A box contains 8 books. It is 1/6 full. If the box were completely full, how many books would be in the box? A) 14 books B) 48 books C) 16 books D) 24 books

First four is BBBC，The last one doesnt make sense to me，you probably didnt write it right

Answer:s

Step-by-step explanation:

To find the measure of angle AOB when given that angle AOC is 108 degrees and m∠AOC = 3m∠AOB, use the relationship between the angles to calculate m∠AOB as 36 degrees.

Given: ∠AOC = 108°, m∠AOC = 3m∠AOB

To find: m∠AOB

Steps to solve:

Since ∠AOC = 108° and m∠AOC = 3m∠AOB, we can set up an equation: 108 = 3x, where x is m∠AOB.

Solving the equation, x = 36°. Therefore, m∠AOB = 36°.

(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...

... 5x = 6(x -1.75)

(B) Subtract 5x, simplify and add the opposite of the constant.

... 5x -5x = 6x -6·1.75 -5x

... 0 = x -10.50

... 10.50 = x

(C) 5x = 5·10.50 = 52.50

... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value

(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.

number is 21

let the number be n then dividing by 3 gives [tex]\frac{n}{3}[/tex] and adding - 3 gives

[tex]\frac{n}{3}[/tex] - 3 = 4 ( add 3 to both sides )

[tex]\frac{n}{3}[/tex] = 7 ( multiply both sides by 3 )

n = 3 × 7 = 21

46 non bubblegum

230 bubble gum

46

sum the parts of the ratio 5 + 1 = 6

divide 276 by 6 to find 1 part of the ratio

[tex]\frac{276}{6}[/tex] = 46 ← 1 part

the store sold 46 non-bubble gum

and 230 bubble gum

Answer: A. 1 in 100,000,000

Step-by-step explanation:

The given digits are  0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

The total number of digits = 10

Now by using the counting principle, the probability of choosing one number is given  by :-

[tex]\text{P(one number)}=\dfrac{1}{10}[/tex]

Therefore, the probability of choosing 8 numbers (with replacement ) will be :

[tex]\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{10}=(\dfrac{1}{10})^8=\dfrac{1}{100,000,000}[/tex]

Answer:

1/16 in

Step-by-step explanation:

The largest possible error in representing a number is half the unit of precision. Here, the error is said to be 1/32 in. That is half of 1/16 in. So, the unit of precision must be 1/16 in.

the correct answer is 63 because they are multiplying the length of each side by 7.

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given two figures:

John's design is similar to Josh's project.

ML = 8 inches

CD = 56 inches

KL = 9 inches

We need to find value of 'BC'.

So, there ratio would be :

[tex]\dfrac{ML}{CD}=\dfrac{KL}{BC}\\\\\dfrac{8}{56}=\dfrac{9}{BC}\\\\\dfrac{1}{7}=\dfrac{9}{BC}\\\\BC=9\times 7\\\\BC=63\ inches[/tex]

Hence, Option 'd' is correct.

The numbers are a bit ugly, but the equation can be solved as is.

... 1.2x/3.6 + (0.2/3.6) = 0.5x/9 . . . . use the distributive property on the left

... x(1/3 -1/18) + 1/18 = 0 . . . . . subtract the right side, simplify fractions

... x(6/18 -1/18) = -1/18 . . . . . . . use 18 for common denominator

... 5x = -1 . . . . . . . . . . . . . . . . . multiply by 18

... x = -1/5 . . . . . . . . . . . . . . . . divide by 5

_____

You can eliminate decimals and fractions by multiplying the given equation by 18.

... 6x +1 = x

... 5x +1 = 0

... 5x = -1

... x = -1/5

_____

The fraction simplification can work like this:

... 0.2/3.6 = 2/36 = 1/18

... 0.5/9 = (1/2)/9 = 1/(2·9) = 1/18 . . . . or . . . . (0.5)/9 × (2/2) = (0.5·2)/(9·2) = 1/18

Answer:

x=-0.2

Step-by-step explanation:

The given equation is

[tex]\frac{0.2(6x+1)}{3.6}=\frac{0.5x}{9}[/tex]

We need to solve the given equation for x.

On cross multiplication we get

[tex]9[0.2(6x+1)]=3.6(0.5x)[/tex]

[tex]1.8(6x+1)=1.8x[/tex]

Using distribution property, we get

[tex]1.8(6x)+1.8(1)=1.8x[/tex]

[tex]10.8x+1.8=1.8x[/tex]

Subtract 1.8x and 1.8 from both sides.

[tex]10.8x+1.8-1.8x-1.8=1.8x-1.8x-1.8[/tex]

[tex]10.8x-1.8x=-1.8[/tex]

[tex]9x=-1.8[/tex]

Divide both sides by 9.

[tex]x=-\frac{1.8}{9}[/tex]

[tex]x=-0.2[/tex]

Therefore, the value of x is -0.2.

slope m =  –4

equation

y - 3 = -4(x + 2)

y - 3 = -4x - 8

y = -4x - 5 where slope = -4 and y intercept = b = -5

Answer

Y intercept (0, -5)

[tex]x_{1} =-2[/tex]

[tex]x_{2}=3[/tex]

Slope intercept form: y = mx + b

mx=-4

b= -5

Intercepts

x intercept=-1.25

y intercept=-5

The correct answer is y intercept =-5

the answer is:

√100 = 0 + 10 i

hope this helps! :o)

The intersection of two coplanar lines forms a point.

Option A is the correct answer.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The intersection of two coplanar lines forms:

a.

a point
This is true.

Because two lines that intersect and form a point are called coplanar.

b.

a line

This is not true.

c.

a plane

This is not true.

Two axis makes a plane.

d.

an angle

This is not true.

An angle is formed when two straight lines or rays meet at a common endpoint.

Thus,

A point is formed by the intersection of two coplanar lines.

Learn more about corresponding angles here:

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Answer:

x = 4

Step-by-step explanation:

We assume that the given expessions represent the measures of the alternate interior angles, so are equal.

... (4x + 12)° = 7x°

... 12 = 3x . . . . . . . divide by degrees, subtract 4x

... 4 = x . . . . . . . . . divide by 3

_____

Then the angles are 7x° = 28° = (4x+12)°.

Since the sign between parentheses is +, we can simply drop the parentheses and combine like terms.

... = x²(6 +3) +x(-2 -4) +(4 -3)

... = 9x² -6x +1

To graph x < 2, draw a number line with an open circle at 2, and shade to the left of the circle. This indicates all numbers less than 2 are included, while 2 itself is not.

To graph the inequality x < 2, you first need to draw a number line. Let's represent x by a point on the number line. The inequality x < 2 means that x can be any value less than 2, but not 2 itself.

To represent this on the number line, you would place an open circle (which represents exclusion) at 2, and then shade or draw an arrow pointing to the left (representing all numbers less than 2). This visually shows that the solution contains all numbers less than 2, but not 2 itself.

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Answer:

1) There were 18582 visitors on the opening weekend.

2) There were approximately 7199 visitors on the 9th weekend.

3) The number of visitors was about 15,051 after 2 weekends. 

Step-by-step explanation:

Given : The curve of best fit to model the data is given below.  

[tex]y=18582(0.90)^x[/tex]

To find : Complete the statements,

1) There were _____ visitors on the opening weekend.

2) There were approximately _____ visitors on the 9th weekend.

3) The number of visitors was about 15,051 after ______ weekends.

Solution :

[tex]y=18582(0.90)^x[/tex] is the exponential equation: 

where, y is the number of visitors and x are the weekends since opening

1. Since the opening weekend is the day of the the park's opening.

So, replace x=0 in our exponential equation to get the number of visitors on the opening weekend:

[tex]y=18582(0.90)^x\\y=18582(0.90)^0\\y=18582(1)\\y=18582[/tex]

Therefore, There were 18582 visitors on the opening weekend.

2. To find the approximate number of visitors on the ninth weekend.

We replace x=9  in our exponential equation:

[tex]y=18582(0.90)^x\\y=18582(0.90)^9\\y=7199.0475[/tex]

Rounded to the nearest integer :  y=7199

Therefore, There were approximately 7199 visitors on the 9th weekend.

3. Here, we know that the number of visitors is 15051

Since y represents the number of visitors.

So, replace y=15051 in our exponential equation and solve for x:

[tex]y=18582(0.90)^x\\\\15051=18582(0.90)^x\\\\ \frac{15051}{18582} =0.90^x\\\\0.90^x= \frac{5017}{6194} \\\\ln(0.90^x)=ln(\frac{5017}{6194})\\\\xln(0.90)=ln(\frac{5017}{6194})\\\\x= \frac{ln(\frac{5017}{6194})}{ln(0.90)} \\\\x=2.0002[/tex]

Rounded to the nearest whole number :  x=2

Therefore, The number of visitors was about 15,051 after 2 weekends.

let a,b be the two numbers. we know that a2-b2=5 and a*b=6

using the formula we are given

[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]

Answer:

13

Step-by-step explanation:

Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,

[tex](x^2-y^2)=5[/tex]......................(1)

[tex]xy=6[/tex]..........(2)

We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :

[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]

Using equation (1) and (2) in above equation, we get :

[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]

[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]

[tex]x^2+y^2=13[/tex]

So, the sum of squares of two numbers is 13. Hence, this is the required solution.

Answer:

i think is d

Step-by-step explanation:

In order to calculate the number of cars the drama club could wash in 4 hours, one needs to know their washing rate per hour. Supposing it to be 2 cars/hour, the multiplication of the rate by the number of hours (2 * 4), shows that they could wash 8 cars.

The subject of this question is mathematics, specifically rate problems in the context of a real-world situation. In order to solve a problem like this, we need to know the rate at which the drama club is washing cars. This information is missing from the question, so let's suppose that they wash 2 cars per hour. In that case, their rate of washing cars is 2 cars/hour. Then, if you want to find out how many cars they could wash in 4 hours if they continue at this pace, you'll need to multiply their rate by the number of hours.

Let's calculate: Rate (2 cars/hour) * Time (4 hours) = 8 cars.

This means that if they keep washing cars at a rate of 2 cars per hour, they will have washed 8 cars in 4 hours.

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"Standard form" is the form ...

... ax +by = c

where a, b, c are mutually prime integers and the leading coefficient is positive. (If a ≠ 0, then it is "leading". If a = 0, then b is the leading coefficient.)

Of the choices offered, the only one that is equivalent to the given equation is ...

... -x + 6y = 5

_____

However, "standard form" requires the leading coefficient be positive, so an appropriate answer would be ...

... x -6y = -5

or

... 6y -x = 5

____

This is another one for my "broken question" file.

The solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.

To solve the equation 2x^2 + 9x + 8 = 0, we can use the quadratic formula. The quadratic formula states that the solutions for any quadratic equation of the form ax^2 + bx + c = 0 can be calculated using the formula:

x = (-b ± √(b^2 - 4ac))/(2a)

For the given equation, a = 2, b = 9, and c = 8.

Plugging these values into the formula, we get:

x = (-9 ± √(9^2 - 4*2*8))/(2*2)

Simplifying, we have:

x = (-9 ± √(81 - 64))/(4)

x = (-9 ± √17)/(4)

So, the solutions for the equation 2x^2 + 9x + 8 = 0 are x = (-9 + √17)/(4) and x = (-9 - √17)/(4), which are approximately 0.44 and -4.94, respectively.

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Remark

You have been told that the slope of the line is 2/3. That means that if the general equation is y = mx + b is the equation for the slope intercept formula and since m = the slope, then m also equals 2/3

y = (2/3)x + b

Use the point to find b

when x = 3

y = 4                       This comes from the point

4 = (2/3) * 3 + b      multiply 2/3 and 3 together

4 = 6/3 + b             Simplify 6/3

4 = 2 + b                  Subtract 2 from both sides

4 - 2 = b                   Combine

2 =  b              

Equation

y = (2/3)x + 2

Hey there!!

What is slope-intercept form ?

Ans :- y = mx + b

Where 'm' is the slope and 'b' is the y-intercept.

Given :

Slope = 2/3

Coordinate : ( 3 , 4 )

Now, plugging in all these values, we get :

... 4 = ( 2/3 )×3 + b

... 4 = 2 + b

b = 2

Hence, the y -intercept is 2.

Getting this into slope-intercept form :

y = ( 2x/3 ) + 2

Hope my answer helps!!

Answer:

The percent increase is [tex]13.33[/tex]%

Step-by-step explanation:

First we need to calculate the increase:

Increase in value = [tex]255-225[/tex]

                             =[tex]30[/tex]

Percent increase = [Increase in value / Initial value]*100

                             =[tex]\frac{30}{225} *100[/tex]

                             =[tex]13.33[/tex]%

Therefore,

the percent increase is [tex]13.33[/tex]%

When only angles are specified, the sides can be any length, so the triangle is not unique. In any event, the sum of angles must be 180°, so three angles measuring 50° cannot be closed to form a triangle.

Three sides measuring 4, 8, and 14 ft cannot be closed, either, as the long dimension exceeds the sum of the other two. The ends can't meet.

The appropriate choice is the 3rd one ...

... three sides measuring 5 in, 12 in, and 14 in.

Answer:

B three sides measuring 5 in, 12 in, and 14 in

Step-by-step explanation:

the three angles measuring 25, 65, and 90 is 180 and can make more triangle.

the three angles measuring 50, 50, and 50, doesn't even add up to 180 degrees.

the three sides measuring 4 ft, 8 ft, and 14 ft can make more triangles.

I got this right in my test and I got it right.I hope this helps you

multiply numerator/ denominator by the same value 4 to create an equivalent ratio

[tex]\frac{4}{5}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{16}{20}[/tex]

\frac{4}{5} × \frac{4}{4} = \frac{16}{20}

MP = MP, so triangle MPN ≅ triangle MPK by SSS. That means ∠NMP ≅ ∠KMP by CPCTC, so

... ∠NMP + ∠PMK = ∠NMK

... 2×∠PMK = 50° . . . substitute ∠PMK for ∠NMP, with which it is congruent

... ∠PMK = 25° . . . . . divide by 2

The value of y = sin (θ) when θ = pi/2 is 1.

It is the branch of maths concerned with the functions of angles and their involvement in calculations.

We can calculate the value of sin(θ) as follows:

θ = π/2

π/2 is the radian form of 90°

y = sin (θ)

= sin (π/2)

= 1

The value of y = sin(θ) is 1. The correct answer is option B.

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Answer:

Copy the second line segment with one endpoint at the same endpoint of the first line segment.

c is correct a is wrong

Answer:

Option A : copy the angle

Step-by-step explanation:

We can see that to make congruent triangles he first copied the segments

He copied the segment and drew segment FG

Then he copied the length of BH  and then keeping compass on point F cut the line segment FG at I

Then he measured the angle ABC and then intersect the previous arc at J

So, we can see that he just copied the angle

So, his recent completed step was copy the angle .

So, Option A is correct

Hence Option A copy the angle is true .