This table shows how many sophomores and juniors attended two school events. What is the probability that the student attended the jazz concert, given

Answer:

x = 15

Step-by-step explanation:

Step 1:  Make an expression

4/6 = 10/x

Step 2:  Cross multiply

4/6 = 10/x

4x = 60

Step 3:  Divide both sides by 4

4x / 4 = 60 / 4

x = 15

Answer:  x = 15

Answer:

15

Step-by-step explanation:

4 is to 6 as 10 is to what

Represent the unknown number as x and write as a ratio

4:6 = 10:x

Write as fractions

4/6 = 10/x

Cross-multiply

4x = 60

Divide both sides of the equation by 4

x = 15

15

Hope this helps :)

Answer:

1/16

Step-by-step explanation:

Each coin flip is an independent event so the probabilities are independent

P(T,H,T,H) = P(T) P(H)  P(T) P(H)

                  = 1/2 * 1/2 * 1/2 * 1/2

                   = 1/16

Answer:

Kendra is watching over 5 children. She wants to be sure that they each have an even number of apple slices. There are 35 apple slices total. She wants to take 35 and put it equally into 5 groups.

Your equation would be 5s=35, where s would be the total amount of apple slices on each plate.

To solve this equation you would divide both sides by 5 to get 7. s=7 (35/5=7)

Each quintuplet would be 7 apple slices.

Hope this helps ;)

Solution:

Given is:

[tex]x^2 + 14x + 40[/tex]

Factor the above polynomial

From given,

[tex]x^2 + 14x + 40[/tex]

[tex]Split\ the\ middle\ term\\\\x^2 + 4x + 10x + 40\\\\Break\:the\:expression\:into\:groups\\\\\left(x^2+4x\right)+\left(10x+40\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\\x(x + 4) + (10x + 40)\\\\\mathrm{Factor\:out\:}10\mathrm{\:from\:}10x+40\mathrm{:\quad }10\left(x+4\right)\\\\x(x + 4) + 10(x + 4)\\\\\mathrm{Factor\:out\:common\:term\:}x+4\\\\\left(x+4\right)\left(x+10\right)[/tex]

Thus, the binomials factor of given is (x + 4) and (x + 10)

Answer:

B.(2,4)

Step-by-step explanation:

The equation for a circle is written as

(x-h)^2 +(y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-2)^2+(y-4)^2=9.

Rewriting this equation

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

The center is at (2,4)

Answer:

it is D (-1 + or - 2i square root of 2)

Step-by-step explanation:

just took test

The value of x obtained after solving the equation  x² + 2x + 9 = 0 will be x = -1 ±2i √(2)(x equals negative 1 plus or minus 2 I square root of 2).Option D is correct.

Any equation of the form ax²+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

it is given that,

x² + 2x + 9 = 0

Rearrange the equation as

x² + 2x  = - 9

Add 1 on both sides of the equation,

x² + 2x +1 = - 9 +1

x² + 2x +1 = - 8

(x+1)² = -8

Taking square root,

(x+1) = √ -8

Subtract 1 from both sides,

x+1-1 = -1 ±√(-8)

x = -1 ±√(-8)

√(-8) can be written as,

√(-8) = 2i√2

Substitute the values,

x = -1 ±2i sqrt(2)

Thus, the value of x obtained after solving the equation  x² + 2x + 9 = 0 will be x = -1 ±2i √(2)(x equals negative 1 plus or minus 2 I square root of 2).Option D is correct.

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Answer:

a=4h

Steps:

4h=a swap the sides

a=4h

So , a=4h

The cost of one tub of brownie mix = $12

Step-by-step explanation:

Step 1 :

Let x represent one tub of cookie mix's cost and y represent one tub cookie mix's cost

Total amount raised by Elaine =  $75

Number of cookie mix tub sold by Elaine = 1

Number of brownie mix tub sold by Elaine = 5

This can be represented by the equation

x + 5 y = 75 => x = 75 - 5y

Step 2 :

Total amount raised by Megan =  $141

Number of cookie mix tub sold by Megan = 3

Number of brownie mix tub sold by Megan = 8

This can be represented by the equation

3 x + 8 y = 141

Step 3 :

Solving the equations obtained in the above steps we have ,

3 ( 75-5y) +8y = 141

225 - 15y + 8y = 141

-7y = -84 => y = 12

Step 4 :

Answer :

The cost of one tub of brownie mix is $12

Answer:

Step-by-step explanation:

12 dollars

Answer:

The answer is B: False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The original price of the granola bars before the 10% discount was $5.00. To determine this, the given discounted price was divided by 0.90, which represents the price after a 10% reduction.

The original price of a box of nut-free granola bars before the discount can be calculated by reversing the 10% discount process. Since Trey paid $4.50 after the discount, we can represent the original price as x. The discount applied to x would be 0.10 times x (which is how a 10% discount is calculated), and the price after the discount is x minus the discount. So the equation to solve is x - 0.10x = $4.50.

Simplify this equation to find x:
0.90x = $4.50.
Now, divide both sides of the equation by 0.90 to find x:
x = $4.50 / 0.90.
x = $5.00.

Therefore, the original price of the box of granola bars before the 10% discount was $5.00.

Answer:I believe it is 20

Answer:

1800

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 27 and d = 6, thus

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex] [ (2 × - 27) + (29 × 6) ]

     = 15( - 54 + 174)

     = 15(120)

     = 1800

The sum of the first 30 terms of the arithmetic sequence, is 1800.

In an arithmetic sequence, the sum of the first n terms can be calculated using the formula:

Sum = n/2 × (2a + (n-1)d), where:

Given:

Plugging in these values, we get:

Sum = 30/2 × (2(-27) + (30-1) × 6)

Calculating step-by-step:

Therefore, the sum of the first 30 terms of the arithmetic sequence is 1800.

Answer:

B-6

Step-by-step explanation:

If (B) represents Bob's time, six minutes less than Bob's time is B-6=T where (T) represents the time six minutes less than Bob's time.

The phrase 'six minutes less than Bob's time' can be translated into the algebraic expression 'B - 6', where 'B' represents Bob's time.

The given phrase 'six minutes less than Bob's time' can be written as an algebraic expression. Algebraic expressions are mathematical phrases containing numbers, variables (like 'Bob's time'), and operations.  In this case, we can symbolize 'Bob’s time' as a variable, let’s choose 'B'. Then 'six minutes less than Bob's time' translates to 'B - 6' in an algebraic expression. That’s because 'less than' implies subtraction and it always means you subtract from the number or variable stated after the expression, in this case, 'Bob's time' or 'B'.

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Answer:

As the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.

Step-by-step explanation:

A function, f, passes through the points (1,1), (2,7) and (3,25).

The equation of the function 'f' can be written as:

The f(x) is obtained by:

                                      [tex]f\left(x\right)=3f\left(x-1_\right)+4[/tex]

                                      [tex]f\left(4\right)=3f\left(3\right)+4=\left(25\times 3\right)+4=75+4=79[/tex]

A function, g, passes through the points (1,36), (2,43) and (3,50).

The g(x) is obtained by:

                                       [tex]g\left(x\right)=g\left(x-1\right)+7[/tex]

                                  [tex]g\left(4\right)=g\left(4-1\right)+7=g\left(3\right)+7=50+7=57[/tex]

So, value of f(x) at x = 4 exceeds the value of g(x) at x = 4.

Therefore, as the value of x increases, the value of f(x) will eventually exceed the value of g(x) is the correct option.                                                                                                                                                          

Answer:

The answer is C

B is reflection over the y-axis

Step-by-step explanation:

C. L’(4, 4), M’(7, 11), and N’(1, 11) are the coordinates of the vertices of the final image.

B is a reflection over the y-axis

Any point (x, y, z) can consequently be written as a sum of factors at the parallelepiped with one vertex on the origin. on this coordinate gadget, we are able to outline the unit cube with the 8 corner points classified (zero, zero, zero), (1, zero, zero), (1, 1, 0), (0, 1, 0), (zero, zero, 1), (1, 0, 1), (1, 1, 1), and (0, 1, 1).

The coordinates of the vertices of a triangle are (x2,y2) and (x3,y3). the line becoming a member of the primary is divided in the ratio l: okay and the road becoming a member of this point of the department to the opposite angular point is then divided by the ratio m:k + l.

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Solution:

The decreasing function is given as:

[tex]y = a(1-r)^t[/tex]

Where,

y is future value

a is initial value

r is decreasing rate

t is number of years

From given,

a = 4800

t = 5

[tex]r = 8.25 \% = \frac{8.25}{100} = 0.0825[/tex]

Therefore,

[tex]y = 4800(1 - 0.0825)^5\\\\y = 4800 \times 0.9175^5\\\\y = 4800 \times 0.6501\\\\y = 3120.841[/tex]

Thus the area after 5 years is 3120.841 square kilometer

Step-by-step explanation:

70

---- × 17=$11.90(saved)(answer)

100

The actual height of building is 1800 feet.

Step-by-step explanation:

Given,

Height of building in model = 3 inches

Scale used by engineer;

1 inch = 600 feet

Therefore;

Actual height of building = Height in model * Scale used

Actual height of building = 3 * 600

Actual height of building = 1800 feet

The actual height of building is 1800 feet.

Answer:

Yes, 10xyz^3 is a monomial.

Step-by-step explanation:

A monomial is an algebraic expression consisting of one term that can have multiple variables of different degrees within.

Answer:

-6/16

Step-by-step explanation:

Step 1:  Find equivalent to -3/8

(-3*2) / (8*2)

-6/16

Answer:  -6/16

Answer:

-0.375

Step-by-step explanation:

If you have a scientific calculator just plug in [tex]-\frac{3}{8}[/tex] then switch it to decimal form

[tex]-\frac{3}{8} = -0.375[/tex]

If you need help going from fraction to decimal form all you need to do is divide -3 by 8 = -0.375

Answer:

$1440

Step-by-step explanation:

First, find the unit rate by dividing 300 by 5, which equals 60. So, Kendra earns $60 in one day. Then, multiply 60 by 24, which equals 1440. So, Kendra makes $1440 in 24 days. Hope this helped!

Answer:1440 dollars earned In 24 hours

Step-by-step explanation: first divide 300 by 5 to get 60 then multiply 60 by 24 to get 1440

Answer:

C =18.84

Step-by-step explanation:

The circumference is given by

C = pi*d

C = 6pi

If we approximate pi by 3.14

C = 6*3.14

C =18.84

Answer:

Substitute, y = -3 and x = k on the equation.

=> k - 2×(-3) = -2

=> k = -2 + (-6)

=> k = - 8

=================

Any Doubts? Please COMMENT

The required value of the k is -8 for which the point (-8, -3) line on the equation of the line.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Point (k, -3) lies on the line whose equation is x-2y=-2.
Put x = k and y = -3 in the given equation of the line,

k - 2 (-3) = -2
k = -2 -6
k = -8

Thus, the required value of the k is -8 for which the point (-8, -3) line on the equation of the line.

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Answer:

  2 solutions

Step-by-step explanation:

I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...

__

To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:

  3x(x -4) +5 -x -(2x -7) = 0

  3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses

  3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms

  3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor

The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.

__

Alternate method

Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...

  d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c

  d = (-15)^2 -4(3)(12) = 225 -144 = 81

This positive value means the equation has 2 real solutions.

Answer:

Step-by-step explanation:

48

Answer:

C they have corresponding sides that are congruent

Step-by-step explanation:

hope this helps

The mean weight of the containers on the ship is found by adding the total weight of all the containers (270 tons) and dividing by the total number of containers (60), giving a mean of 4.5 tons per container.

In this problem, we are asked to find the mean weight of the containers on a ship. The mean is the average value of a set of numbers, found by adding all the numbers together and then dividing by the quantity of numbers.

First, let's compute the total weight of all the containers. The weight of the 30 small containers are 30 containers * 3 tons each = 90 tons. The weight of the 20 medium containers are 20 containers * 5 tons each =  100 tons. The weight of the 10 large containers are 10 containers * 8 tons each = 80 tons.

So, the total weight of all the containers is 90 tons + 100 tons + 80 tons = 270 tons. And the total number of containers is 30 + 20 + 10 = 60 containers.

So, the mean weight of the containers is 270 tons Total Weight / 60 = 4.5 tons/container. So, the mean weight of the containers on the ship is 4.5 tons.

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Final answer:

To find the minimum value of C given the constraints, one must plot these constraints, find the feasible region's vertices, evaluate C at each vertex, and select the minimum value obtained. The minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.

Explanation:

To find the minimum value of C = 4x + 3y subject to the given constraints, we need to first correct the constraints provided, as it seems there might be a misunderstanding in how they were presented. Assuming the constraints meant to be:

1. [tex]\(x \geq 0\)[/tex]

2. [tex]\(y \geq 0\)[/tex]

3. [tex]\(2x + 3y \geq 6\)[/tex]

4.[tex]\(3x - 2y = 9\)[/tex]

5.[tex]\(x + 5y = 20\)[/tex]

We will solve the system of equations (4) and (5) to find the values of x and y that satisfy these conditions, and then we will check if these values satisfy all other constraints including (3). If they do, we'll use these values to find C.

Solving the equations simultaneously:

From equation (4): 3x - 2y = 9

From equation (5): x + 5y = 20

Multiplying equation (5) by 3 to eliminate x, we get:

3(x + 5y) = 3(20)

3x + 15y = 60

Now, subtract equation (4) from this result to eliminate x:

3x + 15y - (3x - 2y) = 60 - 9

3x + 15y - 3x + 2y = 51

17y = 51

y = 3

Substitute y = 3 into equation (5) to find x:

x + 5(3) = 20

x + 15 = 20

x = 5

Now, check if [tex]\(x = 5\) and \(y = 3\) satisfy the constraint \(2x + 3y \geq 6\):[/tex]

[tex]\[2(5) + 3(3) \geq 6\][/tex]

[tex]\[10 + 9 \geq 6\][/tex]

[tex]\[19 \geq 6\] - This is true.[/tex]

Since x = 5 and y = 3 satisfy all the constraints, we can calculate \(C\):

C = 4x + 3y

C = 4(5) + 3(3)

C = 20 + 9

C = 29

Therefore, the minimum value of C = 4x + 3y, given the constraints and the corrected understanding of them, is 29.

Answer:

Volume of the Square pyramid [tex]=378.27 Feet^3[/tex]

Step-by-step explanation:

A Square pyramid is the pyramid whose base is in the shape of a Square.

Volume of a Square Pyramid:

                     [tex]BASE*BASE*\frac{HEIGHT}{3}[/tex]

[tex]Base= 9 feet[/tex]      and    

[tex]Height= 14 feet[/tex]

Volume of the square Pyramid:

                                                 =[tex]9*9*\frac{14}{3}[/tex]

                                               [tex]=81*4.67[/tex]

                                            [tex]=378.27 Feet^3[/tex]

The volume of the Square pyramid [tex]=378.27 Feet^3[/tex]

Answer:

-0.62

Step-by-step explanation: