Reyesburg Corporation is contemplating using a new, more expensive glue in the construction of its laminated veneer lumber. Of importance to the company is the carrying load of the lumber. The company has tested 24 beams using the new glue, recording for each beam the pressure (in pounds per square foot) at which the beam breaks. The data collected are presented in the following histogram.

The orthocenter is only outside of a triangle when the triangle is obtuse. The only obtuse triangle shown is the 25-45-110 triangle.

The orthocenter is only outside of a triangle when the triangle is obtuse. The only obtuse triangle shown is the 25-45-110 triangle.

In a triangle, the orthocenter is the point where the altitudes of the triangle intersect.

Altitudes are lines drawn from each vertex of the triangle perpendicular to the opposite side.

In some cases, the orthocenter can be located outside of the triangle.

One example of a triangle where the orthocenter is located outside of the triangle is an obtuse triangle.

In an obtuse triangle, one of the angles is greater than 90 degrees.

When you draw the altitudes, they will intersect outside the triangle, forming the orthocenter.

For instance, consider a triangle with angle measures of 100 degrees, 40 degrees, and 40 degrees. When you draw the altitudes, you will find that they intersect outside the triangle. Thus, an obtuse triangle can have an orthocenter located outside of the triangle.

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Answer:

MaybeIf you do 12,000 times 5.5 and didved by 100?

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&12000\\ P=\textit{original amount deposited}\dotfill\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]\bf 12000=P\left(1+\frac{0.055}{12}\right)^{12\cdot 3}\implies 12000=P(1.00458\overline{3})^{36} \\\\\\ \cfrac{12000}{(1.00458\overline{3})^{36}}=P\implies 10178.56\approx P[/tex]

Answer:

x=24

Step-by-step explanation:

We can use proportions to solve this problem

5                15

------ =  -------------

8              x

Using cross products

5 * x = 8 *15

Divide by 5

5x/5 = 8*15/5

x = 8*3

x =24

Answer:

The answer is 24in.

Step-by-step explanation:

My explanation isn't very useful, I just looked at the image and say that 5in was 1/3 of 15in. therefore I multiplied 8in by 3 and got 24in.

I hope this helps!

Cheers, July!

Answer:-3 less than -1

Step-by-step explanation: -3 is less than -1

Answer:

The enlargement will be 30 ft by 7.5 ft.

Step-by-step explanation:

A scale drawing is a larger or smaller version of an object. To find the dimensions of the new drawing, multiply each measurement by the scale factor. The scale factor here is 5/2 or 2.5.

12(2.5)=30 ft

3(2.5)=7.5 ft

Answer:

Step-by-step explanation: Do 24 / 3 is 8

and to check your work do 8 x 3 which is 24

Hope This Helps ^_^

Hope this helps!

2/9, 2/7, 2/3, 9/7

Answer:

2/9, 2/7, 2/3, 9/7

Step-by-step explanation:

9th are smaller than 7th so 2/9 goes first.

7th are smaller than thirds so 2/7 goes second

9/7 is an improper fraction so it is more than one, so 2/3 goes third

Then 9/7

Problem 14 and problem 16 are missing the diagrams needed to answer the questions. Thankfully, there is enough info for me to answer problem 15, which I'll do so below.

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

If we have a triangle with side lengths a,b,c then we can write this compound inequality

b-a < c < b+a

If we knew the value of a and b, then we can find a range for c.

In our case, a = 5, b = 12, c = n, so,

b-a < c < b+a

12-5 < n < 12+5

7 < n < 17

The value of n is between 7 and 17. The value of n cannot equal 7, and it also can't equal 17 either.

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

Final Answer for problem 15 is choice C) 7 < n < 17

The fraction form of the given expression is 29/40.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The expression in the percentage form is given as 72.5%.

Divide by 100 to obtain fraction as,
72.5%

= 72.5/100

= 725/1000

= 29/40

Hence, the given expression can be written in fraction as 29/40.

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Answer:

56/6

Step-by-step explanation:

3 1/2 * 2 2/3

first evaluate 3 1/2 = (6+1)/2=7/2

so for that multiply 2 * 3 and +1 and divide by 2

second evaluate 2 2/3 = (6+2)/3 = 8/3

now the product = 7/2 * 8/3 =  (7*8) / (2*3) = 56 / 6

Answer:

40 students

Step-by-step explanation:

Lets multiply:

5:3 = 10:6 = 20:12 = 25:15

Since 25 is 10 more than 15, these are the actual numbers we need.

25 + 15 = 40 students.

Answer:

If the ratio is 5:3 boys to girls and there are 10 more boys than girls, there would be 15 girls and 25 boys, for a total of 40 people.

Step-by-step explanation:

To solve the ratio, we need to set up a proportion and assign a variable to solve for.  In this case, we can make 'x' the number of girls and 'x+10' the number of boys.  We know that the ratio of boys to girls is 5 to 3, so we can set up a proportion where 5/3 = (x+10)/x.  In order to solve a proportion, we would cross-multiply and divide in order to get a two-step equation to solve for the variable.  When we cross-multiply, we get 5x=3(x+10), or 5x=3x + 30.  Using inverse operations, first subtracting the '3x' from both sides to get 2x=30, and then dividing both sides by 2 to get x=15.  Remember, that 15 represents the number of girls.  The number of boys is equal to  'x+10' or 15 +10=25.  Then the total number of people is 15+25=40.

Answer:

24

48

72

96

Step-by-step explanation:

I just know

This question can be solved by using simple algebra to set up equations based on the given conditions. We found that the two numbers are 38 and 26.

To discover the two numbers, we will use a mathematical approach based on the problem. If we denote the larger number as 'x' and the smaller number as 'y', we have two equations based on the statement: 'x + y = 64' and 'x - y = 12'. You can solve this system of equations by adding these two equations together to eliminate 'y'. This operation will give you the result '2x = 76'. Upon dividing both sides of the equation by 2 you find that 'x = 38'. To find 'y', you subtract 38 from 64 based on the summation equation, yielding the result 'y = 26'. So, the two numbers are 38 and 26.

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The sum of the two numbers is 64, and the difference is 12. By setting up and solving a system of equations, we find that the two numbers are 38 and 26.

To find the two numbers, let's set up a system of equations:

Let x be one of the numbers, and y be the other number.

We can write two equations based on the given information:

x + y = 64 (sum of two numbers is 64)

x - y = 12 (difference of two numbers is 12)

To solve this system of equations, we can use the method of substitution or elimination.

Using the method of elimination, we can add the two equations:

(x + y) + (x - y) = 64 + 12

2x = 76

x = 38

Substituting the value of x into one of the equations:

38 + y = 64

y = 26

Therefore, the two numbers are 38 and 26.

Answer:

8 piles for basketball

4 piles for football

3 piles for baseball

Step-by-step explanation:

1. Find the GCF of all three #s

2. 8 is the GCF, so divide each # by 8

3. You get the # of piles for each type of card

Answer:

31 ft²

Step-by-step explanation:

(1) Area of square

A = l²

A = 12²

A = 144 ft²

=====

(2) Area of circle

A = πr²

A = π × 6²

A = π × 36

A = 113 ft²

=====

(3) Remaining area

A = 144 – 113

A = 31 ft²

The area of the remaining board is 31 ft².

Answer:

Step-by-step explanation:

30

Answer:

12n +6

Step-by-step explanation:

5n + 6 + (7n)

The first step is to combine like terms

I put the like terms next to each other.

5n + 7n +6

12n +6

Answer:

It would be 2 hours and 15 minutes

Step-by-step explanation:

Answer:2.26 hours

Step-by-step explanation:

Given

Rich is driving from Philadelphia to Pittsburgh at 70 mph

and Michelle speed is 65 mph

If Philadelphia and  Pittsburgh is 305 miles apart

Let Rich travels x miles in t time

therefore

Michelle travels 305 -x

[tex]\frac{x}{70}=\frac{305-x}{65}[/tex]

[tex]13x=14\times 305 -14x[/tex]

27x=4270

[tex]x=\frac{4270}{27}[/tex]

[tex]x=158.148\approx 158.15 miles[/tex]

time taken t[tex]=\frac{158.15}{70}=2.259 \approx [/tex] 2.26 hours

Final answer:

The integers that satisfy the given condition of the equation x^2 + 2 = 10x - 7 are 1 and 9. To find these integers, the quadratic equation x^2 - 10x + 9 = 0 was factored and solved.

Explanation:

To find the integer(s) that satisfies the given condition, we need to set up an equation based on the description. The condition states: if 2 is added to the square of an integer x, the result equals 10 times that integer minus 7. Mathematically, this can be expressed as x2 + 2 = 10x - 7. To solve this, first rearrange the terms to one side to form a quadratic equation:

x2 - 10x + 9 = 0

Now we factor the quadratic equation:

(x - 1)(x - 9) = 0

Setting each factor equal to zero gives us the solutions:

x - 1 = 0 ⇒ x = 1

x - 9 = 0 ⇒ x = 9

The integers that satisfy the given condition are 1 and 9.

Answer:

413.44 but the whole decimal is 413.4375

Step-by-step explanation:

first I turned the fractions into percents...

1/3- 30% and 1/8- 12.5

$750-10%= $675

675-12.5%= 590.63 (or 590.635)

590.63-30%= 413.441

Hope it helps some!

Answer:

The distance from Old Towne to Bridgeway is 15 11/12 miles.  

Step-by-step explanation:

In order to find the distance from Old Towne to Bridgeway, we need to subtract the posted distances for these two cities.  Since Old Towne is 36 1/3 miles away and Bridgeway is 52 1/4 miles away, we need to subtract 36 1/3 from 52 1/4.  We cannot subtract fractions with unlike denominators, so we need to find the lowest common denominator of 3 and 4, which is 12.  When we make the fraction of 1/4 over a denominator of 12 we get 3/12 and when we convert 1/3 to a fraction with a denominator of 12, we get 4/12.  Since we can not subtract 4 from 3, we need to take one away from 52 and add it to our fraction to become 51 15/12.  Subtracting 51 15/12 - 36 4/12 = 15 11/12 miles.

Final answer:

The distance from Old Towne to Bridgeway is calculated by subtracting the distance to Old Towne from the distance to Bridgeway, resulting in 15 11/12 miles.

Explanation:

To determine the distance between Old Towne and Bridgeway, we subtract the distance from the starting point to Old Towne from the distance to Bridgeway. Old Towne is 36 1/3 miles away, and Bridgeway is 52 1/4 miles away. We must first convert these mixed numbers to improper fractions to do the subtraction.

Convert 36 1/3 to an improper fraction: (36 × 3) + 1 = 108 + 1 = 109/3.

Convert 52 1/4 to an improper fraction: (52 × 4) + 1 = 208 + 1 = 209/4.

Find a common denominator to subtract the fractions. The common denominator for 3 and 4 is 12. Thus, convert both fractions to twelfths: 109/3 becomes 436/12, and 209/4 becomes 627/12.

Subtract the distance to Old Towne from the distance to Bridgeway: 627/12 - 436/12 = 191/12.

Convert 191/12 back to a mixed number to find the distance: 191 ÷ 12 = 15 with a remainder of 11, so the distance is 15 11/12 miles.

Therefore, the distance from Old Towne to Bridgeway is 15 11/12 miles.

Answer:

(28*12)-(18*5) or 246 meters squared

Step-by-step explanation:

It is actually easy really, all you have to do is find the area of the larger polygon (28*12) or 336 and subtract the smaller polygon (18*5) or 90 and subtract it from the larger polygon getting you 246 meters squared

Answer:

The total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.

Step-by-step explanation:

Let x lb flour is used to make brownies.

She used 1/4 pound more flour to make cookies than to make brownies. So, the total flour is used to make cookies is

[tex]x+\frac{1}{4}[/tex]

she used 1/8 lb less flour to make the bread then to make the cookies. So, the total flour is used to make bread is

[tex]x+\frac{1}{4}-\frac{1}{8}[/tex]

It is given that she used a half pound of flour to make bread.

[tex]x+\frac{1}{4}-\frac{1}{8}=\frac{1}{2}[/tex]

[tex]x+\frac{2-1}{8}=\frac{1}{2}[/tex]

[tex]\frac{8x+1}{8}=\frac{1}{2}[/tex]

[tex]8x+1=4[/tex]

[tex]8x=3[/tex]

[tex]x=\frac{3}{8}[/tex]

Therefore total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.

Answer:

Area of plane surface of cylinder = 2772 sq.cm.

Step-by-step explanation:

Let r be the radius and h be the height of the cylinder.

Curved Surface Area = 1848 sq.cm

2πrh = 1848

2×[tex]\frac{22}{7}[/tex]×rh = 1848

rh = 1848 × [tex]\frac{7}{22}[/tex] × [tex]\frac{1}{2}[/tex]

rh = 294

Sum of radius and height = 35

r + h = 35 --- (1)

Now,

r - h = [tex]\sqrt{(r+h)^{2}-4rh }[/tex]

= [tex]\sqrt{35^{2}-4(294) }[/tex]

= [tex]\sqrt{1225-1176}[/tex]

= [tex]\sqrt{49}[/tex]

= 7

r - h = 7 --- (2)

Adding (1) and (2),

2r = 42

r = 21  cm.

Area of the plane surface = 2 × π[tex]r^{2}[/tex]

= 2 × [tex]\frac{22}{7}[/tex] × 21 × 21

= 2772 sq.cm.

To calculate the plane surface area of a cylinder, subtract the area of the two circular bases from the curved surface area. Use the given formula and equations to find the radius and height, then calculate the area of one circular base. Finally, subtract the area of the bases from the curved surface area to find the plane surface area.

To calculate the plane surface area of a cylinder, we need to subtract the area of the two circular bases from the curved surface area.

The formula for finding the curved surface area of a cylinder is given as:

CSA = 2πrh

So, the curved surface area is 1848 cm² and the sum of the radius and height is 35 cm. We can use these values to find the radius and height of the cylinder.

Solving the equation 2πrh = 1848 and r + h = 35 simultaneously will give us the values of r and h.

Once we have the values of r and h, we can calculate the area of one circular base using the formula Area = πr². Finally, we can calculate the plane surface area by subtracting the area of the two circular bases from the curved surface area.

Question

Which two numbers does the √12 fall between? √4 √9 √16 √25

Answer:

√9 √16

Step-by-step explanation:

√4 = 2

√9 = 3

√12 = 3.5

√16 = 4

√25 = 5

Answer:

The geometric mean of 2 and 8 comes out to equal 4.

Step-by-step explanation:

Answer:

-5120

Step-by-step explanation:

Replace the n in the formula by 6.

a6 = -5(4)^(6-1)

= -5 * 4^5

= -5120

Answer:

[tex]a_{6}[/tex] = - 5120

Step-by-step explanation:

To obtain the sixth term substitute n = 6 into the formula

[tex]a_{6}[/tex] = - 5 × [tex]4^{5}[/tex] = - 5 × 1024 = - 5120

Answer:

100%

Step-by-step explanation:

Use this equation:

Answer:

CANT DO IT

Step-by-step explanation:

IM TOO LAZYER

Answer:

8 and 13

Step-by-step explanation:

8+13 = 21

13-8 = 5