A research company wants to test the claim that a new multivitamin helps to improve short term memory. State the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.

(SHOW WORK)​

The value of x = -1

The value of y = -5

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 first equation be A

The value of A is

y = 3x - 2   be equation (1)

Let the second equation be B

The value of B is

x - y = 4   be equation (2)

On simplifying equation (2) , we get

Adding y on both sides of the equation , we get

x = y + 4   be equation (3)

Substituting the value of x in equation (1) , we get

y = 3x - 2

y = 3 ( y + 4 ) - 2

y = 3y + 12 - 2

y = 3y + 10

Subtracting y on both sides of the equation , we get

2y + 10 = 0

Subtracting 10 on both sides of the equation , we get

2y = -10

Divide by 2 on both sides of the equation , we get

y = -5

Substitute the value of y in equation (3) , we get

x = y + 4

x = -5 + 4

x = -1

Therefore , the value of x is -1 and the value of y is -5

Hence , The value of x = -1

The value of y = -5

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Final answer:

To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.

Explanation:

To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.

Step 1: Isolate y in the first equation.

We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.

Step 2: Substitute y into the second equation.

Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.

Step 3: Solve for x.

Now, we simplify and solve for x:

x - 3x + 2 = 4

-2x + 2 = 4

-2x = 4 - 2

-2x = 2

x = -1

Step 4: Substitute x back into the first equation to solve for y.

Using x = -1 in the first equation y = 3x - 2, we get:

y = 3(-1) - 2

y = -3 - 2

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Answer:

4x^2(5x^4 / 2x^2)= 10 x^4

Step-by-step explanation:

We want factorize the expression 4x^2(5x^4 / 2x^2)

And to do this, we need to remember key properties of exponents.

Those are:

[tex]x^{m} / x^{n} = x^{m-n}[/tex]

[tex]x^{m} * x^{n} = x^{m+n}[/tex]

So

4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4

Answer:

[tex]\large\boxed{x=-6\pm\sqrt{30}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+12x+6=0\qquad\text{subtract 6 from both sides}\\\\x^2+2(x)(6)=-6\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-6+6^2\\\\(x+6)^2=-6+36\\\\(x+6)^2=30\Rightarrow x+6=\pm\sqrt{30}\qquad\text{subtract 6 from both sides}\\\\x=-6\pm\sqrt{30}[/tex]

Answer:

Here's one way to do it.

Step-by-step explanation:

-24 ÷ (-4)

-24 is the final number on the number line

-4 means you count by 4s on the number line moving backwards.

Answer: +6 (The sign is + because you are still facing forward).

After modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

" Number line is defined as a straight line which represents the number at the equal interval on it on the both the side of zero."

According to the question,

Given division,

[tex](-24)[/tex] by [tex](-4)[/tex]

As shown on the model of  number line the given division we have,

Hence, after modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

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[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\[1em] [x-6]^2+[y-(-1)]^2=4^2\implies (x-6)^2+(y+1)^2=16 \\\\\\ \stackrel{\mathbb{F~O~I~L}}{(x^2-12x+36)}+\stackrel{\mathbb{F~O~I~L}}{(y^2+2y+1)}=16\implies x^2+y^2-12x+2y+37=16 \\\\\\ x^2+y^2-12x+2y+37-16=0\implies x^2+y^2-12x+2y+21=0[/tex]

ANSWER

Option A

EXPLANATION

When a circle has it's center at (h,k) and and radius r units, then its equation in standard form is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The given circle has its center at (6,-1) and its radius is r=4 units.

We plug in these values to get

[tex]{(x - 6)}^{2} + {(y - - 1)}^{2} = {4}^{2} [/tex]

[tex]{(x - 6)}^{2} + {(y + 1)}^{2} =16[/tex]

We now expand to obtain

[tex] {x}^{2} - 12x + 36 + {y}^{2} + 2y + 1 = 16[/tex]

[tex] {x}^{2} + {y}^{2} - 12x +2 y + 36 + 1 - 16 = 0[/tex]

[tex]{x}^{2} + {y}^{2} - 12x +2 y + 21 = 0[/tex]

This is the equation in general form of the circle.

Answer: G.

Step-by-step explanation: When reading the choices F & J will make you say : "Well F is not true because look at the amount of men compared to women. And J, the choice is unbiased doesn't refers to any kind of opinion based reponse so I'll cross 'em off immediatly". The leave you with G & H H is true but it's also opinion based reponse, and G told you that more men are surveyed than women an it's true because look at the sport section! High off top! But still more than women even if the minivans section is little of men but women also so fair and square!

- I'm sorry this is so long. Just comment if you have questions :)

Answer:

2 is the only even prime number.

Step-by-step explanation:

Two is the only even prime number. It's the only even number that can be divided by only itself (2) and one.

Hope this helped!

~Just a girl in love with Shawn Mendes

C. 112.5

The Angles of Intersecting Chords Theorem  states:

"If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle"

So, the arc intercepted by the angle ∠5 is:

360° - 50° - 115° - 85° = 110°

On the other hand, the arc intercepted by its vertical angle is:

115°

Therefore:

[tex]\angle 5 = \frac{1}{2}(110^{\circ}+115^{\circ}) \\ \\ \boxed{\angle 5 = 112.5^{\circ}}[/tex]

Answer:

Option B 125°

Step-by-step explanation:

In this problem we need to calculate the measure of angle ∠6

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

see the attached figure to better understand the problem

∠6=(1/2)[arc AB+arc CD]

(arc AB+arc CD)=360°-(60°+50°)=250°

substitute

∠6=(1/2)[250°]=125°

Answer:

5

Step-by-step explanation:

[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]

Answer:

28

Step-by-step explanation:

Substitute 8 for x in g(x) = 5x - 12:

g(8) = 5(8) - 12 = 28

By using PEDMAS rule, g(8) = 28

PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.

Given

g(x) = 5x - 12

Substitute x = 8

g(8) = [tex]5\times 8-12[/tex]

Calculate the product

g(8) = [tex]40-12[/tex]

Calculate the sum or difference

g(8) = 28

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In the given Angles and Rays question, Based on the given diagram descriptions, the correct answers are ray AB, ∠DCE, and ray CE.  Therefore, the correct options are: B. ∠DCE, C. ray AB, D. ray CE.

The given question seems to be talking about geometric figures involving rays and angles. From the description, we know that there are two diagrams. The first diagram contains a ray namely AB and the second diagram contains two rays namely CD and CE forming angle DCE at common point C.

Based on the given information, Ray AB is correct because it's mentioned explicitly in first diagram. Angle DCE, represented as ∠DCE, is also correct as it has been stated to exist in the problem description within the second diagram. Lastly, ray CE is a legitimate answer as it is a fundamental part of the second figure forming an angle with ray CD at point C.

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Final answer:

The equation of the line through (7, -4) and (-1, 3) has a slope of -7/8. It can be written in a point-slope form as y + 4 = -7/8(x - 7), and in slope-intercept form as y = -7/8x + 25/8.

Explanation:

To write the equation of the line that passes through the points (7, –4) and (–1, 3), the first step is to find the slope of the line. The slope (m) is given by the rise over run, which is the change in y divided by the change in x:

Now that we have the slope, we can use the point-slope form which is given by the formula:

We can choose one of the points for x1 and y1; let's use (7, -4):

Therefore, the point-slope form of the line is:

Now, to convert this into the slope-intercept form (y = mx + b), we just solve for y:

After simplifying the constant term:

The slope-intercept form is y = -7/8x + 25/8, where -7/8 is the slope and 25/8 is the y-intercept.

Answer:

y^2+12-7y

Step-by-step explanation:

(y-3)(y-4)

I will split it up for us

y*y= y^2

-3*y= -3y. \

y*-4= -4y. / -7y

-3*-4= 12

y^2+12-7y

The product of (y-3)(y-4), is y^2 - 7y + 12.

To find the product of (y-3)(y-4), we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials.

First: Multiply the first terms of each binomial: y × y = y^2.

Outer: Multiply the outer terms: y × -4 = -4y.

Inner: Multiply the inner terms: -3 × y = -3y.

Last: Multiply the last terms of each binomial: -3 × -4 = 12.

Adding these products together, we get: y^2 - 4y - 3y + 12. Simplifying by combining like terms, the final product is: y^2 - 7y + 12.

The astronaut is experiencing approximately 6.21 g's in the centrifuge.

a. To find the angular velocity of the centrifuge in radians per second, we first need to convert the number of revolutions per minute to revolutions per second. Since there are 60 seconds in a minute, the angular velocity (ω) can be calculated as follows:

Angular velocity (ω) = (Number of revolutions per minute) / 60

Given that the centrifuge makes 72 complete revolutions in 2 minutes:

ω = 72 / 2 / 60 = 1.2 revolutions per second

Next, to find the distance an astronaut travels around the center each second, we can use the formula for the circumference of a circle:

Circumference = π × diameter

Circumference = π × 70 feet

Circumference ≈ 220 feet

Distance traveled each second = Circumference × ω

Distance traveled each second = 220 feet × 1.2 revolutions per second ≈ 264 feet

So, the angular velocity of the centrifuge is approximately 1.2 radians per second, and an astronaut travels around the center approximately 264 feet each second.

b. The acceleration (a) of an object moving in circular motion with a constant velocity (v) and a radius (r) is given by the formula:

[tex]a = v^2 / r[/tex]

Since the astronaut is moving at a constant velocity around the center of the centrifuge, we can use the same formula to find their acceleration. The velocity of the astronaut is the distance traveled each second (264 feet) and the radius of the centrifuge is half of its diameter (70 feet / 2 = 35 feet):

Acceleration (a) = (264 feet per second)^2 / 35 feet ≈ 198.86 feet per second squared

So, the astronaut's acceleration is approximately 198.86 feet per second squared.

c. To find how many g's the astronaut is experiencing in the centrifuge, we need to compare their acceleration with the acceleration due to gravity on Earth (32 feet per second squared). One g is equivalent to the acceleration due to gravity.

Number of g's = Acceleration (astronaut) / Acceleration due to gravity on Earth

Number of g's = 198.86 feet per second squared / 32 feet per second squared ≈ 6.21 g's

So, the astronaut is experiencing approximately 6.21 g's in the centrifuge.

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Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

============================================

We have the points (0, 2) → b = 2 and (4, 6).

Calculate the slope:

[tex]m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1[/tex]

Substitute the values of the slope and the y-intercept to the equation of a line:

[tex]y=1x+2[/tex]

Answer:

y=x+2

Step-by-step explanation:

Answer:

(L + 10)/(L + 16) = 0.8

Step-by-step explanation:

She needs to answer L more questions to get a grade of 80%.

When she answers L more questions correctly, she will have answered L + 10 questions correctly.

The total number of questions will be L + 16.

L + 10 must be 80% of L + 16

(L + 10)/(L + 16) = 0.8

Cheryl must use the equation 0.80 = (10 + I) / (16 + I) to determine how many consecutive questions she needs to answer correctly to reach her goal of 80% accuracy on her test.

Cheryl has answered 16 questions on her online test with 10 correct responses. To achieve her goal of 80% accuracy, she must determine how many additional questions she must answer correctly in a row.

To find the necessary total number of correct answers (T) for 80% accuracy, we use the equation:

0.80 = (10 + I) / (16 + I)

where I represents the number of consecutive questions Cheryl answered correctly after the initial 16 questions.

Answer:

Area of the triangle is 25.9 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°

∵ b = 2.92 feet

- b is the side opposite to angle B

∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°

- Lets find c the side opposite to angle C by sing the sine rule

∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]

∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]

- By using cross multiplication

∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]

- The area of the triangle = 1/2 (b)(c)sin∠A

∵ The sum of the interior angles of a triangle is 180°

∴ m∠ A + m∠ B + m∠ C = 180°

∵ m∠ B = (28/3)°

∵ m∠ C = (242/3)°

∴ m∠ A + 28/3 + 242/3 = 180

∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides

∴ m∠ A = 90°

∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)

∵ sin(90) = 1

∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²

* Area of the triangle is 25.9 feet²

Answer:

157.65

Step-by-step explanation:

38*4.1=155.8

155.8+1.85=157.65

For this case we must find the value of the following expression:

[tex]1.85 + 38 * 4.1 =[/tex]

According to the PEMDAS algebraic resolution method, multiplications must be made before the addition. So, we have:

[tex]1.85 + 155.8 =[/tex]

Adding we have:

157.65

Answer:

157.65

Answer:

D. 113°, Consecutive interior angles theorem.

Step-by-step explanation:

We use the interior angle theorem which states that when 2 lines are parallel and are intersected by a transversal, the interior angles on one side add up to 180°

67° and angle 2 are therefore supplementary angles.

67+ angle2=180°

angle2= 180-67 =113°

Answer:

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.

Step-by-step explanation:

The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.

We have that P=10, so 10=2L+2W.

10=2L+2W

10=2(L+W)  By factoring using the distributive property.

2(5)=2(L+W)  I factored 10 as 2(5).

If 2(5)=2(L+W), then 5=L+W.

Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.

I think they want natural numbers {1,2,3,4,...}.  This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.

So now looking for numbers from this set that satisfy: L+W=5.

L+W=5

1+4=5

4+1=5

2+3=5

3+2=5

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.

Answer:

3^9 * 11^9

Step-by-step explanation:

33^9 =

We know that (ab)^c = a^c * b^c

(33)^9 = (3*11)^9 = 3^9 * 11^9

Answer:

1.958 * 10^-5 seconds  or 0.00001958 seconds.

Step-by-step explanation:

3740 = 3.74 * 10^3  in scientific notation.

Time = distance / speed.

= 3. 74 * 10^3 / 1.91 * 10^8

= 1.958 * 10^-5 seconds.

It takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away using the speed of sound in telephone cables.

To find the time it takes for sound to travel a certain distance, we can use the formula time = distance / speed. In this case, the speed of sound along the telephone cable is 1.91 * 10^8 ms⁻¹ and the distance is 3740m.

So the time = 3740 / 1.91 * 10^8 = 1.96 * 10^-5 seconds.

Therefore, it takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away.

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Answer:

Step-by-step explanation:

the curve is representing the projectile. at t=0, the projectile is on the ground.  at t=6, the projectile has finished its journey and is back on the ground.  In between t=0 and t=6 will be the projectile's peak altitude.  the point between t=0 and t=6 is t=3.  So plug in t=3 and solve for s(t), and you get 36ft.  gg

Answer:

Simplify:

[tex](8\frac{2}{3} )^4[/tex]

Step-by-step explanation:

[tex](8\frac{2}{3})^4 =(\frac{26}{3} )^4=\frac{456976}{81}[/tex]

Answer:

The answer is

650/81

Step-by-step explanation:

I think this is a better representation

Of the given expression

(8 2/3^4)

To solve the problem let us perform a step by step operation

Step one

Let's us solve the bracket terms first

=(8 2/3^4)

3⁴= 3*3*3*3=81

=(8 2/81)

=Simplifying we have

=((81*8)+2)/81

=(648+2)/81

=650/81

Answer:

10u+t=18+10t+u

(If this doesn't match one of the equations, please post your options so I can put it in the form of one of your options.)

Step-by-step explanation:

Let there be a number [tu] where t is the tens and u is ones digit.

t+u=16.

Now we reverse the number [ut] is 8 more than [tu].

[ut]=18+[tu]

So [ut]=10u+t because u is the tens  and t is the ones digit

and [tu]=10t+u because t is the tens and u is the ones digit.

The equation you are looking for is

10u+t=18+10t+u.

Let's solve it just for fun:

Subtract u on both sids:

9u+t=18+10t

Subtract 10t on both sides:

9u-9t=18

Divide both sides by 9:

u-t=2

The system is:

u-t=2

u+t=16

--------------add!

2u  =18

u=9

If u=9 and u+t=16, then t=7.

To the original number is 79.

The new number is 97 (is this 18 more than the other; yep).

Answer:

97.

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

395.2

Step-by-step explanation:

Area of a trapezoid is:

A = ½ (a + b) h

where a and b are the top and bottom lengths and h is the height.

If 7.6 refers to the entire side length, then the area is:

A = ½ (2.6 + 7.6) (4)

A = 20.4

If 7.6 refers only to the length right of the right angle, we can use Pythagorean theorem to find the length on the left:

x² + 4² = 5²

x = 3

So the whole side length is 3 + 7.6 = 10.6.  That means the area is:

A = ½ (2.6 + 10.6) (4)

A = 26.4

Answer:

1/3x+4 ≤ 2x+12

Step-by-step explanation:

x ≤ -24/5

Answer:

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Step-by-step explanation:

Given  : The sum of one third a number and 4 is at the most the sum of twice that number and 12.

To find : Write expression .

Solution : We have given statement

According to question :

Let the number = x

One third of a number = [tex]\frac{1x}{3}[/tex].

Sum of one third of number and 4 =  4 +  [tex]\frac{1x}{3}[/tex].

Twice a number  =  2x

Sum of twice that number and 12 =  2x +  12

So,  sum of one third a number and 4 is at the most the sum of twice that number and 12.

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

greater than equal to sign for at most.

Therefore, 4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Final answer:

The measure of the other angle that is complementary to a 13º angle is 77º.

Explanation:

If two angles are complementary, it means they add up to 90 degrees. In this case, one angle is given as 13º. To find the measure of the other angle, we subtract the given angle from 90º because complementary angles sum up to 90 degrees.

So, if we let x represent the measure of the other angle, the equation becomes:

13° + x = 90°

To find x, we subtract 13 from both sides:

The calculation would be:

90º - 13º = 77º.

Therefore, the measure of the other angle is 77º.

Hence, the correct answer is:

B. 77

Answer:

The correct option is 10....

Step-by-step explanation:

The formula of circumference of the circle is:

C = 2πr

where C is the circumference of the circle

r = radius

In this question we have given the circumference and we have to find out the radius:

Thus substitute the values in the formula:

C = 2πr

20π= 2πr

Move 2π to the L.H.S.

20π/2π = r

Cancel out π by π and 20/2 by the table of 2

Therefore we have:

10=r

Thus the correct option is 10....

Answer is provided in the image attached.