\\\\XY = \sqrt{9 + 3721}\\\\XY=61.07[/tex]

Now find the length of WY.

                      [tex]WY = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\\\WY = \sqrt{(-5-(-10))^2 + (10-4)^2}\\\\WY = \sqrt{(5)^2 + (6)^2}\\\\WY = \sqrt{25+36}\\\\WY=7.81[/tex]

So from calculations, we can say that triangle is an obtuse scalene triangle.

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Answer: r = 19.35 ft

Step-by-step explanation:

[tex]Volume = V = \pi r^{2} \frac{h}{3} \\235.5 = \pi r^{2} 15/3\\r^{2} = \frac{235.5}{\pi} 5\\r = \sqrt{374.8} = 19.35[/tex]

Answer:

Step-by-step explanation:

-4(x - 1) + 6x =34

-4x + 4 + 6x = 34

-4x + 6x + 4 = 34

2x + 4 = 34

2x + (4-4) = (34-4)

2x = 30

2x/2 = 30/2

x = 15

The critical value is 2.65

Given,

The confidence interval = 99%

Sample size, n = 12

We have to find the critical value;-

Critical value;-

A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.

Here,

The sample size n = 12,

Then, the degrees of freedom is n - 1 = 12 - 1 = 11

The critical value= t₀.₀₀₁/2 = t₀.₀₀₅

Using the t-table and selecting df =12  and  since it’s a 2 tail the corresponding t-score is 2.65

Therefore, the critical value is 2.65

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Answer:

C (41)

Step-by-step explanation:

A straight line has 180 degrees in it. all you would have to do is is add the known numbers, 16 + 123, getting 139. Then subtracting 139 from 180m. You would then get 41.

Answer:

x=41

Step-by-step explanation:

(X+16)+123=180

x+139=180

 -139. -139

x=41

Hopes this helps please mark brainliest

The solution to the system is x = 0, y =2, z = 5

Given the following system:

x+ 2y+z=9      -------- (1)

x- y+3z = 13    -------- (2)

2z = 10            -------- (3)

From (3):

2z = 10

z = 10/2 = 5

Put z = 5 into (1) and (2):

x+ 2y+z=9

x+ 2y+5 = 9

x +2y = 9-5

x +2y = 4     -------- (4)

x- y+3z = 13

x -y + 3(5) = 13

x-y + 15 = 13

x-y = 13 -15

x-y = -2     --------   (5)

Using elimination method on (4) and (5):

Subtracting (5) from (4):

x +2y = 4

x-y =   -2

3y = 6

y = 6/3 = 2

Put y = 2 into (4):    

x +2y = 4

x + 2(2) = 4

x + 4 = 4

x = 4-4 = 0

Therefore, the solution is x = 0, y =2, z = 5. The 3rd option is the answer.

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Answer:

$28

Step-by-step explanation:

5.5%=0.055

1.54/0.055=28

The given expression rewritten in simplified exponential form is [tex]5x^{\frac{3}{2}}[/tex]

From the question, we are to rewrite the given expression is simplified exponential form.

The given expression is

[tex]\sqrt{\sqrt{25^{2} x^{6} } }[/tex]

First, we will evaluate the inner square root

[tex]\sqrt{25^{\frac{2}{2} } x^{\frac{6}{2} } }[/tex]

[tex]\sqrt{25 x^{3 } }[/tex]

Simplifying further

[tex]\sqrt{25 } \times \sqrt{x^{3}}[/tex]

[tex]5\times x^{\frac{3}{2}}[/tex]

= [tex]5x^{\frac{3}{2}}[/tex]

Hence, the expression in simplified form is [tex]5 x^{\frac{3}{2}}[/tex]

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The best solution for the given equation is x=4

What are logarithmic functions?

The inverse function to exponentiation in mathematics is called the logarithm. Accordingly, the exponent to which b must be raised in order to obtain a number x is determined by its logarithm to the base b.

Use Property:

logb(xy)=logbx+logby and logby = x ⇔ x^b = y

log2(x(x−2))=3
2^3 =x^2 −2x
8=x^2−2x
0=x^2−2x−8
0=(x−4)(x+2)
x−4=0
or
x+2=0
x=4
or
x=−2
Hence, x=4

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Answer: X=16

Step-by-step explanation:

trust,, also good luck to plato 2b algebra people

Answer:  y=(3/4)x+2

Step-by-step explanation:

1. Find the slope (change of y/change of x)

(5-(-4))/(4-(-8)

9/12

SLOPE: 3/4

2. Find the y-intercept. Insert the points into an equation and find b.

5=(9/12)(4)+b

5=3+b

b=2

Y-INTERCEPT=2

You can ask where you don't understand.

Answer:

x = 11

Step-by-step explanation:

Let's have  one of the numbers be represented by the variable, x,  and the other number be represented with the variable, y

Since the sum of the two numbers is 55, we can write the following equation:

x + y = 55

Then since one number is 4 times as large as the other, we can write:  y = 4x

We can now substitute this expression for y into the second equation and solve by

combining like terms and using inverse operations to solve for x:

x + y = 55

x + 4x  = 55

5x = 55

5x/5 = 55/5

x = 11

One of the numbers is 11.

Since the sum of the numbers is 55, the other number will be 44.

Answer:

11 and 44

Step-by-step explanation:

→ Write 2 equations

x + y = 55

y = 4x

→ Substitute bottom equation into top

x + 4x = 55

→ Solve

x = 11

→ Find y

4 × 11 = 44

36.3 inches the tall is she in.

Given that;

Percentage of vertical jump height = 27.5%

Dagne's height = 13.2 inches

We need to find:

Height of jump

We know that the formula for Computation:

Height of jump = Percentage of vertical jump height × Dagne's height

so,

Height of jump = 13.2 × 27.5

That equals to

Height of jump = 36.3 inches

Hence the answer is 36.3 inches the tall is she in.

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Answer: miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:

18.75 miles in 1/4 hour.

that is the ratio 18.75 / 1/4

but we want the miles in an hour.

so, how many 1/4 are in a whole ?

well, 4.

so we need to multiply the ratio by 4/4 (so that on one hand we multiply the denominator by 4 to make it a whole, and on the other hand we are not changing the value of the ratio) :

18.75 × 4 / (1/4 × 4) = 75 miles / 1 hour = 75 mph.

Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

The principal amount = $2500

The interest rate = 1.75%

The time period = 8 years

Part a

The simple interest

A = P(1  + rt)

Substitute the values in the equation

A = 2500(1 + (1.75/100)×8)

A = 2500( 1 + 0.14)

A = 2500( 1.14)

A = $2850

Part b

The time period = 5 years

Simple interest = Prt

= 2500 × (1.75/100) × 5

= 2500 × 0.0175 × 5

= $218.75

Hence,

Part a

There will be $2850 in the account after 8 years

Part b

The amount of interest earned in 5 years is $218.75

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The joint relative frequency of students who use a computer in a traditional class is of:

37%.

The relative frequency of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, we want the joint relative frequency of students who use a computer in a traditional class, hence the total and desired outcomes are given as follows:

Hence the joint relative frequency of students who use a computer in a traditional class is calculated as follows:

28/74 = 37%. (rounded down).

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Answer:

14%



Step-by-step explanation:

1. I took the test

2.Likes running and swimming=28

Total=200

28/200=.14

.14 in percent form is 14%

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