The cost of a book is twice that of a magazine.
1 book and 4 magazines cost £24.
How much does a book cost?

There are total 378 students in seventh grade.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the standard operations on numbers—addition, subtraction, multiplication, division, operation, and extraction of roots.

Main body:

The total number of students that are in the seventh grade are 378 students.

The number of students that had already bought tickets will be:

= 158 - 32 = 126 students.

Therefore, based on the information given, the equation to calculate the total students will be:

= (1/3 × x) = 126

x = 3 × 126

x = 378

Therefore, there are 378 students.

Read related arithmetic link on:

https://brainly.com/question/13378503

#SPJ1

The midpoint of the line AN is (3(1/2) , -1).

What is midpoint?

Midpoint of the line(x , y) = (x₁ + x₂ / 2) , (y₁ + y₂ / 2)

x₁  = 2, x₂ = 5

y₁ = -3, y₂ = 1

So,

Midpoint of the line(x , y) = (2+5/2) , ((-3)+1 / 2)

= (7/2 , -2/2)

= (7/2, -1)

We can write 7/2 as 3(1/2)

Hence, the midpoint of the line AN is (3(1/2) , -1)

To know more about midpoint check the below link:

https://brainly.com/question/5566419

#SPJ1

The measure of the angle PQR is 90° as Segment QR is tangent to the circle with center P. Hence, option C is the correct answer.

A tangent draw to a circle always makes a right angle with the radius of the circle. In simple words, we can say that the radius of the circle and the tangent segment are always perpendicular to each other.

Now we have, PQ as the radius of the circle, and segment QR is tangent to the circle with center P.

Thus, segment PQ is perpendicular to segment QR, so the angle PQR is equal to 90°.

Read more about Tangents of the circle:

brainly.com/question/4470346

#SPJ4

Answer:

the range of possible weights for the letters is 98-105 ounces.

Step-by-step explanation:

To determine whether 101 ounces is a reasonable estimate for the weight of 25 letters that each weigh between 3.92 ounces and 4.2 ounces, we need to calculate the range of possible weights for the letters.

The minimum weight for the letters is 25 * 3.92 ounces = 98 ounces. The maximum weight for the letters is 25 * 4.2 ounces = 105 ounces. Therefore, the range of possible weights for the letters is 98-105 ounces.

Since 101 ounces falls within this range, it is a reasonable estimate for the weight of the letters.

It will take about 39 years for a principal of $4600 to grow to $29900 continuously compounded

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula to calculate compound interest is given as

A = P(1 + r/n)^nt

A = Pe^rt (Continuously compounded)

Let's substitute the values into the formula and solve

29900 = 4600e^(0.048 * t)

t = 39 years

The time it takes to compound the principal to $29900 is approximately 39 years

Learn more on compound interest here;

https://brainly.com/question/25297315

#SPJ1

The pk[tex]_b[/tex] of given acid conjugate base is 9.74 if k[tex]_a[/tex] of the same acid is equal to 5.57×10⁻⁵

The Bronsted-Lowry corrosive base hypothesis incorporates the ideas of form acids and form bases. At the point when a corrosive separates into its particles in water, it loses a hydrogen particle. The species that is shaped is the corrosive's form base.

A more broad definition is that a form base is the base part, X-, of a couple of mixtures that change into one another by acquiring or losing a proton. The form base can acquire or retain a proton in a synthetic response. The form corrosive gives the proton or hydrogen in the response.

In a corrosive base response, the substance response is:

Corrosive + Base ⇌ Form Base + Form Corrosive

We know very well that from equilibrium state theories that  pk[tex]_b[/tex] +pk[tex]_a[/tex] =14

where  pk[tex]_a[/tex] = - log( k[tex]_a[/tex] )

So, we have k[tex]_a[/tex] =5.57×10⁻⁵

Taking log of  k[tex]_a[/tex] ,we get

=>pk[tex]_a[/tex]= -log(5.57×10⁻⁵)

Using properties of logarithm, log(a × b)=log(a)+log(b)

=>pk[tex]_a[/tex]= -log(5.57) -log(10⁻⁵)

=>pk[tex]_a[/tex]= -0.745 +5

=>pk[tex]_a[/tex]=4.25

Therefore, from above written formula, we get

=>4.25+pk[tex]_b[/tex]=14

=>pk[tex]_b[/tex]=14-4.25

=>pk[tex]_b[/tex]=9.74

Hence, pk[tex]_b[/tex] value is 9.74

To know  more about conjugate base, visit here:

https://brainly.com/question/12883745

#SPJ4

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

Answer:  2.39

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

Given:  [tex]\textsf{185/100 + 50\% + 4\%}[/tex]

Find:  [tex]\textsf{Convert to simplified decimal}[/tex]

Solution: In order combine the numbers together we must first convert all of them to a fraction.  The first number is already in fraction form, but the other ones are in a percent form.  What a percent value means is just a number out of 100 which we can use to change 50% to 50/100 and 4% to 4/100.

Now we have 185/100 + 50/100 + 4/100 which we can combine together to 239/100 to which we can use a calculator and figure out that the answer in decimal form would be 2.39

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{185}{100} + 50\% + 4\%}\\\\\mathsf{= \dfrac{185}{100} + \dfrac{50}{100} + \dfrac{4}{100}}\\\\\mathsf{= \dfrac{185\div 5}{100\div 5} + \dfrac{50\div50}{100\div50} + \dfrac{4\div4}{100\div4}}\\\\\mathsf{= \dfrac{37}{20} + \dfrac{1}{2} + \dfrac{1}{25}}\\\\\mathsf{= 1\dfrac{17}{20} + \dfrac{1}{2} + \dfrac{1}{25}}\\\\\mathsf{= \dfrac{47}{20} + \dfrac{1}{25}}\\\\\mathsf{= 2 \dfrac{7}{20} + \dfrac{1}{25}}\\\\\mathsf{= 2\dfrac{39}{100}}\\\\\mathsf{= \dfrac{239}{100}}\\\\\mathsf{\approx 2.39}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{239}{100}\ or\ 2.39}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Graph the inequality by finding the boundary line, then shading the appropriate area. y < 1 /2 x − 2

Hope this helps!

Answer:

The ordered pair that satisfies the system of equations is (7, -1)

Step-by-step explanation:

⭐What is a system of equations?

When we solve for an ordered pair that satisfies the system of equations, we are finding at what point do the equations intersect.

⭐How can we solve a system of equations?

For this problem, I find elimination to be the easiest. I will demonstrate how to use elimination to solve this system of equations.

⭐What is the elimination method?

We have the system: [tex]{ x+7y = 0\\\\2x - 8y = 22[/tex]. Let's eliminate the variable "x".

To do so, multiply the first equation by -2, then add both equations.

[tex]-2(x+7y = 0)\\-2x -14y = 0[/tex]

Now add this new equation with the second equation. This eliminates the x variable.

[tex]-2x - 14y = 0 \\+2x -8y = 22\\\\-22y = 22\\y = -1[/tex]

∴ y = -1

Next, we need to solve for the x variable. To do so, substitute the y variable into one of the equations we added and solve for x.

I will substitute y into the equation [tex]2x - 8y = 22[/tex], but you can also substitute it into [tex]-2x-14y = 0[/tex]

[tex]2x - 8y = 22[/tex]

[tex]2x-8(-1) = 22[/tex]

[tex]2x + 8 = 22[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

∴ The ordered pair that satisfies the system of equations is (7, -1)

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

3 years

Step-by-step explanation:

L=Lawson. TL=total inches for Lawson's tree

E=Ezra. TE=total inches for Ezra's tree

x=number of years

L ==> TL=3x+14

E ==> TE=5x+8

Now, try to find when the heights are equal by setting both equations equal to each other:

TL = TE

3x+14 = 5x+8

3x-3x+14 = 5x-3x+8  ==> subtract 3x on both sides to isolate x to one side

14 = 2x + 8

14 - 8 = 2x + 8 - 8  ==> subtract 8 on both sides to isolate x

6 = 2x

x = 6/2 ==> simplify

x = 3 years

Answer: He would have $1,500 alone from making $150 each year, and the total would be $3,500.

Step-by-step explanation: To find how much money he makes in 10 years (not including the $2,000) we would multiply 150 by 10 to get 1500.

Now, we need to add 2000 + 1500, and we get 3,500.

I hope this helps!

Answer: p = 3

Step-by-step explanation:

7−4p−(−5)

7-4p + 5

Because negative one times negative five equal positive 5

12 - 4p

To solve further

-4p = -12

p = 3

Answer:

1/16

Step-by-step explanation:

Rational Exponents can be rewritten as Radicals:

[tex](\frac{1}{8})^{\frac{4}{3}}=\sqrt[3]{\frac{1}{8}}^{4}[/tex]

Take the cube root of 1/8 = 1/2.

Raise (1/2) to the 4th power

Step-by-step explanation:

the numerator (top part) of a fractional exponent means "to the power of ...".

the denominator (bottom part) of a fractional exponent means "the ...th root".

so,

(1/8)^(4/3) means the cubic root of 1/8 to the power of 4.

these 2 operations can be done in any sequence.

it is the same if we first put 1/8 to the power of 4 and then get the cubic root, or if we first get the cubic root of 1/8 and then put that result to the power of 4.

to keep the numbers small, I prefer here to start with the cubic root :

cubic root (8) = 2, because 2³ = 8.

and so, cubic root (1/8) = 1/2

(1/2)⁴ = 1/16

that's it.

(1/8)^(4/3) = 1/16

The value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.

A polygon can be defined as a flat or plane, two-dimensional closed object circumscribed with straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

Given:

m ∠ a = (2z + 54)°

The number of sides = 5,

Calculate the value of the sum of the interior angle by the formula given below,

[tex]S = 180(n - 2)[/tex]

S = 180 (5-2)

S = 180 × 3

S = 540°

Calculate the value of a as shown below,

[tex]a = S/5[/tex]

a  = 540 / 5

a = 108

108 = 2z + 54

2z = 108 - 54

z = 54 / 2 = 27

Therefore, the value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.

To know more about polygons:

https://brainly.com/question/24464711

#SPJ1

Answer:

slope of original line; m = -3/-4

                                         =3/4

slope of parallel line = 3/4

slope of perpendicular line = m1*m2=-1

                                               =(3/4)*m2=-1

                                               =-4/3

equation passes through point (4,-3) is : 3x + 4y = -12

The value of y will be 104 using direct proportion property between x and y.

What is direct proportion ?

Direct proportion is the relation between two quantities where ratio of these two is equal to a constant.

It is represented by proportional symbol , "∝"

Let's consider constant is m.

For given que,

As y and x are in direct proportion,

y ∝ x

or x ∝ y

eliminating the proportionality,

y = x*m where m is any constant.

y/x = m

Given when y = 64 , then x = 8

So, m = 64/8

          = 8

And when x = 13 then y = ?

y/13 = 8

y = 13*8

  = 104

Learn more about direct proportion using link :

https://brainly.com/question/1266676

#SPJ1

32% of students does not plan to go to graduate school.

We have given that,

total number of college seniors is 400.

The percentage of a value of x from N total is given as,

percentage of x = [tex]\frac{x}{N}[/tex] × 100%

Therefore

percentage of students does not go to graduate level = [tex]\frac{128}{400}[/tex] × 100%

                                                                                           = 32%

Hence the percentage of the students does not plan to go to graduate school is 32%.

Survey is defined as the act of examining a process or questioning a selected sample of individuals to obtain data about a service, protect, or process. Data collection surveys collect information from a targeted group of people about their opinions, behavior or knowledge. A survey is a method of gathering information using relevant questions from a sample of people with the aim of understanding populations as a whole.

To know more about percentage here

https://brainly.com/question/14019573

#SPJ4

Answer:4(x+3)

Step-by-step explanation:

8(x + 3)^2 /2(x + 3)

4(x+3)

Answer:

Step-by-step explanation:

Simplify

8(x + 3)^2 divided by 2(x + 3)

8·(x + 3)² : 2·(x + 3) =

8⋅(x²+6x+9):2⋅(x+3) =

(8x²+48x+72):2⋅(x+3) =

(4x²+24x+36)⋅(x+3) =

4x³+36x²+108x+108

Answer:

16 cookies

Step-by-step explanation:

24 cookies/1.5 cups= 16 cookies per 1 cup

The y-intercept of the linear function is 0.

What is linear function?

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nevertheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair expressed in function notation. When an is an independent variable on which the function depends, the expression f(a) is referred to as a function. A straight line on a graph of a linear function has the equation or formula;

y = f(x) = mx + c

The formula of distance(y), time(x), and speed is

S = y/x.

Given that he walked at a pace of 4 miles per hour.

S = 4 miles per hour.

4 = y/x

y = 4x

Compare y = 4x with y = mx + c

c = 0

Thus y intercepts is 0.

To learn more about y-intercept, click on below link:

https://brainly.com/question/14320010

#SPJ1

Answer:

Below

Step-by-step explanation:

IF b is even :   b+2      b+4      b+6    b+8    b+10    b+12

If b is ODD  :   b+1     b+3    b+5   .....  b+11

By using the concept of percentage, it can be calculated that

65% people are completely satisfied with the car

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here, 2 is expressed as a fraction of 100.

This is a word problem on percentage

Number of people who are completely satisfied with the car = 1495

Total number of people surveyed = 1495 + 210 + 595 = 2300

Percentage of people who are completely satisfied with the car = [tex]\frac{1495}{2300}\times 100[/tex]

  = 65%

To learn more about percentage, refer to the link-

https://brainly.com/question/24304697

#SPJ1

Answer:

Step-by-step explanation  you add the 25.50 +2.50=27.00

and then add 115 to it 143.00

Answer:

  x = 3

Step-by-step explanation:

You want to know how to solve 2x +3 = 9.

A solution is an equation of the form ...

  x = constant

You can get a clue to the solution process by considering what happens to the variable. Here, ...

The solution process reverses these operations, starting with the last one first. The properties of arithmetic and equality are used.

We can undo the addition of 3 by adding -3 to both sides of the equation.

  2x +3 -3 = 9 -3

  2x +0 = 6 . . . . . . . . . . . adding 3 and its additive inverse gives zero

  2x = 6 . . . . . . . . . . . . . 0 is the additive identity element, so 2x+0 = 2x

We can undo the multiplication by multiplying by the multiplicative inverse of 2. That is, we can multiply by 1/2.

  (1/2)2x = (1/2)6

  1x = 3 . . . . . . . multiplying 2 and its multiplicative inverse gives 1

  x = 3 . . . . . . 1 is the multiplicative identity element, so 1x = x

Please note that multiplying by 1/2 is the same thing as dividing by 2. That is, multiplication and division are inverse operations.

The solution is x = 3.

It is wise to check that the solution you found makes the equation be true.

  2x +3 = 9

  2(3) +3 = 9 . . . . . substitute for x

  6 + 3 = 9 . . . . . . . true

__

Additional comment

This solution process works for just about any "solve for ..." situation, if an algebraic solution is possible. In high school math, you are introduced to just about every kind of equation we know how to solve. The list is fairly short.

<95141404393>

In case of a normal distribution, the mean, median, and mode are equal . So option A is correct

What is normal distribution?

The most significant continuous probability distribution in probability theory and statistics is the normal distribution, also referred to as the gaussian distribution. On occasion, it is referred to as a bell curve.

The probability distribution of data is expressed mathematically as a normal distribution. It is symmetrical from both ends and has only one mode. The equal mean, median, and mode of the given data are highlighted by the normal distribution.

The options are b) It has two modes. c) It is asymmetrical. and d) the points of the curve meet the x-axis at z are incorrect.

Therefore, The correct option is A, the equal mean, median, and mode of the given data are highlighted by the normal distribution.

To learn more about distribution refer here

brainly.com/question/29509087

#SPJ4

Answer:

∠D = 127°

Step-by-step explanation:

Let's define the properties of a parallelogram to understand how to solve for ∠D.

⭐The opposite angles in a parallelogram are congruent.

⭐The sum of the interior angles of a parallelogram is 360°.

First, let's solve for x knowing that the opposite angles are congruent.

∠A = ∠C

[tex]13x - 25 = 9x - 1[/tex]

[tex]13x - 9x = 25 - 1[/tex]

[tex]4x = 24[/tex]

[tex]x = 6[/tex]

∴ x = 6

Next, substitute x into ∠C.

∠C = 9x - 1

∠C = 9(6) - 1

∠C = 54 - 1

∴ ∠C = 53°

Finally, substitute ∠C into the equation 2(∠D) + 2(∠C) = 360° to solve for ∠D.

2(∠D) + 2(∠C) = 360°

2(∠D) + 2(53) = 360

2(∠D) + 106 = 360

2(∠D) = 254

∴ ∠D = 127°

⭐if this response helped you, please mark it the "brainliest"!⭐

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-100\% + 0.58}\\\\\mathsf{= \dfrac{-100}{100} + \dfrac{0.58}{1}}\\\\\mathsf{= -100 \div 100 + 0.58 \div 1}\\\\\mathsf{= -1 + 0.58}\\\\\mathsf{= -0.42}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-0.42}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

To solve the inequality 4y>12 we use the multiplication or division property of inequality

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Stuart solves the inequality 4 y greater than 12

We can write this as 4y>12

Then in the next step is y>3

We need to find which step is used in second step.

As Four times of y is greater than 12.

4y>12

When we divide both sides by 4 we get 3

y>3

Hence, multiplication or division property of inequality is used to solve the inequality.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

The solution of the inequality 3r ≤ 4r - 6 is  r ≥ 6.

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

An inequality have the symbol <, >, ≤ and ≥. Hence, the inequality can be solved as follows:

3r ≤ 4r - 6

subtract 4r from both sides of the inequality,

3r ≤ 4r - 6

3r - 4r ≤ 4r - 4r - 6

3r - 4r ≤ - 6

- r ≤ -6

divide both sides of the inequality by -1

Therefore, the solution is r ≥ 6

learn more on inequality here: https://brainly.com/question/11784045

#SPJ1