Please help me with these square root problems, Part 1. Please show and check the work.

[tex]1. \sqrt{2x-5} - \sqrt{x+6} =0\\\\2. \sqrt{2x-5} + \sqrt{x+6}=0\\ \\3. \sqrt{x-5} - \sqrt{x+6}= 2\\ \\4. \sqrt{2x-5} -\sqrt{x+6}=2[/tex]

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal([tex]\mu=460,\sigma^{2} =40^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

                               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 460 seconds

            [tex]\sigma[/tex] = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

       P(X > x) = 0.10   {where x is the required time which boy need to beat}

       P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-460}{40}[/tex] ) = 0.10

        P(Z > [tex]\frac{x-460}{40}[/tex] ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

                       [tex]\frac{x-460}{40} =1.2816[/tex]

                         [tex]{x-460}{} =1.2816\times 40[/tex]

                          [tex]x[/tex] = 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Answer: The required confidence interval is (56.1,66.9).

Step-by-step explanation:

Since we have given that

53.1, 60.2, 60.6, 62.1, 64.4, 68.6

[tex]\bar{x}=\dfrac{53.1+60.2+60.6+62.1+64.4+68.6}{6}=\dfrac{369}{6}=61.5[/tex]

n = 6

Margin of error = 5.4

At 95% level of confidence, z = 1.96

So, the confidence interval would be

[tex]\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)[/tex]

Hence, the required confidence interval is (56.1,66.9).

Hey there,

The question given is as follows:

When we add polynomials we add like terms (e.x. we add 3x² with -x²) and combine the two to make one polynomial. When we add the two polynomials given above:

So our answer to the problem would be 2x² - 6x.

Hope I helped,

Amna

Answer:

− 21 x + 28 ,  7 ,  3 x − 4 ,  − 7 ( 3 x − 4 ) ,  − 7 , 3 x + 4 ,  − ( 21 x − 4 )

Step-by-step explanation:

too much to explain sorry

Hope this helped!

The factor of the expression -21x + 28 is equal to  -7(3x – 4). The correct option is B.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.

Given expression is -21x + 28, The value of the expression will be calculated as,

E = -21x + 28

Take -7 common from the whole expression,

E = -21x + 28

E = -7 ( 3x - 4 )

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Answer:

let water evaporated be x ml

...

acid 8% ------60 ml

...

final quantity = 10% ----(60-x)

..

60*8 = 10(60-x)

480=600-10x

10x=600-480

10x= 120

/10

x=12 ml should be evaporated.

Step-by-step explanation:

Answer:

Wavelength

Step-by-step explanation:

The picture below is an example of a wavelength which is very similar.

Step-by-step explanation:

The closest approximation to the number of seconds in a year is [tex]3\times10^7[/tex], which is option B.

There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. So, to find the number of seconds in a day, you would multiply these values together:

[tex]\[60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400 \text{ seconds/day}.\][/tex]

In a year, there are typically 365 days. So, to find the total number of seconds in a year, you would multiply the number of seconds in a day by the number of days in a year:

[tex]\[86,400 \text{ seconds/day} \times 365 \text{ days/year} = 31,536,000 \text{ seconds/year}.\][/tex]

Since [tex]\(31,536,000\)[/tex] is closest to [tex]\(3 \times 10^7\)[/tex], the best approximation among the given options is B) [tex]\(3 \times 10^7\).[/tex]

Complete Question:

There are about 31,500,000 seconds in a year ?

Choose the best approximation of the number of seconds in a year

A) 3x[tex]10^6[/tex]

B) [tex]\(3 \times 10^7\).[/tex]

Answer:

0.3. and 2

Step-by-step explanation:

For this equation: a=1, b=0.3333333333333333, c=0.8333333333333334

1x2+0.333333x+0.833333=0

Step 1: Use quadratic formula with a=1, b=0.3333333333333333, c=0.8333333333333334.

x=

−b±√b2−4ac

2a

x=

−(0.333333)±√(0.333333)2−4(1)(0.833333)

2(1)

x=

−0.3333333333333333±√−3.222222

2

i think this is right :)

Answer:

2/1

then simplify it

= 1/6

The probability of selecting the letter 'N' from the word EXAMINATIONS is 1/6 or approximately 16.67%.

The word EXAMINATIONS consists of 12 letters, and the letter 'N' appears twice in this word. The probability of selecting an 'N' from the word is calculated by dividing the number of occurrences of 'N' by the total number of letters in the word. Therefore, the probability is 2/12, which simplifies to 1/6.

To express this mathematically, the probability P of selecting 'N' from EXAMINATIONS is given by P = n/N, where n is the number of times the event 'selecting N' occurs, and N is the total number of possible outcomes (total letters in the word).

So, P = 2/12 = 1/6. Therefore, the probability of selecting 'N' is approximately 0.1667, or 16.67%.

Answer:

The mean is all the numbers added together divided by the number of numbers. Greater the numbers the greater the mean. Since the goal of the game is to have as few centimeters away as possible the lowest number (107 or Robin) is winning

Step-by-step explanation:

Answer:

Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.

Step-by-step explanation:

this is the answer on the curst platform

An exponential function is a mathematical concept characterized by a constant base elevated by a variable exponent. The rate of growth or decay of the function is proportional to its current value, leading to exponential growth or decay.

An exponential function is a mathematical concept where a constant base is elevated by a variable exponent. The base could be any positive value different from one. A simple example of this type of function is f(x) = 2^x, where 2 is the constant base and x is the variable exponent.

The unique property of an exponential function is that the rate of growth or decay is proportionate to its current value. This means, as the variable x increases, the function value increases exponentially when the base is greater than one - thus showing exponential growth. Conversely, if the base is less than one but greater than zero, the function value decreases as x increases - thus representing exponential decay.

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Answer:

58.077 cubic cm

Step-by-step explanation:

Given that:

As we know that, the volume of a conical perfume bottle is as following:

V = (1/3) * π * r² * h

So perfume can the bottle hold is:

V = (1/3) * 3.14 * 3.4² * 4.8 = 58.077 cubic cm

Hope it will find you well

Answer:

[tex]V \approx 58.107\,cm^{3}[/tex]

Step-by-step explanation:

The volume of a cone is:

[tex]V = \frac{1}{3}\pi\cdot r^{2}\cdot h[/tex]

Where:

[tex]r[/tex] - Radius, in centimeters.

[tex]h[/tex] - Height, in centimeters.

The volume of liquid that bottle can hold is:

[tex]V = \frac{1}{3}\pi \cdot (3.4\,in)^{2}\cdot (4.8\,cm)[/tex]

[tex]V \approx 58.107\,cm^{3}[/tex]

Answer:

The top angle is 60 degrees

Step-by-step explanation:

Triangle angle sum equals to 180. 90 plus 30 is 120 and when you subtract that from 180 tada! 60

Answer:

(6x² + 4x +1) - (4x + 20) = 6x² + 21

Step-by-step explanation:

(6x² + 4x +1) - (4x + 20)

= 6x² + 4x -4x + 1 + 20

= 6x² + 21

Answer:

Pyramid

Step-by-step explanation:

Answer:

Therefore a= 90°,b=54°, x=54°, y= 162°

Step-by-step explanation:

a=90°

a:b=5:3

5+3= 8

5/8 x A = 90

A is the sum of the angles of a and b divided in the ratio 5:3

5A/8 = 90

cross multiply

5A= 90 X8 = 720

5A=720

A= 720/5= 144°

b= 3/8 x 144 = 3x144/8 = 432/8 = 54

a= 90

b= 54

x:y is in the ratio of 1:3

the Sum of angles in a Quadrilateral is 360°

if the sum of a and b is 144°

then the reamining angles is 360-144= 216°

then x:y=1:3

1+3=4

x= 1/4 x 216= 54°

y= 3/4 x 216= 162°

Therefore a= 90°,b=54°, x=54°, y= 162°

we can see that b = x = 54°

Answer:

The width is 4 feet

Step-by-step explanation:

Yes, I might be able to answer it! Hello there!

In this question, we are asked to calculate the height of a pool which has a shape of right rectangular prism.

The key to solving this problem is simply by knowing the formula for the volume of a right rectangular prism.

Mathematically the volume V is w * h * l where w , h and l are the width, height and length respectively.

Now let’s input these values and get what the height of the pool is.

It would be easier if you had the measurements are in decimals;

137 1/2 becomes 137.5

6 1/4 becomes 6.25

5 1/2 becomes 5.5

kindly note the fraction 1/2 is 0.5 in decimals while the fraction 1/4 is 0.25 in decimals

So now let’s compute the height;

137.5 = w * 6.25 * 5.5

w = 137.5/(6.25 * 5.5)

w = 137.5/(34.375)

w = 4 feet

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

So we know that triangle ABC and QRS are similar.

There is a theorem that states that corresponding sides of similar triangles are proportional.

This means that we can set up a proportion to find the missing side of the triangle.

3/7=6/n

Cross multiply.

3*n=7*6

3n=42

Divide both sides by 3.

n=14

[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) = \\ = {x}^{2} {y}^{2} {z}^{2} - {x}^{3} {y}^{3} - {x}^{4} {z}^{2} + {x}^{5} y - {y}^{3} {z}^{3} + \\ + x {y}^{4} z + xy {z}^{3} - {x}^{2} {y}^{2} z[/tex]

I don't know if it was necessary to open the brackets, but I think you can write it like this:

[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) \\ [/tex]

Answer:

A) (2+x)/(4+x) × 100 = 75

B) 4

Step-by-step explanation:

2 out of 4

(2+x) out of (4+x)

(2+x)/(4+x) × 100 = 75

(2+x)/(4+x) = 3/4

8 + 4x = 12 + 3x

x = 4

Answer:

y-7= -2 (x-4)

Step-by-step explanation:

We can use the point slope formula, since we have a point, and a slope

[tex]y-y_{1} =m(x-x_{1})[/tex]

m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point

We know -2 is the slope, 7 is the y coordinate, and 4 is the x coordinate, so we can substitute them in

y-7= -2 (x-4)

Since we don't need to solve, this is the answer. The first bracket is -2, and the second is 4

Point-slope form:  y - y₁ = m(x - x₁)

(m is the slope, (x₁, y₁) is the point you are given that's on the line)

You know:

m = -2

(x₁, y₁) = (4, 7)         So plug it into the equation

y - y₁ = m(x - x₁)  

y - 7 = -2(x - 4)

[so the first bracket is -2, the second bracket is 4]

Answer:

8/5

Step-by-step explanation:

I'd write the following:

2       1

---- ÷ ----

 5      4

To divide by a fraction (such as 1/4), invert the divisor fraction and multiply instead:

2       4

---- · ---- = 8/5

 5      1

i believe the answer is independant.

if i'm wrong, please tell me so i can fix my mistake =)

Final answer:

The probability of a spinner, with equal chances of landing on any of its six regions, landing on Region 1 first and then on Region 3 in a second spin is 1/36, reflecting independent events.

Explanation:

The question concerns the concept of dependent probability, which involves calculating the likelihood of a sequence of events where the outcome of one event affects the outcome of another.

Since the spinner has an equal chance of landing on each of its six numbered regions, the probability of the first spin landing in region one is 1/6.

However, the second spin is independent of the first, making the probability of landing in region three also 1/6. Since these are independent events, the combined probability of both events happening in sequence is the product of their probabilities, which is 1/6 x 1/6 = 1/36.

Answer: 0.25

Step-by-step explanation:

0.75-0.5= 0.25

Answer:

d= 0.75-0.5

d= 0.25

Step-by-step explanation:

so firstly you subtract 0.5 from both sides

d= 0.75-0.5

d=0.25

the answers are c and d

Answer:

No

Step-by-step explanation:

If the ratios of the corresponding sides are equal then they would be the sides of 2 similar triangles.

Calculate the ratio of corresponding sides.

[tex]\frac{6}{1.5}[/tex] = 4

[tex]\frac{10}{2.5}[/tex] = 4

[tex]\frac{12}{3.5}[/tex] ≠ 4

Thus the sides are not the corresponding sides of similar triangles.

Answer:

Step-by-step explanation:

A "term" is a (signed) number, variable, or product of numbers and variables, separated from other terms by + or - signs. That is, it is the largest such product that includes any given number or variable.

A "factor" is a piece of a product. It is multiplied by other factors to form a product. It can be a (signed) number or variable or some expression.

One way to think of it is that terms are delimited (separated) by + or - signs. Factors are delimited by × or / signs.

__

The terms of 4x -10 are "4x" and "-10".

_____

The sign typically goes with the term. That is, an expression is a sum of terms.

Answer:

The expected number of times that Noah wears either boots or loafers is 99.

Step-by-step explanation:

Given:-

- Noah has 8 different pairs of shoes to wear, Out of 8 pairs:

                    two pairs of boots

                    one pair of loafers

Find:-

For how many days of the next 264 is it expected that Noah will wear either boots or​ loafers?

Solution:-

- Denote an Event (A) that Noah selects a pair of boots.

- Denote an Event (B) that Noah selects a pair of loafers.

- The probability of each event is to be determined:

                p ( A ) = Pair of boots / Total pair of shoes

                p ( A ) = 2 / 8

                p ( A ) = 1/4

                p ( B ) = Pair of loafers / Total pair of shoes

                p ( B ) = 1 / 8

- The probability that Noah selects a pair of boot or loafers is independent from each other:

               p ( A U B ) = P (A) + P (B)

               p ( A U B ) = 0.25 + 0.125

                                 = 0.375

- The expected number of days out n = 264 days do we expect Noah to wear either boots or loafers.

- The number of days (trials) n = 264 days

- The probability of success = p ( A U B ) = 0.375

- The expected value = n*p

                                   = 264*0.375

                                   = 99 days

Big guy up there done wrote a whole pg. The answer is 99 days. Have a good day.

Pls mark Brainliest.

Answer:

If we write the final answer with negative exponents, then it will be:

(x^-7)(y^-4)

If we write this as a fraction, it will be:

1/(x^7)(y^4)

Step-by-step explanation:

x^-3 is equivalent to 1/x^3. We can put this in the denominator expression and calculate the product:

[tex]\frac{y^{2} }{(x^4)(x^3)(y^6)}[/tex]    This simplifies into:

[tex]\frac{y^{2} }{(x^7)(y^6)}[/tex]    after the denominator simplifies.

If we write the final answer with negative exponents, then it will be:

(x^-7)(y^-4)

If we write this as a fraction, it will be:

1/(x^7)(y^4)

The simplified form of [tex]\(\frac{{x^{-3} \cdot y^2}}{{x^4 \cdot y^6}}\)[/tex] is [tex]\(\frac{1}{{x^7 \cdot y^4}}\)[/tex], with all exponents as positive values in the denominator.

To simplify the expression [tex]\(\frac{{x^{-3} \cdot y^2}}{{x^4 \cdot y^6}}\)[/tex], we can apply the rules of exponents. First, we subtract the exponent in the denominator from the exponent in the numerator for each variable (x and y).

For x, we have [tex]\(x^{-3 - 4} = x^{-7}\)[/tex], and for y, we have [tex]\(y^{2 - 6} = y^{-4}\)[/tex].

So, the expression simplifies to [tex]\(x^{-7} \cdot y^{-4}\).[/tex]

To express this in a more conventional form, we can move the negative exponents to the denominator, resulting in [tex]\(\frac{1}{{x^7 \cdot y^4}}\).[/tex]

In this simplified form, the expression has all positive exponents and represents the same mathematical relationship as the original expression but in a more compact and manageable format.

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