The ratio of the number of boys to the number of girls at school is 4:5. a. What fraction of the students are boys? b. If there are 120 boys, how many students are there altogether? *

See the figure below for a better understanding of the problem. Since we have a 45-45-90 triangle, this is an isosceles triangle, so both the adjacent and opposite sides measure the same value, say, x. Then the hypotenuse would be:

[tex]H=\sqrt{x^2+x^2} \\ \\ H=2\sqrt{2}[/tex]

Then. the ratio of the length of the hypotenuse to the length of a side is:

[tex]\boxed{r=\frac{2\sqrt{x}}{x}}[/tex]

In a 45-45-90 triangle, the ratio of the length of the hypotenuse to the length of a side is √2:1. This means that if one of the legs (the sides opposite the 45-degree angles) has a length of "x" units, then the hypotenuse (the side opposite the 90-degree angle) will have a length of "x√2" units.

The diameter of the base of the tower is approximately 15m.

The height of the leaning tower = 56 m

The leaning tower is cylindrical in shape.

Suppose the diameter of the base of the tower is d

The volume of a cylinder with a diameter d and height h is [tex]\frac{\pi }{4} d^{2} h[/tex].

Given that the volume of the tower is about 9,891 cubic meters.

This means [tex]\frac{\pi }{4} d^{2} h=9891[/tex]

[tex]\frac{\pi }{4} d^{2} *56=9891[/tex]

[tex]d=15m[/tex]

Hence, the diameter of the base of the tower is approximately 15m.

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Answer:

0.0000052 kg

Step-by-step explanation:

Per one kilogram, there are one thousand grams. By dividing 0.0052 grams by 1000, we can find kilograms.

0.0052/1000 = 0.0000052 kg

(This could also be written as 5.2 x 10^-6 kg)

Hope this helps!

Answer:

Emma needs one more $5 bill and 3 more $1 bills to buy the game that costs $45.

Step-by-step explanation:

10+10=20

5+5+5=15

1+1=2

20+15+2= 37

45-37=8

5+3 =8

Emma will need $8 more to buy the game

$10+$10= $20

$5+$5+$5= $15

$1+$1=$2

$20+$15+$2= $37

$45-$37= $8

The bills you can use to show how much more money Emma needs is a $5 bill and 3 $1 bills. Or you can use 8 $1 bills.

Hope this helps :)

Answer:n=-1

Step-by-step explanation:n=-6+5

n=-1

Answer:

n = -1

Step-by-step explanation:

Given

n - 5 = -6

Add 5 to both sides in order to isolate the unknown

n - 5 + 5 = -6 + 5

n = -1

To find the value of x for which WXYZ must be a parallelogram, set up an equation by equating the lengths of opposite sides. Solve the equation to find the value of x.

To find the value of x for which WXYZ must be a parallelogram, we first need to understand the properties of parallelograms. One important property is that opposite sides are equal in length. Given that WZ = XY, we can set up an equation: 4x + 20 = x + 26. By solving this equation, we can find the value of x.

4x + 20 = x + 26

Subtracting x from both sides, we get:

3x + 20 = 26

Subtracting 20 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

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Answer:

Pound of Apples = 2$

Pound of Banana = 2.75$

Step-by-step explanation:

Data

Yesterday Christopher sold 35 pounds of apples (35A) and 34 pounds of bananas (34B) for a total revenue of $163.5 (=163.50)

Today he sold 15 pounds of apples (15A) and 17 pounds of bananas (17B) for a total revenue of $76.75. (=76.75)

Now well, we have a system of the equation

35A+34B=163.50

15A+17B=76.75

we must eliminate A or B,  As you can see 34 is twice 17, so we multiply on both sides of the equation so as not to alter it

35A+34B=163.50                35A+34B=163.50                            

15A+17B=76.75 (-2) ⇒        -30A-34B=-153.50

                                              5A-0B = 10

5A=10 ⇒ A=10/5 ⇒ A=2

and B:

35(2)+34B=163.5 ⇒ 70+34B=163.5 ⇒ 34B=163.5-70

34B=93.5 = 93.5/34

B=2.75

Let x represent the price of each pound of apples and y represent the price of each pound of bananas.

Since 35 pounds of apples and 34 pounds of bananas for a total revenue of $163.50. Hence:

35x + 34y = 163.50      (1)

Also, 15 pounds of apples and 17 pounds of bananas for a total revenue of $76.75. Hence:

15x + 17y = 76.75        (2)

Solving equations 1 and 2 simultaneously gives x = 2, y = 2.75

The price of each pound of apples is $2 while price of each pound of banana is $2.75

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Answer:

24x − 8y

Step-by-step explanation:

8(3x-y)

apply distributive property;

1. 8 (3x) + 8 (−y)

multiply 3 by 8 ;

2. 24x + 8 (-y)

multiply -1 by 8;

3. 24x - 8y

Regroup terms ;

4. 24x − 8y

Answer:

the answer is 36 degrees

The difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.

Solution:

Length of Monarch butterfly = [tex]3\frac{1}{2}[/tex] in

Length of Bumble bee = [tex]\frac{5}{8}[/tex] in

Difference between their lengths

                                   [tex]=3\frac{1}{2}-\frac{5}{8}[/tex]

To convert mixed fraction into improper fraction.

                                    [tex]=\frac{7}{2}-\frac{5}{8}[/tex]

To make the denominator same, multiply and divide the first term by 4.

                                    [tex]=\frac{28}{8}-\frac{5}{8}[/tex]

                                   [tex]=\frac{23}{8}[/tex]

Difference between length of Monarchy and Bumble bee is [tex]\frac{23}{8}[/tex] in.

Length of Walking stick = 4 in

Length of Grasshopper = [tex]1\frac{3}{4}[/tex] in

Difference between their lengths

                                   [tex]=4-1\frac{3}{4}[/tex]

To convert mixed fraction into improper fraction.

                                    [tex]=\frac{4}{1}-\frac{7}{4}[/tex]

To make the denominator same, multiply and divide the first term by 4.

                                    [tex]=\frac{16}{4}-\frac{7}{4}[/tex]

                                   [tex]=\frac{9}{4}[/tex]

Difference between length of Walking stick and Grasshopper is [tex]\frac{9}{4}[/tex] in.

Compare: [tex]\frac{23}{8}[/tex] and [tex]\frac{9}{4}[/tex]

To compare the fractions, make the denominator same.

So multiply and divide [tex]\frac{9}{4}[/tex] by 2, we get

[tex]\frac{23}{8}[/tex] and [tex]\frac{18}{8}[/tex]

[tex]$\frac{23}{8}>\frac{18}{8}[/tex]

Hence the difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.

.answer:

120

step-by-step explanation:

10+10+10+10=40

8+8+8+8.     =32

12+12+12+12=48

add everything up (the numbers that we got) and you would get 120cm

Answer:

960

Step-by-step explanation:

You multiply the base x height x width. So you do 10 x 8 x 12 = 960 cm.

Answer:

0

Step-by-step explanation:

19z-19z=0

this is because z is always equivalent to itself, and therefore 19z is equivalent to 19z

When you subtract two numbers that are equivalent, you will always get 0

Answer:

  31.205

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  8.73 +12.4 +10.075 = 31.205

_____

If you're after an answer that has the appropriate precision (assuming these are measured values), that would be one that is rounded to 1 decimal place: 31.2.

Answer:

8y - 16

Step-by-step explanation:

Step 1:  Distribute

32 + 8(y - 6)

32 + 8y - 48

8y - 16

Answer:  8y - 16

If needed solve for y:

8y - 16 + 16 = 0 + 16

8y / 8 = 16 / 8

y = 2

Answer:

8y - 16  

Step-by-step explanation:

Answer:

C- 15 cars.

Step-by-step explanation:

To do this, you will need to set up an equation as follows:

8x+15=6x+45

Then you will subtract 6x from each side. Then you will have this:

2x+15=45

Then you will subtract 15 from each side, and then you will have:

2x=30

Then you will divide each side by 2 and you will get 15. Hope this helped!

Answer:

B. [tex]x\leq 8[/tex]

Step-by-step explanation:

[tex]3(x+4)\leq 36[/tex]

[tex]3x+12\leq 36[/tex]  use distributive property to multiply 3 by (x + 4)

[tex]3x+12\leq 36\\-12\leq -12\\3x\leq 24[/tex]  subtract 12 on both sides (cancel out 12)

[tex]3x\leq 24[/tex]

[tex]\frac{3x}{3} \leq \frac{24}{3}[/tex]  divide 3 on both sides (cancel out 3)

[tex]x\leq 8[/tex]

Answer:

x > 8

Step-by-step explanation:

-2x + 12 < -4 (Given)

-2x < -16 (Subtracted 12 on both sides.)

x > 8 (Divided by -2 on both sides.)

*Note that if you multiply or divide by a negative number, the sign will flip.*

The factored forms are [tex]\((p + 4c)(p - 4c - 1)\)[/tex] for the first expression and [tex]\(-(x - 7)(y - 7)\)[/tex] for the second expression.

Let's factor the given expressions:

1. [tex]\(p^2 - 16c^2 - p - 4c\)[/tex]:

  To factor this quadratic expression, we can use the difference of squares formula, [tex]\(a^2 - b^2 = (a + b)(a - b)\)[/tex]. In this case, [tex]\(p^2 - 16c^2\)[/tex] is a difference of squares, so we can factor it as [tex]\((p + 4c)(p - 4c)\)[/tex]. The remaining terms are [tex]\( - p - 4c\)[/tex], and thus, the factored form is [tex]\((p + 4c)(p - 4c) - (p + 4c)\)[/tex]. Factoring out the common factor of -1 from the last two terms gives us the final factored expression: [tex]\((p + 4c)(p - 4c - 1)\)[/tex].

2. [tex]\(x^2 - 7x + 7y - y^2\)[/tex]:

  This expression is a quadratic trinomial, and to factor it, we need to find two binomials whose product equals the given expression. The expression can be rewritten as [tex]\(x^2 - 7x - y^2 + 7y\)[/tex]. Now, we can group the terms as [tex]\((x^2 - 7x) - (y^2 - 7y)\)[/tex]. Factoring out \(x\) from the first group and y from the second group, we get [tex]\(x(x - 7) - y(y - 7)\)[/tex]. Now, we notice that both terms have a common factor of -1, so we can factor that out to obtain the final result: [tex]\(-(x - 7)(y - 7)\)[/tex].

The maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.

In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following x-intercept:

x-intercept = (200, 0)

In this context, we can logically conclude that the maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.

Complete Question:

A city pool sells full-day and half-day passes during the summer. The goal is to make $1000 each day from pool pass sales. The graph shows the number of full-day and half-day passes they need to sell to make $1000.

What is the maximum number of half-day passes the pool can sell and make exactly $1000?

Answer:

7.071 cm

Step-by-step explanation:

Final answer:

To find the length AG in the cuboid ABCDEFGH, use the three-dimensional Pythagorean theorem twice. First finding the diagonal AC (which is equal to 5 cm), and then using it to find AG. The length AG, to three significant figures, is approximately 7.07 cm.

Explanation:

The length AG of a cuboid ABCDEFGH can be found by using the Pythagorean theorem in three dimensions. This theorem is an extension of the traditional Pythagorean theorem used in two dimensions. For the given cuboid, we start by using the Pythagorean theorem on triangle ABC to find the diagonal AC. The formula for the Pythagorean theorem is:

c2 = a2 + b2

Where c is the diagonal and a and b are the sides of the right triangle:

AC2 = AB2 + BC2

Plugging in the given values, we have:

AC2 = 32 + 42 = 9 + 16 = 25

So, AC = 5 cm.

Now, to find AG, we use the diagonal AC and side CG in another application of the Pythagorean theorem for the right triangle ACG:

AG2 = AC2 + CG2

AG2 = 52 + 52 = 25 + 25 = 50

AG = √50 ≈ 7.071 approximately.

Therefore, the length AG, expressed to three significant figures, is approximately 7.07 cm.

Answer:

682,500 people

Step-by-step explanation:

so just find how many people per year it grows by then add that number 15 times to 300,000

so 8.5% of 300,000 is 25,500 people

now multiply that by 15 to get 382,500

add that to 300,000

Final answer:

Using the exponential growth formula, the population of a city with an initial population of 300,000 and an annual growth rate of 8.5% will be approximately 962,100 after 15 years.

Explanation:

To calculate the future population of a city with an initial population of 300,000 people and an annual growth rate of 8.5% over 15 years, we use the formula for exponential growth:

P = P_0 (1 + r)[tex]^{t}[/tex]

where:

P is the future population,

P_0 is the initial population (300,000),

r is the annual growth rate (expressed as a decimal, so 8.5% becomes 0.085), and

t is the number of years (15).

Substituting the values we get:

P = 300,000 (1 + 0.085)¹⁵

Calculating this, we find:

P = 300,000 (1.085)¹⁵

P = 300,000 (3.207)

P ≈ 962,100

Therefore, after 15 years, the population is expected to be approximately 962,100, rounding to the nearest whole number.

Answer: x=-9

Step-by-step explanation:

First, we want to isolate x by subtracting ten from both sides

4x=-36

Then divide by four to get:

X=-9

Answer:-6

Step-by-step explanation:

you'd want to subtract the ten and move it under the 26, adding to make a negative 36 then divide by 4 on both sides

Answer:

80cm^2/s

Step-by-step explanation:

This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.

So lets consider the area of a square:

A = s^2 (where s represents the length of one side of the square)

Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:

[tex]\frac{dA}{dt} = 2s(\frac{ds}{dt})[/tex]

The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:

[tex]\frac{dA}{dt} = 16s[/tex]

Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.

25 = s^2

s = +/- 5 (since side lengths are only positive we only consider +5)

s = 5

Now we can plug this back in for s:

[tex]\frac{dA}{dt} = 80[/tex]

Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.

Answer:

10.92m

Step-by-step explanation:

See attached picture for more illustration

Using SOH CAH TOA,

Tan 20° = opposite / adjacent

Tan 20° = x / 30

x = 30 * tan20

x = 10.919m = 10.92m

The height of the tree is 10.92m

Final answer:

The height of the cat in the tree is 10.44m

Explanation:

The question involves finding the height of a cat caught in a tree using trigonometry, specifically the tangent function. If the firefighter is standing 30m from the base of the tree and the angle to the cat is 20 minutes (which should be converted to degrees for typical trigonometric calculations), we can calculate the height of the cat in the tree. First, we need to convert the angle from minutes to degrees. Since 1 degree = 60 minutes, 20 minutes is equal to 20/60 degrees or approximately 0.33 degrees.

To find the height of the cat, we can use the tangent function (tan) in trigonometry, which is the ratio of the opposite side (the height of the cat in the tree, which we're trying to find) to the adjacent side (the distance from the firefighter to the base of the tree). Thus, the formula becomes height = tan(angle) × distance.

Using the formula:

distance = 30m

angle = 0.33 degrees

height = tan(0.33 degrees) × 30

Tan(20') x Distance

Calculating: Height = Tan(20') x 30m = 10.44m

The slope-intercept form is y = 2x-3.

Step-by-step explanation:

Given,

Comparing the given equation with general equation, it can be determined that :

m = 2 and c = 7 (y-intercept).

The given line passes through the point (3,3) which is equal to (x1,y1)

Therefore, x1=3 and y1=3.

Substitute m=2 and the values of (x1,y1) in the slope-intercept form,

The slope-intercept form is (y-y1) = m (x-x1)

(y-3) = 2(x-3)

y = 2x-6+3

y = 2x-3