The ratio of boys to girls in a school is 4:5. How many boys are in the school if there are 720 students.

Answer: x ≈ 18 ft

Step-by-step explanation:

We will use our trig knowledge to solve this.

The man is standing 10 ft away, but we also need to add the 5 ft shadow as well as that is a point on our triangle.

We can set up a simple trig equation of: tan(50) = x/15

x being the height of the lamppost.

Now we solve.

tan(50) = 1.1918

1.1918 *15 = x

x = 17.876

Now round to the nearest foot.

x ≈ 18 ft

Answer: The median of the date you gave would be -71. Hope that helps!

Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

[tex]r = \frac{1}{4}[/tex]

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

[tex]s_n=\frac{a_1(1-r^n)}{1-r}[/tex]

common ratio, n=4 and equate to 170.

[tex]\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170[/tex]

[tex]\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128[/tex]

Answer:

The first term is 128

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

Answer:

she needs to walk 6.5 kilometers more.

Step-by-step explanation:

8km/0.55 = 14.5454 - 8 = 6.5454 = 6.5km

The  lemonade does Rosanne'a brother drinks is  [tex]1\div 2[/tex] liter

The remaining should be

[tex]= (1\ 1\div 2) -(1\div 4) \\\\= 1\ 2\div 4 -1\div 4 \\\\= 1\ 1\div 4 \ liters[/tex]

Since The brother drinks 2/5 of that,

So,

[tex]= (2\div 5)(1\ 1\div 4 L) \\\\= (2\div 5)(5\div 4 L) \\\\= 2\div 4 L \\\\= 1\div 2 L[/tex]

learn more: https://brainly.com/question/13981855?referrer=searchResults

Answer: if we want to find a point of  17*m(x) + 2, one is (1, 155)

Step-by-step explanation:

I guess you want to know a point in the function

h(x) = 17*m(x) + 2

we know that m(1) = 9 (because m(x) has the point (1, 9) in it's graph)

then h(1) = 17*m(1) + 2 = 17*9 + 2 = 155

so this function has the point (1, 155)

Answer:

[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

98=49x2

7x7=49

98=[tex]7\sqrt{2}[/tex]

Answer: 3^3 = 27

Step-by-step explanation:

The formula is:

[tex]log_{3} 27=3[/tex] is just [tex]a^c=b\\a=logbase\\b=number\\c=answer\\\\3^3=27[/tex]

Answer:

[tex] {3}^{3} = 27 \\ [/tex]

Step-by-step explanation:

[tex] log_{a}(c) = b[/tex]

[tex] log_{3}(27) = 3[/tex]

so,

[tex] {3}^{3} = 27[/tex]

hope this helps you

brainliest appreciated

good luck! have a nice day!

Answer:3

Step-by-step explanation:720 (the amount he uses) and divide it by 240 (which is the amount to make one cake) and it gives you 3

Answer:

Step-by-step explanation:

Distributive  property

a(b - c) = ab - ac

3(x-4) = 3*x - 3*4  

         = 3x - 12

Answer:

the answer is A≈1639.91

Answer:

A≈1639.91

Step-by-step explanation:

Shape: Cylinder

Solved for surface area

Radius: 9

Height: 20

Total surface area formula: =2πrh+2πr2

R is the radius

H is the height

So for this question H is 20 and R is 9in

Answer: A≈1639.91

Hope this helps.

Answer:

the first one the both must have a right angle for it to be hl theorem

Answer:

Step-by-step explanation:

5) Perimeter = 15 + 21 + 15 + 21 = 72 cm

6) diameter = 12 cm

Radius r = 12/2 = 6 cm

Circumference = 2πr

                         = 2 * 3.14 * 6

                        = 37.68 cm

8) Distance around the track =  2 *circumference of semi circle + 80 + 80

= circumference of circle + 80 + 80

= 2 * 3.14 * 10 + 80 +80

= 62.8 +80 +80

= 222.8 cm

Answer:

A.

Step-by-step explanation:

The volume is LWH

L = 16

W = 9

H = 12

16 * 9 * 12 = 1728

Answer:

gallons of water = 38784 gallons

Step-by-step explanation:

He builds a pool in his backyard .The pool measures 16 yards long, 6 yards wide and 2 yards deep. The pool is a rectangular prism. The number of gallons it can take to fill the pool can be calculated when we know the volume of the pool. Therefore,

volume of the pool = length × width × height

volume = lwh

l = 16 yards

w = 6 yards

h = 2 yards

volume = 16 × 6 × 2

volume = 192 yards³

1 cubic yards = 202 gallons

192 cubic yards = ?  gallons

cross multiply

gallons of water = 192 × 202

gallons of water = 38784 gallons

Answer:

49°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

let x be the other exterior angle then sum and equate to 360

37 + 84 + 49 + 38 + 35 + 68 + x = 360

311 + x = 360 ( subtract 311 from both sides )

x = 49

The other exterior angle = 49°

Answer:

The coordinates of the point is (5.5, -2)

Step-by-step explanation:

Okay, what we want to do here is to get the point that divides the line that joins the points (3,3) to (7,-5) in the ratio 5 to 3

Generally, given the ratio a:b and we want to divide the line joining the points (x1,y1) and (x2,y2) in that ratio, we use the condensed formula below;

Let’s call the point dividing the line in the given ratio z.

The coordinates of Z is;

{(bx1 + ax2)/(a+b), (by1 + ay2)/(a+b)}

In this question (x1,y1) = (3,3)

While (x2,y2) = (7,-5)

while a:b = 5:3

Substituting these values into the coordinate equation for point z, we have ;

{((3(3) + 5(7))/(5+3), ((3)(3) + 5(-5))/(5+3)}

= {44/8 , -16/8} = {5.5, -2}

Answer:

72

Step-by-step explanation:

you start with 27

27 divided by three is 9

9 apples cut into 8 pieces each would be

72

Answer: Similar - AA

Just took the quiz, Its Similar AA not sure why just trust me homie

The two triangles are similar triangles by AA similarity theorem (Option A).

The AA similarity theorem proves that if two triangles have two pairs of angles that are congruent, then they are similar triangles.

The two triangles shown in the figure have two pairs of corresponding angles that are congruent to each other, therefore, they are similar triangles by AA similarity theorem (Option A).

Learn more about AA similarity theorem on:

https://brainly.com/question/2166570

Complete Question:

The enrollment at East Valley High School over a six-year period is displayed in the scatterplot. Student Enrollment at East Valley High School (1st picture)

Which is the equation of the line of best-fit for this scatterplot? (2nd picture)

Answer:

D) y = (81/2)x - (160,069/2)

Step-by-step Explanation:

From the scatter plot in the graph attached below, we are given the ordered pairs of the coordinates (2009, 1330), (2013, 1492), we can derive the equation of the line of best-fit for the scatter plot using the slope-intercept formula.

Thus, the slope-intercept formula is y = mx + b, where m is the slope of the line; and b is the y-intercept.

We need to find m, and then b to input into the formula to get our equation of the line.

==> Finding m using the two sets of coordinate given on the graph [ (2009, 1330) and (2013, 1492) ]:

slope (m) = (y2 - y1)/(x2 - x1)

m = (1492 - 1330)/(2013 - 2009)

= 162/4

m = 81/2

Next is to find b, which is the y-intercept

Recall, y = mx + b

Using one of the coordinates given (2009, 1330), we can find b by inputting 1330 for y, 2009 for x, and 81/2 for m in the slope-intercept formula:

Thus, we would have ==>

1330 = (81/2 * 2009) + b

1330 = (162,729/2) + b

1330 - 162,729/2 = b

(2,660 - 162,729)/2 = b

- 160,069/2 = b

Having known the values of m, and b, let's input their values to get the equation of the line.

Thus, using the slope-intercept formula y = mx + b, the equation of the line of best-fit for the scatter plot would be

==> y = (81/2)x +(-160,069/2)

y = (81/2)x - (160,069/2)

Answer:

d

Step-by-step explanation:

Answer:

5x + y

Step-by-step explanation:

4(2x + y) - 3(x + y) = 4*2x + 4y - 3x - 3y = 8x - 3x + 4y - 3y = 5x + y

Hello!

:[tex]\boxed{ \bf The~answer~is~5x~+~y}[/tex]

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

Multiply everything inside the brackets by the number outside.

= 8x + 4y - 3x - 3y

Next, combine like terms.

= 8x - 3x + 4y - 3y

= 5x + y

Answer:

no

Step-by-step explanation:

2 does not go into 35 but one goes into anything

hope this helps :)

Answer: 14, 16, 13,3.5, 50

Step-by-step explanation:

Basically, what you do is find half of each number in the number of customers column and yeah that's it.

Answer:

  c.  54.6°

Step-by-step explanation:

The Law of Cosines can be used to find the first of the unknown angles in a triangle with only three side lengths given.

  b² = a² +c² -2ac·cos(B)

Solving for B, we have ...

  2ac·cos(B) = a² +c² -b²

  B = arccos((a² +c² -b²)/(2ac)) = arccos((10.4² +21.9² -18²)/(2(10.4)(21.9)))

  B = arccos(0.579053) ≈ 54.6° . . . . . matches choice C

Answer:

C 54.6°

Step-by-step explanation:

Using cosine law:

18² = 10.4² + 21.9² - 2(10.4)(21.9)cosB

cosB = 2029/3504

B =54.6160711

Answer:

fourth one = 780

Step-by-step explanation:

-4-30-3 =-37

8/10-2 = -6/5

3(-92)+28 = 248

-26* -30 = 780

Answer:

This is the distributive property

Step-by-step explanation:

You use the distributive property to allocate a number outside of the parentheses to inside the parentheses.

For this example, they distributed a to both b and c making it a*b + a*c

This will result in the same answer:

3/5(-2 + 10/13) = 3/5*-2 + 3/5*10/13

3/5(-1.23..) = -6/5 + 30/65 (..= approx)

approximately- 0.74  = -0.74

Answer:

You can use a calculator to find all the tan, sin, cos values! Simply enter the number, for example, 52, then press the tan button! For question d, you are finding what number that decimal is the tangent of. Press the 2nd function on your calculator, and you can see that -1 beside the tan. Enter the decimal then use that button to find the reverse tangent.

tan52 = 1.2799

sin19 = 0.3256

cos34 = 0.8290

tan-1(0.9876) = 44.6426

To solve the conveyor belt problem, you'll have to use the sine of 15. (remember, sine = opposite/hypotenuse). Set up an equation:

sin15 = ?/12m

Use a calculator to find sin15, then you can solve it like algebra.

sin15 = ?/12m

sin15*12m = ?

0.2588*12m = ?

3.1056m = ?

Hope this helped :)