to test the effect of a new drug on depression, we randomly assign people to control and experimental groups. those in the control group take a pill that contains no medication. this is a .

Answer:

10.7 °

Step-by-step explanation:

In this problem, there are two angles with degrees of 2x + 6 and two angles of degrees of 15x - 8. We know the sum of the four angles is 360, as stated in the problem. Thus we can set up the following equation:

2(2x + 6) + 2(15x - 8) = 360

4x + 12 + 30x -16 = 360

34x - 4 = 360

34x = 364

x ≈ 10.7 °

Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

Step-by-step explanation

1 euro = 1.07 dollars

£1 = 1.25 dollars

Now ,

⇒ £1 = 1.25 dollars

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =

⇒ £1 =1.17 euros

Therefore , Bethany says, Using these exchange rates, £1 is worth 1.17 euros.

Answer:

-3, 4

Step-by-step explanation:

First, we can simplify this expression by diving both sides by 6. Thus, we get x² - x - 12 = 0. Solving this, we get (x-4)(x+3). Thus, the solutions for x are 4 and -3. So, the answer is x = -3, 4

Answer:

B

Step-by-step explanation:

it says why

The horizontal line of length 7cm is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Line = 7 cm

The following steps would create the perpendicular bisector

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Answer:

Step-by-step explanation:

The most precise term for the quadrilateral ABCD with vertices A(4, 7), B(6, 5), C(4, 1), and D(2, 5) is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

The two numbers that can be true for the equations are 5 and 12

From the information given, we have the equations;

x+y=17

x-y=7

From equation (1), make 'x' the subject of formula

x = 17 - y

Now, substitute the value into the formula, we have;

17 - y - y= 7

collect like terms

-y-y = 7 - 17

Subtract the iike terms

-2y = -10

Make 'y' the subject

y = 5

Substitute the value

x = 17 -5

x = 12

Hence, the values are 12 and 5

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When a region is rotated about the x-axis, a cylinder is formed. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder.

The volume of a cylinder is the amount of space the cylinder takes up. It is found by multiplying the area of the cylinder's base by its height. The formula for finding the volume of a cylinder is V = πr²h, where r is the radius of the cylinder's base, and h is its height.

The radius of the cylinder is equal to the distance from the x-axis to the highest point on the graph of y = 9/(x² + 3x + 2).

To find the highest point on the graph, we differentiate the function and find the critical points.

Differentiating y = 9/(x² + 3x + 2):

dy/dx = -18x / (x² + 3x + 2)²

Setting dy/dx = 0 and solving for x:

-18x / (x² + 3x + 2)² = 0

x = -3, 2

For x = -3, y = 9/(-3² + 3(-3) + 2) = 9/1 = 9

For x = 2, y = 9/(2² + 3(2) + 2) = 9/8 = 1.125

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The length of the cable is, 252.57 m.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A cable is used to support a 245-m television tower.

And, the angle the cable makes with the ground is 78°.

Let the length of the cable = x

Hence, We can formulate;

⇒ sin 78° = 245 / x

⇒ 0.97 = 245 / x

⇒ x = 245/0.97

⇒ x = 252.57 m

Thus, The length of the cable is, 252.57 m.

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The equation of line is y = 12x and the number of boxes the shipping company can pack in 18 hour period is 216 boxes

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of hours be x

Let the number of boxes be y

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 5 , 60 )

Now , the slope of the line m = y/x

Substituting the values in the equation , we get

Slope m = 60 / 5 = 12

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 60 = 12 ( x - 5 )

y - 60 = 12x - 60

y = 12x

Now , when x = 18 hours

y = 12 ( 18 ) boxes

y = 216 boxes

Hence , the number of boxes is 216 boxes

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The height of the other tree is 7.25 meters

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Ratio = Height : Shadow

So, we have

Height : Shadow = 4 : 16

Simplify

Height : Shadow = 1 : 4

So, we have

Height : 29 = 1 : 4

This means that

Height = 29 * 1/4

Evaluate

Height = 7.25

Hence the height is 7.25 meters

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Answer:

The height of the other tree is 7.25 meters

Step-by-step explanation:

The factor of quadratic equation is x√17

A quadratic equation is one that contains a second-degree polynomial. They are extensively utilized in a wide range of disciplines, including engineering, architecture, finance, biology, and, of course, mathematics.

Factoring is frequently the simplest way to solve a quadratic equation. Finding expressions that can be multiplied together to get the expression on one side of the problem is the process of factoring. A quadratic equation is represented as a product of linear terms if it can be factored.

First you need to find perfect square factors of 17

17 = 1*17

√17  = √1*√17 = 1√17 = √17

we had also √x² = x

So the answer is x√17

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116 years it take  for the account value to reach 26500 dollars

percentage, a relative value indicating hundredth parts of any quantity.

Given that 7700 dollars is placed in an account with an annual interest rate of 5.5%.

We need to find the time it  take for the account value to reach 26500 dollars

[tex]A=P(1+r)^{t}[/tex]

A = final amount=26500

P = initial amount (7700)

r = annual interest rate (5.5%)

n = number of times interest is compounded per year

t = time in years

Solving for t, we get:

[tex]25600=7700(1+5.5/100)^{t}[/tex]

[tex]25600=7700(1.055)^{t}[/tex]

Divide both sides by 7700

[tex]25600/7700=1.055^{t}[/tex]

3.32=tlog1.055

3.32=0.02t

t=116 years

Hence, 116 years it take  for the account value to reach 26500 dollars

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The summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms.

Given is an arithmetic series, 4+8+12+16, we need to find the summation notation for the given arithmetic series,

To generate the terms of a series given in sigma notation, successively replace the index of summation with consecutive integers from the first value to the last value of the index.

To generate the terms of the series given in sigma notation above, replace n by 1, 2, 3 and 4

[tex]\sum_1^4(4n)[/tex] = 4(1) + 4(2) + 4(3) + 4(4)

= 4 + 8 + 12 + 16

= 40

Therefore, the sum of the series is 40

Hence, the summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

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Note that the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D' is given as attached. Note that when a shape is reflected, it must be reflected over a line. In this case, the line of reflection is y = -3.

A line of reflection is a line that acts as a mirror, reflecting a figure across the line so that the image is a mirror image of the original.

When a shape is reflected, it must be reflected over a line. The line of reflection of quadrilateral ABCD onto quadrilateral A'B'C'D is

From the given graph, we have the following observations

ABCD was flipped over to form A'B'C'D'

The line of reflection is between both shapes.

Using points C and C' as references;

We have:

C = (-3, -1)

C" = (-3, -5)

Notice that both points have the same x-coordinate

This means that the line of reflection is parallel to the x-axis and passes through the y-axis.

The point at which it passes through the y-axis is calculated using the mid-point formula.

Therefore, we have:

y = (y1+y2)/2

y = (-1-5)/2

y = -6/2

y = -3

Hence, the line of reflection is y = -3
See the attachment for the line of reflection.

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Answer:

Step-by-step explanation:

The amount in the account after t years is given as follows:

A(t) = A(0)(1 + r)^t.

In which:

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

For an increasing exponential function, the rate of change is given as follows:

b = 1 + r.

In which r is the growth rate, as a decimal.

Considering that the balance increases according to the yearly dividend, the equation is given as follows:

A(t) = A(0)(1 + r)^t.

The problem is incomplete, hence the general procedure in obtaining the equation was presented, which can be used to analyze the statements.

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Two gardeners can cut a similar field in three hours. A soccer field might be cut in two hours by six grounds-keepers, every one of whom works at a pace of one-6th of the field every hour.

To get the number of grounds-keepers expected to cut the very field in that timeframe, we should initially decide the speed at which the field can be cut in 3 hours, which is 1/3 of the field consistently.

To get the required number of groundskeepers, we partition this rate by the pace of every nursery worker, which is 1/6 of the field every hour, yielding the condition 1/3 / 1/6 = 2.

Subsequently, two nursery workers might cut similar regions in three hours.

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The equations with no solutions are   −60x+32=−60x+60 and −60x+32=−60x−32. Options B and D

Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, constants and factors.

They are also composed of arithmetic operations, such as;

From the information given, we have that the expression or equation without solutions are those with the value of x as 0.

−60x+32=−60x+60

collect like terms

-60x + 60x = 28

Hence, the equations are  −60x+32=−60x+60 and −60x+32=−60x−32

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The expected value of M does not change in a predictable manner when sample size increases; it can increase, decrease, or stay the same.

The expected value of M, or the mean of a sample, is determined by the values of the individual elements that comprise it. As such, when the sample size increases, the expected value of M could increase, decrease, or remain constant, depending on the particular values of the individual elements in the sample. This is because the expected value of M is the average of the individual elements and the contribution of each element to the average depends on its value and the number of elements in the sample. Therefore, the expected value of M does not change in a predictable manner when sample size increases. Depending on the individual elements in the sample, the expected value of M could be higher, lower, or constant.

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Answer: true

Step-by-step explanation:

The solution to the equation is a = 3 1/3

From the question, we have the following parameters that can be used in our computation:

a + 5 and two-thirds = 9

Express properly

So, we have

a + 5 2/3 = 9

Subtract 5 2/3 from both sides of the equation

This gives

a = 9 - 5 2/3

Evaluate the difference

a = 3 1/3

Hence, the solution is a = 3 1/3

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One way we can check this is to simply multiply 15 by 12 to get 180.

Or you could even switch the numbers around.

But if we wanted to check it further, we can take the total and divide that by one of the multiplican or multipliers (15 or 12) to get the correct product.

Therefore, these are some ways to use the numbers 180, 15 and 12 in expressions.

The area of the given given shape which consists of a triangle and a quarter circle to 1 decimal place would be =161.04m².

The formula used to calculate the are of triangle= ½base×height.

where; Base= 12m

height= 20-12 = 8 m

area = 1/2×12×8 = 48m²

The formula for the area of a quarter circle = πr²/4

where r = 12m

Area = 3.14 × 12²/4

= 3.14×144/4

= 452.16/4

= 113.04m²

Therefore, the area of the figure = 48+ 113.04 = 161.04m²

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Answer:

1 1/3  or just 1/3

Step-by-step explanation:

What percent of the shape is shaded in?

Alright to start, let's look at the shape, it is divided into 4 equal parts, one part is shaded, which gives us 1/4, or 25% or 0.25. Then there's another part, which is half shaded, that'll be half of 1/4 or 25% or 0.25, which is 1/8 or 12.5% or 0.125. Now all you have to do is add them together.

1/4 + 1/8 = 3/8

25% + 12.5% = 37.5%

0.25 + 0.125 = 0.3725

These are your three answers you can choose from, I guess the second one won't work because the problem states not to include a % sign.

Hope this helped!

Let's call the number of candles Roma sold for $5 each "x".

What is the unitary method's formula?

What is the unitary method's formula? The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

Since she sold 200 candles in total, we know that x + 3y = 200, where y is the number of sets of three candles she sold for $11.

We also know that the total revenue was $788, so we can set up another equation based on the total revenue:

5x + 11y = 788

Now that we have two equations, we can use substitution to solve for x. First, let's solve for y:

y = (200 - x) / 3

Plugging this expression for y into the second equation:

5x + 11((200 - x) / 3) = 788

Expanding and simplifying the equation:

5x + (2200 - 11x) / 3 = 788

Multiplying both sides by 3 to get rid of the fraction:

15x + 2200 - 11x = 2364

Combining like terms:

4x = 164

Finally, dividing both sides by 4 to solve for x:

x = 41

So Roma sold 41 candles for $5 each at the craft fair.

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Answer:

4min:1min

Step-by-step explanation:

60:15

divide by 5

12:3

divide by 3

4:1

Applying the secant-secant theorem, the value of x is: 12.

The secant-secant theorem states that if you draw two lines from a point outside a circle that intersect the circle at two different points, then the product of the length of one line segment and the length of the portion of the line outside the circle is equal to the product of the length of the other line segment and the length of its portion outside the circle.

Based on the secant-secant theorem, we have:

EF * ES = ED * EC

Substitute the values:

8(8 + 10) = 9(2x - 17 + 9)

Solve for x:

144 = 18x - 72

144 + 72 = 18x

216 = 18x

216/18 = x

x = 12

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Originally our equation looks like [tex]x^{2}[/tex] + 2y

First, we want to substitute x = [tex]\frac{1}{2}[/tex]  & y= 0 into the equation.

The equation now looks like [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] + 2 x 0

The brackets are added to the fraction as we are squaring the WHOLE fraction, and the 2y has a hidden multiplication sign, with it being 2 x y, so it is 2 x 0.

Now that we have our values substituted into the equation, we can solve it!

 [tex]([/tex][tex]\frac{1}{2}[/tex][tex])^{2}[/tex] = [tex]\frac{1}{4}[/tex]  

therefore,

[tex]\frac{1}{4}[/tex]  + 2 x 0

= [tex]\frac{1}{4}[/tex]

Answer:

8 hours

Step-by-step explanation:

We know that since Lila earns $12/hr and works 6 hr/week, she earned 72 since 12 * 6 = 72.

We can let the amount Patrick earns each week represent 9h, where h is the amount of hours he works.

We can solve for h by setting Patrick's equation equal to 72, which is Lila's earnings:

[tex]9h=72\\h=8\\\\9(8)=72\\12(6)=72[/tex]

Step-by-step explanation:

What graph are we talking about?