Kristen spent many days at the community pool last summer. She noticed that five out of fourteen flying insects she saw at the pool were mayflies. If Kristen saw fourteen flying insects at the pool one day, how many were mayflies? If, over several days, Kristen saw forty two flying insects, how many were mayflies? If, over a few weeks, Kristen saw thirty mayflies, how many flying insects did she see?

Answers

Answer 1

Answer:

(a) 5 mayflies

(b) 15 mayflies

(c) 84 flying flies

Step-by-step explanation:

Represent Mayflies with M and the total flying insects with F

The ratio can be represented as:

[tex]M : F = 5 : 14[/tex]

Solving (a):

[tex]F = 14[/tex]

Find M

Substitute 14 for F in [tex]M : F = 5 : 14[/tex]

[tex]M : 14 = 5 : 14[/tex]

Convert to fraction

[tex]\frac{M}{14} = \frac{5}{14}[/tex]

Multiply through by 14

[tex]14 * \frac{M}{14} = \frac{5}{14} * 14[/tex]

[tex]M = 5[/tex]

Solving (b):

[tex]F = 42[/tex]

Find M

Substitute 42 for F in [tex]M : F = 5 : 14[/tex]

[tex]M : 42 = 5 : 14[/tex]

Convert to fraction

[tex]\frac{M}{42} = \frac{5}{14}[/tex]

Multiply through by 42

[tex]42 * \frac{M}{42} = \frac{5}{14} * 42[/tex]

[tex]M = \frac{5}{14} * 42[/tex]

[tex]M=5*3[/tex]

[tex]M= 15[/tex]

Solving (c):

[tex]M = 30[/tex]

Find F

Substitute 30 for M in [tex]M : F = 5 : 14[/tex]

[tex]30 : F = 5 : 14[/tex]

Convert to fraction

[tex]\frac{F}{30} = \frac{14}{5}[/tex]

Multiply through by 30

[tex]30 * \frac{F}{30} = \frac{14}{5} * 30[/tex]

[tex]F = \frac{14}{5} * 30[/tex]

[tex]F = 14*6[/tex]

[tex]F = 84[/tex]


Related Questions

Can someone help with this?

Answers

Answer:

Its the second one

Step-by-step explanation

the reason why is because

<= less than- so it goes to the left and since its not less than or equal to its an open circle instead of a closed circle.

A game room has a floor that is 350 feet by 40 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing? Enter your answer as length by width.

Answers

Answer:

70 by 8?

Step-by-step explanation:

lmk if its right lol..

someone please help

f(x) = 2x2 - 5
and
g(x) = 5x + 7
Find
f(g(x)) = [ ? ]x2 +[ ]x + [ ]

Answers

9514 1404 393

Answer:

  f(g(x)) = 50x² +140x +93

Step-by-step explanation:

Put the function argument in place of x and simplify.

  f(g(x)) = f(5x+7) = 2(5x+7)² -5

  = 2(25x² +70x +49) -5

  f(g(x)) = 50x² +140x +93

_____

We took advantage of the knowledge that ...

  (a + b)² = a² +2ab +b² . . . . . where a=5x and b=7

Alonzo's game started at 9:20 AM.
The game lasted 2 hours and 15 minutes.
What time did the game end?

Answers

Answer:

11:35 AM

Step-by-step explanation:

Lets start with the hours:

9+2=11

Now the minutes:

15+20=35

Now put them together:

11:35 AM

Answer:

11:35

Step-by-step explanation:

9 plus 2 equals 11

20+15 equals 35

Part 3 of i need these

Answers

Answer:

x=11

a=116°

b=29°

c=35°

hope is helpful

Which of the equations can be used to solve for the value of X?

A. 2x = 52
B. 2x + 54 = 90
C. 2x + 52 = 180
D. 2x + 52 + 90 = 180

Answers

Answer:

The answer is A.

the angles are opposite angles, therefore they have the same value. they're equal to each other. you set them equal to each other to find the value of x.

Step-by-step explanation:

i hope this helps :)

How do I do this/solve help me if you know it!

Answers

Answer:

it should be B, sorry if im wrong! :(

Step-by-step explanation:

A baker evenly divides 55 muffins into 9 boxes.
Each box contains
muffins and
muffins remain.

Answers

Answer:

each box has 6 muffins and 1 remains

hope this helps! :)

6 muffins in each box with one remaining

A rope was tied up so that it was only 7 inches long. When the rope is untied, it is 4 times as long. How many inches long is the rope when it is untied?

Answers

Answer:

28 inches long

Step-by-step explanation:

just multiply 7 and 4

If the rope is 6 inches long when tied than you would do 7 times 4 and get 28 inches or 2 ft and 4 inches

The graph of cosine function has an amplitude of 4 and a period of 3x find an equation in the form of y=a cos bx

Answers

Answer: f(x) = 4*cos(x*2*pi/3)

Where I assumed that the period is 3, instead of 3x

Step-by-step explanation:

In a general equation like:

f(x) = a*cos(b*x)

a is the amplitude.

b is the angular frequency, which is equal to two pi times the inverse of the period.

In this case, we know that the amplitude is 4, then a = 4.

And the period is 3x (i guess that this is wrong because the period should not depend on the variable, as we will see later), then the frequency is:

b = 2*pi/3x

Replacing these in the equation we get:

f(x) = 4*cos(x*2*pi/3x) = 4*cos(2*pi/3)

Then we have no longer a dependence on x.

If the period is equal to 3, then the frequency will be:

b = 2*pi/3

Then the equation now is

f(x) = 4*cos(x*2*pi/3)

This is a cosine function, as we wanted.

Perform the indicated operation. State the domain restrictions

Answers

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Domain has all values of x ( think X marks the spot on your domain) so the restrictions come in those cases from the fact that a fraction can NOT have the denominator 0 because dividing by 0 is not allowed.

5.

here x+1 [tex]\neq[/tex] 0 and x+3 [tex]\neq[/tex] 0 so the domain restrictions are x [tex]\neq[/tex] -1 and x[tex]\neq[/tex] -3

to solve you need to factor x^2 -6x-27

you can do it by using  

x^2 - Sx +P = 0 where S= root 1 +root 2 and P = root 1*root2

so in our case Sum has to be 6 and Product -27, what 2 numbers add to 6 and their product is -27? ....-3 and 9; S= -3+9 = 6 and P= -3*9 = -27

it will factor in (x-root 1) (x-root 2)  

x^2 -6x-27 = (x+3)(x-9)

[tex]\frac{(x+3)(x-9)}{x+1} * \frac{x+1}{x+3} =\\[/tex]

simplify x+1 and x+3

x-9

1 1/2 - (5/6x + 1/3) = 8/9 Really urgent pls help

Answers

Answer:

x = 1/3

Step-by-step explanation:

Rewrite the mixed number 1 1/2 as 1 9/18.  The denominator here is 18, which is the smallest number divisible by 2, 6, 3 and 9.  Then we have:

1 9/18  -(15/18)x - 6/18 = 16/18

or:

27/18 -(15/18)x = 22/18

Clear this of fractions by multiplying all terms by 18:

27 - 15x = 22, or

5 = 15x, or

x = 5/15, or x = 1/3

The value of the equation x = 1/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

1 1/2 - [ ( 5/6 )x + 1/3 ] = 8/9   be equation (1)

On simplifying the equation , we get

3/2 - ( 5/6 )x - 1/3 = 8/9

Adding (5/6)x on both sides of the equation , we get

( 5/6 )x + 8/9 = ( 7/6 )

Subtracting 8/9 on both sides of the equation , we get

( 5/6 )x = ( 7/6 ) - ( 8/9 )

( 5/6 )x = ( 63 - 48 ) / 54

Multiply by ( 6/5 ) on both sides of the equation , we get

x = ( 15/54 ) x ( 6/5 )

x = 3/9

x = 1/3

Hence , the value of the equation is x = 1/3

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

A jar black beans and pinto beans in a ratio of 1 : 4, and 180 of the beans are black beans. How many beans in total are there in the jar?

Answers

Answer:

720 beans in total

Step-by-step explanation:

I would set this up with proportions, so-

1             180

4             x

Then cross multiply-

4 x 180 = 720

Divide-

720/1 = 720

720 is your answer

solve the inequality j + 6 < 9​

Answers

J < 3 hope this helps

Please help!! Thank you so much

Answers

Answer:

I think answer is

b. (2,1)

:-)

11) Write an equation of the line that passes through the point (–7, –9) with slope –4.

A. y+7=−4(x+9)
B. y+9=4(x+7)
C. y+9=−4(x+7)
D. y+7=4(x+9)

Answers

Answer:

C

I am asian and a jedi master

is it A B C or D o just need help with that ​

Answers

Answer:

B

Step-by-step explanation:

B I already did this! Hope it helps!

What is the product?
[-3 4 2 -5] x [3 -2 1 0]

Answers

Answer:

Answer is C

Step-by-step explanation:

When you multiply the numbers you get the answer.

Answer:

The correct answer is A. I took the test.

For the following system of equations, the value of x is______

The system of equation is x + 3y = 6
6x - 6y = 4


PLEASE HELP!!

Answers

x=6-3y then the other would be x=(4+6y)/6

Answer: x = 2, y = 4/2

Step-by-step explanation:

Solve the System of Equations

x + 3y = 6 6x − 6y = 4

Subtract 3y from both sides of the equation.

x = 6 − 3y 6x − 6y = 4

Replace all occurrences of x with 6 − 3y in each e quation.

Replace all occurrences of x in 6x − 6y = 4 with 6 − 3y.

6 (6 − 3y) − 6y = 4

x = 6 − 3y

Simplify 6 (6 − 3y) − 6y.

36 − 24y = 4

x = 6 − 3y

Solve for y in the first equation.

Move all terms not containing y to the right side of the equation.

−24y = −32

x = 6 − 3y

Divide each term by −24 and simplify.

y = 4/3

x = 6 − 3y

Replace all occurrences of y with 4/3 in each equation.

 

Replace all occurrences of y in x = 6 − 3y with 4/3

x = 6 − 3 ( 3 )

y= 4/3

Simplify 6 − 3 ( 4 )

x = 2  

y = 4/3

The solution to the system is the complete set of ordered pairs that are valid solutions.

(2, 4 /3 )

The result can be shown in multiple forms.

Point Form:  2, 4 /3

Equation Form:  x = 2, y = 3

Help ill mark u brainliest

Answers

answer:

8x - 16 + 5x + 15 = 90

and

8x - 6 + 18x + 4 = 180

Solve for the variable.
1. 78 = x - 11

Answers

Answer:

x = 89

Step-by-step explanation:

78 = x - 11

add 11 to both sides of the equation

78 + 11 = x - 11 + 11

78 + 11 = x

89 = x

Answer:

x = 89

Step-by-step explanation:

78 = x - 11

+ 11 = +11 <— we add 11 since we are doing inverse operation

89 = x

i need help with geometry

Answers

Answer:

AAS only

Step-by-step explanation:

vertical angle


What is the radical form of the expression
2 3/4

Answers

this is the answer i didn’t know how to type the answer
Top comment is correct

help please help. help help​

Answers

Answer:

Step-by-step explanation:

10 students participated in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz

Solution: Number of girls = x

Number of boys = y

x + y = 10 -------------------(I)

Number of girls is 4 more than the number of boys

x - y = 4 ----------------------(I)

  x =  4 + y

Substitute x = 4 +y in equation (I)

4+ y + y = 10

4  + 2y = 10

       2y = 10-4

       2y= 6

          y = 6/2

y = 3

Plug in y = 3 in eqution (I)

x + 3 = 10

        x = 10 - 3

x = 7

Number of girls = 7

Number of boys = 3

What is the equation of the line that passes through the point (-3,4) and has a slope of zero?

Answers

Answer:

y = x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1, thus

y = x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = x + 7 ← equation of line

Hope this helps.

11. UZ, VX, and TW are medians of Triangle TUV. If UZ = 21, find UY.​

Answers

Answer:

UY = 14

Step-by-step explanation:

The median of a triangle is the segment that joins a vertex and the midpoint of the side opposite to this vertex.The point of intersection of the medians of a triangle, divide each median at ratio 2: 1 from the vertex

In the given figure

∵ TUV is a triangle

UZ, VX, and TW are medians

∵ UZ ∩ VX ∩ TW at point Y

∴ Y is the point of intersection of the 3 medians

→ By using the 2nd rule above

∵ The point Y divide UZ at the ratio of 2: 1 from the vertex U

UY: YZ = 2: 1

∴ [tex]\frac{UY}{YZ}[/tex] = [tex]\frac{2}{1}[/tex]

→ By using cross multiplication

∵ UY × 1 = YZ × 2

UY = 2YZ

UZ = UY + YZ

∴ UZ = 2 + 1 = 3 parts

∵ UY = 2 parts

∴ [tex]\frac{UY}{UZ}[/tex] = [tex]\frac{2}{3}[/tex]

→ Multiply both sides by UZ

UY =  [tex]\frac{2}{3}[/tex] UZ

∵ UZ = 21

∴ UY =  [tex]\frac{2}{3}[/tex] (21)

UY = 14

please solve.
-7 = z over 2 + 1

Answers

Answer:

wdym by this I can solve it just type it properly or take a screenshot

Step-by-step explanation:

A car rental company’s standard charge includes an initial fee plus an additional fee for each mile driven. the standard charge S (in dollars) is given by the function S = 0.40M +18.95, where M is the number of miles driven.
The company also offers an option to ensure the car against damage. The insurance charge I (in dollars) is given by the function I= 0.15 M + 5.70
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
C=
What does ac equal?? ^^

Answers

Answer:

C=0.55M+24.65

Step-by-step explanation:

0.40M+0.15M=0.55M

18.95+5.70=24.65

VOO AM
advwritingsystemsquiz (1)
Jan 28, 2021 at 11:04 AM
Two numbers add to 154. The same two numbers have a difference of 24.
match the situationO

Answers

Answer:

The answer is 44! The answer is 44!

Step-by-step explanation:

The answer is 44!

Reduce to simplest form.
-7/12 +3/8

Answers

Answer:

ok so you should get -5/24 in simplest form.

Decimal form- -0.2083 repeating

Step-by-step explanation:

Hope this helped :)

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