4r + 17 = 23. here is a diagram and its corresponding equation. find the solution to the equation and explain your reasoning.

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

(a)

(b)Discrete

(c)Ratio Scale and Discrete Variable

(d) Experimental Method

Step-by-step explanation:

The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.

(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).

The memory test involves measuring the number of items each participant remembers from the past three weeks of news.

Therefore:

(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.

(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.

Since the dosage is given in multiples of 50mg, it is a discrete variable.

(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

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The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

Step-by-step explanation:

17(7x−3) =1

Divide both sides by 17

7x - 3 = 1/17

Collect like terms

7x = 1/17 + 3

x = (1/17 + 3) /7

x = 52/17 ÷ 7

x = 52/17 × 1/7

x = 52/119

The quantity of red blood cell that is in the sample would be = 42 × 10⁵

Blood cells are those vascular cells that makes up the circulating blood of living organism which includes the white blood cells and the red blood cells.

The amount of white blood cells = a

The amount of red blood cells = 6 x 10² (a)

The amount of white blood cells in the sample = 7 × 10³

Therefore the amount of red blood cell in that sample =

6× 10² × 7 × 10³ = 42 × 10⁵

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Answer:

800

Step-by-step explanation:

First what you need to do is find the scale of magnification, which you can do with 500/1.2. You will get 416.6667 as the scale. You then need to multiply the scale by 1.92, which nets you the actual distance of 800 miles.

Hope this helps!

Answer:

3.12 * 10 ^ -4

the first digit of your scientific notation should be anything other than 0, in this case a 3

Answer:

3.12 x 10^4

Step-by-step explanation:

There are 3 zeros and there also has to be a number before the decimal in scientific notation. Hope this helps!

Answer:

The chance that the usual language in that household will NOT be English = 0.4

Step-by-step explanation:

As given ,

Total households in which languages spoken is English = 180

Total households in which languages spoken is Spanish = 80

Total households in which languages spoken is other than English or Spanish  = 40

So,

Total households = 180 + 80 + 40 = 300

Now,

Household in which English language is not spoken = 80 + 40 = 120

So,

The chances that the usual language in that household will NOT be English = \(\frac{120}{300} = \frac{12}{30} = \frac{4}{10} = 0.4\)

∴ we get

The chance that the usual language in that household will NOT be English = 0.4

By answering the presented question, we may conclude that As a result, the slope of \(y_3\) = -4(x - 5) is -4.

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).

The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.

The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

The above equation is in point-slope form: y - \(y_1\)= m(x - \(x_1\)), where (\(x_1\), \(y_1\)) is a point on the line and m is the slope.

We can see by comparing the provided equation to the point-slope form that \(x_{1} ,y_1\)) = (5, 3) and m = -4.

As a result, the slope of \(y_3\) = -4(x - 5) is -4.

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Answer:

Step-by-step explanation:

\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)

Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

well, we know is a square, so that means all sides are equal, so if we just find one side and multiply it by 4, that's our perimeter, hmmmm let's use the points of K(-2 , 0) and J(3 , 5)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ K(\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad J(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ KJ=\sqrt{(~~3 - (-2)~~)^2 + (~~5 - 0~~)^2} \implies KJ=\sqrt{(3 +2)^2 + (5 -0)^2} \\\\\\ KJ=\sqrt{( 5 )^2 + ( 5 )^2} \implies KJ=\sqrt{ 25 + 25 } \implies KJ=\sqrt{ 50 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE perimeter} }{4\sqrt{50} ~~ \approx ~~ }\text{\LARGE 28.3}\)

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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The correct options are B. C. E, For events A and B to be independent, the occurrence of event B should not affect the probability of event A. In other words, P(A|B) = P(A) and P(A|BC) = P(A), where BC is the complement of B.

Therefore, the following equalities would indicate that events A and B are independent:

P(A) = P(B) (This equality is not always true, so it does not indicate independence.)

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|B) = P(B) (This equality is not always true, so it does not indicate independence.)

P(A|BC) = P(A)

So, the equalities that indicate that events A and B are independent are:

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|BC) = P(A)

Therefore, the correct options are:

P(A|B) = P(A|BC)

P(A|B) = P(A)

P(A|BC) = P(A)

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A company also tries to encourage sales by periodically offering 10% off coupon codes. Suppose that we select a day at random. Let A = a coupon code is offered and let B = the customer makes a purchase. Which of the following equalities would indicate that events A and B are independent? Check all that apply.

A. P(A) = P(B)

B. P(A|B) = P(A|BC)

C. P(A|B) = P(A)

D. P(A|B) = P(B)

E. P(A|BC) = P(A)

Answer:

1) dividend

2) divisor

3) quotient

Answer:

x^2-2x-48

Step-by-step explanation:

FOIL

Firsts = x*x = x^2

outside = x*-6 = -6x

inside = 8*x = 8x

lasts = 8*-6 = -48

add all together x^2-6x+8x-48 = x^2-2x-48

Answer:

x² + 2x - 48

Step-by-step explanation:

( x + 8 ) ( x - 6 )

=  x ( x - 6 ) + 8 ( x - 6 )

= x*x - 6*x + 8*x + 8*( - 6 )

= x² - 6x + 8x  - 48

= x² + 2x - 48

Answer:

Its D

Step-by-step explanation:

Its D because each one is multiplied by 16

Answer:

kg

Step-by-step explanation:

Answer:

$7.25

Step-by-step explanation:

7.00 x 3.5 = 24.5     round it 0ff its 25 = 25 cents

$7.00 + .25 =$7.25

Answer:

y= 50+8x

Step-by-step explanation:

Given data

Charges

Membership= $50

Each game= $8

Let the number of games be x and the total charges be y

so that the expression for the total charges be

y= 50+8x

The value of f after solving the expression, 2-f/4 = f-3f/4+3, is -2.

According to the question,

We have the following expression:

2-f/4 = f-3f/4+3

We know that to find the value of f we will have to move the terms with the same variable on one side. Now, moving f and 3f/4 from the right hand side to the left hand side will result in the change of their signs.

3f/4-f/4-f +2 = 3

Moving 2 from the left hand side to the right hand side:

3f/4-f/4-f = 3-2

Taking the least common factor as 4:

(3f-f-4f)/4 = 1

(-2f)/4 = 1

Using the cross multiplication method:

-2f = 4

f = -4/2

f = -2

Hence, the value of f for the given expression is -2.

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Answer:

a), c)

Step-by-step explanation:

These are the conversion factors you need for this problem.

1 ft = 12 in

1 ft = 30.48 cm

1 ft = 0.3048 m

3 ft = 1 yd

Now we convert 6 ft into each of the units in the choices, in., m, cm, and yd.

a) 6 ft × (12 in.)/(1 ft) = 72 in.                      option a) is correct

b) 6 ft × (0.3048 m)/(1 ft) = 1.8288 m        option b) is incorrect

c) 6 ft × (30.48 cm)/(1 ft) = 182.88 cm       option c) is correct

d) 6 ft × (1 yd)/(3 ft) = 2 yd                         option d) is incorrect

Answer: a), c)

Answer:

The concept of beta impacts financial decision making by providing information volatility or systematic risk of a security.

The information that provided by the concept of beta would take form in a comparison between your chosen securities with other securities that exist in the market. For investors who prefer low risk but small and steady return, they can use the concept of beta to find out the securities with low level of volatility.

Step-by-step explanation: I hope this helps! If not sorry!

Answer:

a is a 1 and then you subtraction the b is equal 0

You just need to integrate 3 times:

\(f'''(t)=t^{1/2}-9\cos t\)

\(f''(t)=\displaystyle\int f'''(t)\,\mathrm dt=\frac23 t^{3/2}-9\sin t+C\)

\(f'(t)=\displaystyle\int f''(t)\,\mathrm dt=\frac4{15} t^{5/2}+9\cos t+Ct+D\)

\(f(t)=\displaystyle\int f'(t)\,\mathrm dt=\frac8{105} t^{7/2}+9\sin t+\frac C2 t^2+Dt+E\)

D.

Y decreases when x increases, so it should be negative. Y also starts at 12 when x is 2, so Y should be at a higher number when x is 0. To find it, take 13.877 and subtract my 0.717. It's a bit off but it's more accurate than the other equations.