1. Between what two consecutive integers does -√42 fall?


____&_____


2. What are the roots for √16?

_____&______

The potential distances for Transport An are any qualities more noteworthy than 8 miles and under 23 miles.

To decide the potential distances for transport A, we want to think about the given distances between the transports.

Given data:

- Transport C is 8 miles from Transport B.

- Transport C is 23 miles from Transport A.

We should break down the potential distances for Transport A:

1. In the event that Transport B is situated between Transport An and Transport C, the distance between Transport An and Transport B would be not exactly the distance between Transport C and Transport A. Be that as it may, this goes against the data gave (Transport C is 23 miles from Transport A). Accordingly, this situation is preposterous.

2. If Transport An is situated between Transport B and Transport C, the distance between Transport An and Transport B would be not exactly the distance between Transport C and Transport A. This implies that the conceivable distance for Transport An eventual any worth more prominent than 8 miles yet under 23 miles. Hence, the potential distances for Transport A in this situation are more noteworthy than 8 miles and under 23 miles.

All in all, the potential distances for Transport A are any qualities more noteworthy than 8 miles and under 23 miles.

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The sample, which better represents the entire population;

200 people in the city are randomly selected from the phone directory and surveyed to find out the favorite game of the city residents.

The correct option is D.

An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.

A). 150 members of a golf club are surveyed to find out the favorite game of the city residents.

Here, the survey is not done unbiasedly.

Similarly with the other options B and C.

But in (D),

200 people in the city are randomly selected from the phone directory and surveyed to find out the favorite game of the city residents.

The survey is done unbiasedly.

Not in any sport-specific stadium.

Therefore, the correct option is D.

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The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:

$1,830.

The total cost is obtained applying the proportions in the context of the problem.

The number of kilowatt hours is given as follows:

Hence:

200 x 61 x 3 = 36,600 kwh.

The cost is of $0.05 per kwh, hence the total cost is given as follows:

0.05 x 36600 = $1,830.

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Answer:

40

Step-by-step explanation:

Answer:

25/4 or 6.25

Step-by-step explanation:

Given that the general equation of  a quadratic equation is given as ax^2 + bx + c = 0, to complete the square, we subtract c from both sides of the equation and add the square of (b/2a) to both sides.Hence given x^2-5x-19=0, to complete the square, we add (-5/2)^2 to both sides following the illustration given.This is 25/4 or 6.24

Answer:

The slope of a line is:

\(m=-3\)

Hence, option B is true.

Step-by-step explanation:

Given the points

Finding the slope between (-2, 9) and (0, 3)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-2,\:9\right),\:\left(x_2,\:y_2\right)=\left(0,\:3\right)\)

\(m=\frac{3-9}{0-\left(-2\right)}\)

\(m=-3\)

Therefore, the slope of a line is:

\(m=-3\)

Hence, option B is true.

The Federal Reserve should buy $5000 of government bonds to increase the money supply by $500 when the reserve ratio is 10 percent and the actual money multiplier equals the potential money multiplier.

If the actual money multiplier equals the potential money multiplier, and the Federal Reserve wishes to increase the money supply by $500 when the reserve ratio is 10 percent, it should:
4. buy $5000 of government bonds.

Here's the step-by-step explanation:

1. Calculate the money multiplier using the formula: Money Multiplier = 1 / Reserve Ratio
In this case, the reserve ratio is 10%, so the formula would be: Money Multiplier = 1 / 0.1 = 10.

2. Determine the number of government bonds to buy or sell using the formula: Change in Money Supply = Money Multiplier × Change in Bank Reserves.
In this scenario, the Federal Reserve wants to increase the money supply by $500, so we can set up the equation as: $500 = 10 × Change in Bank Reserves.

3. Solve for the Change in Bank Reserves: Change in Bank Reserves = $500 / 10 = $50.

4. Since the Federal Reserve wants to increase the money supply, it should buy government bonds. The amount of government bonds to buy is calculated by multiplying the Change in Bank Reserves by the Money Multiplier: $50 × 10 = $5000.

Therefore, the Federal Reserve should buy $5000 of government bonds to increase the money supply by $500 when the reserve ratio is 10 percent and the actual money multiplier equals the potential money multiplier.

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Using the vertical angles theorem, the equation created is: 3x - 3 = 2x + 13

The value of x = 16.

To solve the problem given, use the vertical angles theorem to create an equation then find the value of x.

(3x - 3)° and (2x + 13)° are vertical angles, therefore, based on the vertical angles theorem, the equation created is:

3x - 3 = 2x + 13

Combine like terms:

3x - 2x = 3 + 13

x = 16

The value of x is: 16.

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The given expressions are: (a) 3ln2+2ln3, (b) ln(3x+2)+ln(x+4), (c) ln(x·y2), and (d) log(x3/y2).a) Simplify 3ln2+2ln3Using the property of logarithm that log a + log b = log(ab)Therefore, 3ln2+2ln3=ln(2³)+ln(3²)

=ln(8)+ln(9)

=ln(8×9)

=ln72

Thus, the simplified form of the expression is ln72.b) Simplify ln(3x+2)+ln(x+4)Using the property of logarithm that log a + log b = log(ab)

Therefore, ln(3x+2)+ln(x+4) =ln[(3x+2)(x+4)]

Thus, the simplified form of the expression is ln(3x²+14x+8).c) Simplify ln(x·y2)Using the property of logarithm that log a + log b = log(ab)

Therefore, ln(x·y2) =ln(x)+ln(y²)

Thus, the simplified form of the expression is ln(x)+2ln(y).d) Simplify log(x³/y²)Using the property of logarithm that log a - log b = log(a/b)

Therefore, log(x³/y²) =log(x³)-log(y²)

=3log(x)-2log(y)

Thus, the simplified form of the expression is 3log(x)-2log(y)X.

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Answer:

----------------------

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

The speed of both printers operating together is 1.333 hours which was found using the given data.

The formula used to explain the connection between speed, distance, and time is speed = distance/time.

Given: Newspapers can be printed twice as quickly on a modern printing press as they can on an old one. The old one takes four hours to publish the afternoon edition.

Let,

a = Speed of New printing press

b = Speed of Old printing press

x = Speed of both printers operating together

We know that,

(1/a)+(1/b)=(1/x)

(1/2)+(1/4)=(1/x)

(4/8)+(2/8)=(1/x)

6/8=1/x

x=8/6

x=1.333

Therefore, the speed of both printers operating together is 1.333 hours which was found using the given data.

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C. A line has one dimension, length.

E. A plane consists of an infinite set of lines.

I uploaded a picture. Does it help??

Answer:

opposite operation

Step-by-step explanation:

divide 35 by 5 so x=7

Answer:

x = 50 :)

Step-by-step explanation:

2 (x + 10) = 3x - 30

2x + 20 = 3x - 30

-x = -50

-50/-x = 50

x = 50

The maximum Height the rocket reaches is 38.4 feet.

The maximum height reached by the rocket, we need to determine the vertex of the quadratic function f(t) = -15t^2 + 48t. The vertex of a quadratic function represents the maximum or minimum point.

The vertex of a quadratic function in the form f(t) = at^2 + bt + c can be found using the formula:

t = -b / (2a)

In our case, a = -15 and b = 48. Plugging these values into the formula, we get:

t = -48 / (2*(-15))

t = -48 / (-30)

t = 8/5

Now, to find the maximum height, we substitute this value of t back into the function f(t):

f(8/5) = -15(8/5)^2 + 48(8/5)

f(8/5) = -15(64/25) + 384/5

f(8/5) = -960/25 + 384/5

f(8/5) = -38.4 + 76.8

f(8/5) = 38.4

Therefore, the maximum height the rocket reaches is 38.4 feet.

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Answer:

1/729

Step-by-step explanation:

Step-by-step explanation:

By looking at the points (2, 0) and (2, 2),

The x-value of 2 gives the y-values 0 and 2.

Since this is a one-to-many relationship,

it is not a function.

Answer:

No.

Step-by-step explanation:

No because the x-intercept repeat. If the y-intercept repeat it's ok, it would be a function, however if the x-intercept repeat the graph is NOT a function.

Ace Carlos

Answer:

The area of a rectangle with length 4 cm and width 6 cm is 24 square cm. To find the area of a semi-circle, we use the formula for the area of a circle and divide by 2. The formula for the area of a circle is πr^2, where r is the radius. The radius of the semi-circle is half the width of the rectangle, so r = 6/2 = 3 cm. Thus, the area of the semi-circle is π(3^2) = 9π square cm.

The total area of the figure would be the sum of the area of the rectangle and the semi-circle, so the answer would be 24 + 9π square cm.

Answer:

3.5

Step-by-step explanation:

13-2.50= 10.5

10.5/3 is 3.5

Answer:

Step-by-step explanation:

-21x - 8y = 0

Answer:

hey there, the answer is 8.9429 × 10^8

Answer:

8.9429 × 10^8

Step-by-step explanation:

ya the answer is 8.9429 × 10^8

Answer:

The slopes of parallel lines are the same

The slopes of perpendicular lines are negative reciprocals

Line AB

\(\textsf{let}\:(x_1,y_1)=(3,4)\)

\(\textsf{let}\:(x_2,y_2)=(7,7)\)

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}\)

Line CD

\(\textsf{let}\:(x_1,y_1)=(0,0)\)

\(\textsf{let}\:(x_2,y_2)=(-6,8)\)

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}\)

As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.

Answer:

2i

Step-by-step explanation:

Answer:

The answer is 20

Step-by-step explanation:

Hello!

\(\large\boxed{x = 3}\)

2x + 1 = 5x - 8

Solve by subtracting both sides by 2x:

2x - 2x + 1 = 5x - 2x - 8

1 = 3x - 8

Add 8 to both sides:

1 + 8 = 3x - 8 + 8

9 = 3x

Divide both sides by 3:

9/3 = 3x/3

x = 3

Answer:

x = 3

Step-by-step explanation:

1. Write the equation

2x + 1 + 5x - 8

2. Add 8 on both sides

2x + 9 = 5x

3. Get the variables together

9 = 3x

4. Solve for x and divide both sides by 3

x = 3

Answer:20/100

Step-by-step explanation:

Answer:

i think the answer would be 20/100

Step-by-step explanation:

The antiderivative function F(x) is given by: F(x) = -4cos(x) - 4/3cot(x) + sec(x) + 4To find the antiderivative function F(x) given that f(0) = 4sin(0)sec^2(0) + sec(0)tan(0) and F(0) = 0, we need to integrate f(x) with respect to x.

First, let's simplify f(x) using trigonometric identities:

f(x) = 4sin(x)sec^2(x) + sec(x)tan(x)

Since sec^2(x) = 1 + tan^2(x), we can rewrite f(x) as:

f(x) = 4sin(x)(1 + tan^2(x)) + sec(x)tan(x)

    = 4sin(x) + 4sin(x)tan^2(x) + sec(x)tan(x)

Now, let's find the antiderivative of f(x) using integration techniques:

∫ f(x) dx = ∫ (4sin(x) + 4sin(x)tan^2(x) + sec(x)tan(x)) dx

We can integrate each term separately:

∫ 4sin(x) dx = -4cos(x) + C1, where C1 is the constant of integration

∫ 4sin(x)tan^2(x) dx = -4/3cot(x) + C2, where C2 is the constant of integration

∫ sec(x)tan(x) dx = sec(x) + C3, where C3 is the constant of integration

Now, we can combine these results to find the antiderivative function F(x):

F(x) = -4cos(x) - 4/3cot(x) + sec(x) + C, where C = C1 + C2 + C3 is the constant of integration

Given that F(0) = 0, we can substitute x = 0 into the expression for F(x):

F(0) = -4cos(0) - 4/3cot(0) + sec(0) + C = -4 + C = 0

From this, we find that C = 4.

Therefore, the antiderivative function F(x) is given by:

F(x) = -4cos(x) - 4/3cot(x) + sec(x) + 4

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Answer:

If  p  is the smallest of  n  consecutive integers of the same sign than we have  p ,  p+1 ,  p+2 ,  … ,  p+(n−1) ,

So the sum is

∑k=0n−1(p+k)=∑k=0n−1p+∑k=0n−1k=np+n2−n2  

Here  n=4  

So we have  4p+6  

And checking

p+(p+1)+(p+2)+(p+3)=4p+6  

Note if  p=−v  

Than you have the same thing as if  p=v−n+1  just negative for example  3  consecutive integers the smallest is  −5  so the sum is  −5+(−4)+(−3)=3×−5+32−32=−15+3=−12  

On the other hand:

−(3+4+5)=−(3×3+32−32)=−(9+3)=−12  

If  p=−v  the sum of next  v+1  integers is  −(∑k=0vk)=−(v2+v2)  

Than needs an other  v  integers to bring it up to  0  again. From there it is

∑k=0hk=h2+h2  

Where  h=n−(2v+1) .

So recap if  p  is the smallest of  n  consecutive integers their sum is

p+(p+1)+(p+2)+…+(p+(n−1))=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪np+n2+n2−(n|p|+n2+n2)((n−|p|)2+(n−|p|)2)−(|p|p+|p|2+|p|2)((n−|p|)2+(n−|p|)2)n≥0p<0∧n<|p|+1p<0∧|p|<n<2|p|+1p<0∧n>2|p|+1

Step-by-step explanation:

The values of x and y on the triangle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

The side x is adjacent to the angle of 30º, while the opposite side to the angle of 30º is of 5 units, hence:

tan(30º) = x/5

\(\frac{\sqrt{3}}{3} = \frac{x}{5}\)

\(x = \frac{5\sqrt{3}}{3}\)

Considering that side 5 is opposite to the angle of 30º, the hypotenuse y is obtained as follows:

sin(30º) = 5/y

1/2 = 5/y

y = 5 x 2

y = 10.

The triangle is given by the image presented at the end of the answer.

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Answer:

680 Bacteria

Step-by-step explanation:

378 is evenly divisible by 126, which is equal to 3.

The first 126 minutes, the 85 bacteria will double to 170 bacteria.

The second 126 minutes (252 minutes total), the 170 bacteria will double to 340 bacteria.

The final 126 minutes (378 minutes total), the 340 bacteria will double to 680 bacteria total.

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