The mean age of several boys in a class is 12. The total is 156. How
many boys are there?

The pressure in kilopascal if the pressure is equal to 380 mmHg is 50.6625 kilopascal.

Pressure can be described as the physical force that can be exerted on  an object  when it come in contact with it, this can be measured in different units such as the  kilopascal.

It should be noted that

1 millimeter mercury (mmHg) = 0.13332 kilopascal (kPa) and this can be used to calculate the value of pressure in kilopasca with the given values as :

1mmHg = 0.13332kPa.

380 mmHg = X

Then if we cross multiply we have ,

X = (0.13332kPa * 380 mmHg )/ 1mmHg

= 50.6625 kilopascal.

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Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is \(2^{-4}\)

Answer:

Answer:

A) 44%

Step-by-step explanation:

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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The required total number of grams is 13.5 gram.

From figure we have,

The masses of 4 samples are the masses are 1.5 gram, 3.5 gram , 5 gram and 5 gram respectively.

To calculate the total number of grams of salt in the 3 samples with the most mass,

Add the masses of the three largest samples.

In this case,

The three largest samples are 3.5 grams, 5 grams, and 5 grams.

We have: 3.5 grams + 5 grams + 5 grams = 13.5 grams

Therefore, the total number of grams of salt in the 3 samples with the most mass is 13.5 grams.

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Answer: b= - -log10(7)+3/2

Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)

so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)

Simplify -2b= -log10(7)+3

Divide both sides by -2  -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!

Answer:

x=3

Step-by-step explanation:

Simplifying

9x + -4 = 3x + 14

Reorder the terms:

-4 + 9x = 3x + 14

Reorder the terms:

-4 + 9x = 14 + 3x

Solving

-4 + 9x = 14 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

-4 + 9x + -3x = 14 + 3x + -3x

Combine like terms: 9x + -3x = 6x

-4 + 6x = 14 + 3x + -3x

Combine like terms: 3x + -3x = 0

-4 + 6x = 14 + 0

-4 + 6x = 14

Add '4' to each side of the equation.

-4 + 4 + 6x = 14 + 4

Combine like terms: -4 + 4 = 0

0 + 6x = 14 + 4

6x = 14 + 4

Combine like terms: 14 + 4 = 18

6x = 18

Divide each side by '6'.

x = 3

Simplifying

x = 3

Answer:

Explanation:

Write your equation

Subtract 9x from both sides

3x + 14 − 9x = 9x − 4 − 9x

−6x + 14 = −4

Subtract 14 from both sides

−6x + 14 − 14 = −4 − 14

−6x = −18

Divide both sides by -6

−6x / -6 = −18 / -6

[ zyxx ]

Answer:

B) \(\frac{-5}{4}\)

Step-by-step explanation:

Take any two points

(x₁ , y₁) = ( -4 , 0)  & (x₂ , y₂) = (0 , -5)

\(slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

        \(=\frac{-5-0}{0-[-4]}\\\\=\frac{-5}{0+4}\\\\=\frac{-5}{4}\)

Answer:

330 degrees

Step-by-step explanation:

look at 4th quadrant of unit circle

(cos,sin)

(sqrt3/2,-1/2)=330

Answer:

10 Cups of Milk

Step-by-step explanation:

2/3  cup of milk --->10 cookies

  x  cup of milk --->150 cookies

x=((2/3)*150)/10=(2/3)*15=10 cups of milk

\(\huge\fbox{Answer ☘}\)

Volume of water displaced = Volume of shape

‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎\(\bold{⇢ ( \:44 \:- \:40\: ) \:mL}\\\bold{⇢ 4 \:mL}\)

Weight = 28 g

\(\bold\blue{density = \frac{mass}{volume}} \\ \\ \pink{ ⇢ \cancel \frac{28}{4} }\\ \\ \pink{⇢ 7 \: g \: ml {}^{ - 1}} \)

hope helpful ~

Answer:

The algebraic expression for "Subtract 5x−2 from x−1" is:

(x - 1) - (5x - 2)

Simplifying this expression:

x - 1 - 5x + 2

= -4x + 1

Therefore, the simplified algebraic expression is -4x + 1.

The zero(s) of the function is 6 if  the function is f(x)=x³ - 4.9x² +6.79x-2.871.

The Newton's method is use to estimate the zeros is valuable, in spite of the way that it probably won't work. The central issue here is find digression lines, and applying that equation over and over till it draws nearer to the roots.

It fits for any polynomial condition despite the fact that it is significantly more utilized, to more serious level polynomial.

*For the function given, f(x)=x³ - 4.9x² +6.79x-2.871, starting from the root is a whole number, 6, in couple of preliminaries we'll find the root, every one of them greater than 0.001 so how about we supplant the

1) Really look at chart beneath.

2) Investigating, f(x)=x³ - 4.9x² +6.79x-2.871. we can see that the root is somewhere in the range of x=5 and x=7, we definitely know is - 6.

So,we check for x=7

Plugging in the formula,we get

=>\(X_n_+_1\) = \(x_n\) - f(x)/ f'(x)

=> x₂ =7- (x³ - 4.9x² +6.79x-2.871) / (3x² -9.8x +6.79)

=>x₂=7- (-7+6) / -1

=>x₂ = 7-1

=>x₂=6

Similarly, if we find x₃ then its value will be also 6.

In the given function, the root is a whole number, every one of the approximations were number numbers and bigger than 0.001.Then again, in the event that the function had nonsensical roots, we could undoubtedly show results lesser than 0.001.

Hence,zero(s) of the given function is 6.

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L as a function of x is written as:

L = √(5x² - 3x + 9/16)

The distance between a point (x, y) and the origin is given by the formula:

distance = √(x² + y²)

Here we know that the distance must be L, the points must be on the line:

8x + 4y = 3

Isolate y in that equation to get:

4y = 3 - 8x

y = 3/4 - 2x

Then the function is:

L =  √(x² + y²)

L =  √(x² + (3/4 - 2x)²)

L = √(x² + 9/16 + 4x² - 3x)

L = √(5x² - 3x + 9/16)

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Answer:

22 Hours

Step-by-step explanation:

26400/20 = 1320m

1320m = 22h

22 Hours

Answer:

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

Step-by-step explanation:

We do completing the square as follows:

1. Put all terms with variable on one side and the constants on the other side.

5x^2 - 3x = 25

2. Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other  side we add 9/20.

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

4. We simplify as follows:

5(x^2 - 3x/5 + 9/100) = 25 + 9/20

5(x - 3/10)^2 = 509/20

(x - 3/10)^2 = 509/100

x1 = √(509) /100 + 3/10

x2  = -√(509) /100 + 3/10

Answer:

y=5/3x-79/7

Step-by-step explanation:

(-4, -7)

x1    y1

(8,-13)

x2   y2

y2-y1/x2-x1=

13+7/8+4= 20/12= 10/6= 5/3

y=5/3x+b

-7=5/3(-4)+b

The equation of a line passing through the points (-4,-7) and (8,-13) will be x + 2y + 18 = 0.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The given points are (-4,-7) and (8,-13).

Then the equation of a line passing through the points (-4,-7) and (8,-13) will be

\(\begin{aligned} y + 13 &= \dfrac{-13+7}{8+4} (x - 8)\\\\y + 13 &= - \dfrac{1}{2} (x - 8)\\\\2y + 26 &= -x + 8\\\\x + 2y + 18 &= 0 \end{aligned}\)

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer

8

Step-by-step explanation:

Ratio: 40 : 60

Total amount - $20

40/100 x 20

= 8  (ANS)

i hope my answer is correct if not i apologize.

Answer: This was a bit hard to understand, x times the 5th root of x

Step-by-step explanation:

When you multiply square roots of the same root and inside value, they essentially get rid of the square roots. So the first two terms boil down to just x. Then multiply x by the 5th root of x to get:

\(x\sqrt[5]{x}\)

Answer:

\(x\)

Step-by-step explanation:

Apply exponent rules.

\(\sqrt{x} =x^\frac{1}{2}\\\:a^b\times \:a^c=a^{b+c}\)

\(\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x}\)

\(x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}\)

\(x^1\)

The outlier of the graph is

An outlier is an isolated data point that significantly differs from the entirety of the points within a dataset. It is an observation that resides an exceptional distance away compared to other values in a random sample from a population.

Outliers can be identified employing various statistical techniques, like graphical methods (for instance, box plots, scatterplots) and numerical procedures (e.g., Z-score, IQR method).

The problem used a scatter plot plot to show that the outlier is (5, 1)

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

It is proven that the other nth roots of z can be found by multiplying the initial one by the nth roots of unity.

A complex number satisfying the equation \(z^{n-1} = 0\) is known as the nth root of unity. There are about n nth roots of a unit, according to the fundamental theorem of algebra. We know that,\(1=e^{2\pi i}\). Then, the nth root is written as \(\omega=e^{2\pi i/n}\).

The integer of powers of this root between 0 and n-1 provides the other nth roots. Then, the roots are \(1, \omega, \omega^2 ,\cdots \cdots, \omega^{(n-1)}\). Now, factorize the equation \(z^{(n-1)} = 0\) we get the required identity as, \(z^{(n-1)} = (z- 1)(z^{(n-1)}+ z^{(n-2)} + \cdots \cdots+ z + 1) = 0\).  

This indicates that the equation \(1+\omega+ \omega^2+\cdots \cdots+ \omega^{(n-1)}\) is true for all nth roots of unity other than 1.

Roots of unity also have the great quality of being periodic, which results from the fact that n = 1. It is equal to a power of that power mod n if the power is bigger than n.

When ω is a third root of unity, \(\omega^5 + \omega^4 + 1 = \omega^2 + \omega + 1 = 0\).

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The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

C

Step-by-step explanation:

The mean will be higher than the median and the mode. The correct option is C.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated by the ratio of the sum of all the data and the total number of the data.

Given the effect of fertilizer on plant growth no fertilizer height of plants (cm) 24.1, 25.9, 25.4,24.1, 35.6, 30.5, 32.1, 40.6, 30.5, and 33.8.

The mean will be calculated as follows:-

Mean = ( 24.1 + 25.9 + 25.4 + 24.1 + 35.6 + 30.5 6 +32.1 + 40.6 + 30.5 + 33.8 ) / 10

Mean = 274.6 / 10

Mean = 27.6

Therefore, the mean will be higher than the median and the mode. The correct option is C.

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Answer:

44 years old

Step-by-step explanation:

Let the age of Jasper be j years old now.

Now:

Jasper➣ j

Simon ➣ j/2

12 years ago:

Jasper➣ j -12

Simon➣ j/2 -12

Given that Simon's age=⅕(Jasper's age),

j/2 -12= ⅕(j -12)

Multiply by 5 on both sides,

2.5j -60= j -12

2.5j -j= 60 -12

Simplify:

1.5j= 48

÷1.5 on both sides:

j= 48 ÷1.5

Simplify:

j= 32

12 years time:

Jasper➣ j +12

Thus, Jasper's age

= 32 +12

= 44

Answer:

44 years

Step-by-step explanation:

Let Jasper's and Simon's ages be represented by J and S respectively.

From the first statement, J = 2S

From the second statement, (S - 12) = 1/5(J - 12)

J = 2S

S = J/2

S - 12 = 1/5(J - 12)

J/2 - 12 = J/5 - 12/5

Multiply each term by 10

5J - 120 = 2J - 24

5J - 2J = -24 + 120

3J = 96

J = 96/3 = 32

Jasper's present age is 32 years

In 12 years' time, Jasper's age will be 32 + 12 = 44 years

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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