Find the square root of 1681
​

Answer:

Hi,

Step-by-step explanation:

a)

\(if\ \dfrac{x}{2}-3\ > \ 0\ then\ |\dfrac{x}{2}-3|=\dfrac{x}{2}-3\\\\\dfrac{x}{2}-3 > 4\\\\\dfrac{x}{2} > 7\\\\x > 14\\\)

b)

\(if\ \dfrac{x}{2}-3\ < \0 \ then\ |\dfrac{x}{2}-3|=-(\dfrac{x}{2}-3)=-\dfrac{x}{2}+3\\\\-\dfrac{x}{2}+3\ > \ 4\\\\-\dfrac{x}{2}\ > \ 4-3\\\\-\dfrac{x}{2}\ > \ 1\\\\\dfrac{x}{2}\ < \ -1\\\\x\ < \ -2\\\)

\(S=\{x\in\mathbb{R}\ :\ |\dfrac{x}{2}-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\\)

Answer:

Don has to sell 61 marbles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

Don has to sell x marbles.

Mark has to sell y marbles.

The total number of marbles is 75:

This means that:

\(x + y = 75\)

Since we want to find x.

\(y = 75 - x\)

Don has 5 more than 4 times the number of marbles Mark has

This means that:

\(x = 4y + 5\)

Since \(y = 75 - x\)

\(x = 4(75 - x) + 5\)

\(x = 300 - 4x + 5\)

\(5x = 305\)

\(x = \frac{305}{5}\)

\(x = 61\)

Don has to sell 61 marbles.

Answer:

x = 17

Step-by-step explanation:

When two lines are intersected by a transversal, the interior on the same side of the transversal are called co interior angles and they are supplementary.

6x + 8 + 4x + 2 = 180

6x + 4x + 8 + 2 = 180   {Combine like terms}

         10x + 10  = 180  {Subtract 10 from both side}

                 10x = 180 - 10

                 10x = 170  {Divide both sides by 10}

                    x = 170/10

x = 17

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

unnun

Step-by-step explanation:

Answer:

F(1) = 0

F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1

F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2

F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3

...

F(n) = F(1) - 6 x (n - 1)

Hope this help!

:)

Answer:

0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.

Step-by-step explanation:

We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%.

This means that the null hypothesis is:

\(H_{0}: p = 0.79\)

And the alternate hypothesis is:

\(H_{a}: p > 0.79\)

We know that the p-value is 0.2307. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is?

0.2307 > 0.05, which means that we accept the null hypothesis, that is, that the population proportion in favor of candidate A is close to 0.79, that is, it is not significantly more than 0.79.

We know that

E is midpoint of DF, that means DE is equal to EF, so we can form the following equation

Replacing the given equations, we have

Now, we replace this value in each equation to find each part of the segment.

Answer:

300

Step-by-step explanation:

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

\(d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}\)

\(d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}\)

\(d = \sqrt{(0)^2+ (0)^2 + (-5)^2}\)

\(d = \sqrt{(25)}\)

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

\(d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}\)

\(d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}\)

\(d = \sqrt{(-3)^2 + (0)^2+ (0)^2}\)

\(d = \sqrt{(9)}\)

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

\(d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}\)

\(d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}\)

\(d = \sqrt{(0)^2 + (4)^2+ (0)^2}\)

\(d = \sqrt{(16)}\)

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

By using the general sphere equation and what we know about planes, we will get:

The general sphere of radius R centered in the point (a, b, c) is given by:

(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2

If we want a sphere centered in (3, -4, 5) we will have:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2

a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2

b) This time is the yz-plane, so the radius must be equal to the x-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2

c) Finally, the xz-plane, this time the radius must be equal to the y-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2

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Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

Answer:

true

Step-by-step explanation:

rjdkejdkdkekewnensjwkw

Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer: false

Step-by-step explanation:

The median of each set is the middle term (after the term are arranged in increasing order)

Thus, the statement is false.

Step-by-step explanation:

it's false,

it should be a point

Answer:

\( \frac{25}{10} . \frac{875}{100} \)

Answer:

David

Bc it said David's parents lol

nice one tho

Answer:

593

Step-by-step explanation:

when you are subtracting a negative it is the same as adding

The number of watts will be 4700 watts to the nearest 100 watt.

It should be noted that 1 watt equals to 3.41 Btu per hour.

In this case, the air conditioner is rated at 16000 BTU per hour.

Therefore, the number of watt will be:

= 16000/3.41.

= 4692

= 4700 watts to the nearest 100 watt.

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The answer is No. The points exhibit some systematic pattern that is not a straight-line pattern. (A)

The normal quantile plot is a special case of the Q–Q plot that compares a given distribution to the standard normal distribution. If the plotted points fall along a straight line, the distribution is approximately normal.

There are actually four variations of the normal plot, or eight since depending on preference the X and Y axes are often swapped:

1. Normal quantile plot. Observations plotted against expected normal score (Z-score, known as quantiles)

2. Normal quantile-quantile plot (also known as normal QQ plot). Normal score (Z-score, known as quantiles) of the observations plotted against expected normal score (Z-score, known as quantiles)

3. Normal probability plot. Observations plotted against expected CDF (cumulative area under the normal curve, known as probability)

4. Normal probability-probability plot (also known as normal PP plot). CDF (cumulative area under the normal curve, known as probability) of the observations plotted against expected CDF (cumulative area under the normal curve, known as probability)

The normal quantile plot does not depict sample data from a population with a normal distribution because the points exhibit some systematic pattern that is not a straight-line pattern.

Thus,  the points exhibit some systematic pattern that is not a straight-line pattern.

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Answer:

Step-by-step explanation:

3.25+.65x=6

-3.25

2.75=.65x

divide by .65

4.23=x

so marco can get 4 toppings

I thnk this should be right

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

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

2 watermelon, 3 lemon-lime, and 5 grape gumballs

Rewrite the items according to their frequencies

So, we have the following representation

watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

The above represents the sample space

Hence, the sample space is (a)

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The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

The difference between the distance travelled by any point on the record and it's label is; 27.57cm.

According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;

Difference = π(17.78 - 9)

Difference = (22/7) × 8.78

Difference = 27.57cm.

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Answer:

{xcR} (x is all real numbers) and {y\(\leq\)2\(\sqrt{\frac{y-1}{2} }\)+1}

Step-by-step explanation:

1st: Find x by squaring both sides, subtracting 1 from both sides, and dividing by 2 from both sides to get x= \(\sqrt{\frac{y-1}{2} }\)

2nd: Plug in x for y=\(2x^{2}\)+1 which equals y=2(\(\sqrt{\frac{y-1}{2} }\))+1

3rd: This gives you the range (y) which is {y\(\leq\)2\(\sqrt{\frac{y-1}{2} }\)+1}

4th: domain is all real numbers

I hope this helped because this took me 30 minutes to do. I had to pull out my algebra math book to check I did it right. I hope I was right!

Answer:

x=0

Step-by-step explanation:

Distribute -4

-8x - 24 = -24

Add 24 to both sides

-8x = 0

x=0

Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4(2x+6)=−24

(−4)(2x)+(−4)(6)=−24(Distribute)

−8x+−24=−24

−8x−24=−24

Step 2: Add 24 to both sides.

−8x−24+24=−24+24

−8x=0

Step 3: Divide both sides by -8.

−8x

−8

=

0

−8

x=0

Answer:

x=0

Answer:

Step-by-step explanation:

x = 8