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marta [7]
3 years ago
5

There are 420 students in kindergarten through third grade if 1/4 of the students are in first grade 20% are in the second grade

and 115 students are in the third grade how many students are in kindergarten explain
Mathematics
2 answers:
Sedbober [7]3 years ago
7 0
Let x be kindergarten students

x = 420 - [(0.25*420) + (0.2*420)+115]

x= 420 - (105 + 84 + 115)

x= 420 - 304

x= 116 kindergarten students
Oduvanchick [21]3 years ago
5 0
The answer would be around 120
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natita [175]
Y=16*2 -c*2
y=32-2c
y=-2c+32
c= - (y-32)/2
8 0
3 years ago
I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.
Amiraneli [1.4K]

Answer:  a) zeros: x = {0, 4, -2}

               b) as x → ∞,  y → ∞

                   as x → -∞,  y → ∞

<u>Step-by-step explanation:</u>

I think you mean (a) find the zeros and (b) describe the end behavior

(a) Find the zeros by setting each factor equal to zero and solving for x:

      x (x - 4) (x + 2)⁴ = 0

  • x = 0   Multiplicity of 1  --> odd multiplicity so it crosses the x-axis
  • x = 4  Multiplicity of 1  --> odd multiplicity so it crosses the x-axis
  • x = -2 <u>Multiplicity of 4 </u> --> even multiplicity so it touches the x-axis

                       Degree  =  6

(b) End behavior is determined by the following two criteria:

  1. Sign of Leading Coefficient (Right side): Positive is ↑, Negative is ↓
  2. Degree (Left side): Even is same direction as right side, Odd is opposite direction of right side

Sign of the leading coefficient is Positive so right side goes UP

                                                                        as x → ∞,  y → ∞

Degree of 6 is Even so Left side is the same direction as right (UP)

                                                                        as x → -∞,  y → ∞

7 0
3 years ago
A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum
Ivan

Answer:

Differential equation

\frac{dy}{dt} =ky(1-y)

Solution

y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

\frac{dy}{dt} =ky(1-y)

Solving the differential equation

\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}

Initial conditions:

y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48

The rumor reaches 80% at 8.48 days.

8 0
3 years ago
Three girls download a total of 36 songs on their iPods. Jane downloaded twice as many as Inez and since Tracy wanted to have th
lesya692 [45]
J + i + t = 36
j = 2i
t = j + 1.....t = 2i + 1

(2i + 1) + i + (2i) = 36
5i + 1 = 36
5i = 36 - 1
5i = 35
i = 35/5
i = 7 <=== Inez downloaded 7 songs

j = 2i = 2(7) = 14 <==Jane downloaded 14 songs
t = 2i + 1 = 2(7) + 1 = 15 <== Tracy downloaded 15 songs

7 0
3 years ago
angle A is a compliment of angle b and m angle b = (6-5x) degrees and m angle a =(7-2x)degrees find m angle a
Anuta_ua [19.1K]

Answer:

61

Step-by-step explanation:

A + B = 90

6 - 5x + 7 - 2x = 90

13 - 7x = 90

- 7x = 90 - 13

- 7x = 77

- x = 77 / 7

x = - 11

A: 6 - (5 * - 11) = 6 + 55 = 61

B: 7 - (2 * -11)  = 7 + 22 = 29

Together they equal 90 as they should.

7 0
3 years ago
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