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3 years ago

6

Olivia picked 482 apples from the orchard’s largest apple tree. She divided the apples evenly into 4 baskets. How many apples ar

e in each basket? How many are left over?

1 answer:

AleksandrR [38]3 years ago

4 0

Answer:

there are 120 apples in each basket and 5 are left over

Step-by-step explanation:

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2(4x - 8y) - 9x + 7 as a simplifying expression.

Alina [70]

Answer:

2(4x - 8y) - 9x + 7

8x - 16y - 9x + 7

-1x - 16y + 7

6 0

3 years ago

Find the solutions to the equation 102x 11 = (x 6)2 – 2. Which values are approximate solutions to the equation? Select two answ

otez555 [7]

You can try finding the roots of the given quadratic equation to get to the solution of the equation.

There are two solutions to the given quadratic equation

$x = 0.202, x = 113.798$

<h3>How to find the roots of a quadratic equation?</h3>

Suppose that the given quadratic equation is $ax^2 + bx +c = 0$

Then its roots are given as:

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

<h3>How to find the solution to the given equation?</h3>

First we will convert it in the aforesaid standard form.

$102x + 11 = (x-6)^2 - 2\\102x + 11 + 2 = x^2 + 36 - 12x\\0 = x^2 -114x + 23\\x^2 -114x + 23 = 0\\$

Thus, we have

a = 1. b = -114, c = 23

Using the formula for getting the roots of a quadratic equation,

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{114 \pm \sqrt{114^2 - 92}}{2} \\\\ x = 0.202 (\text{used "-" sign})\\\\x = 113.798 ( used "+" sign})$

Thus, there are two solutions to the given quadratic equation

$x = 0.202, x = 113.798$

Learn more here about quadratic equations here:

brainly.com/question/3358603

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3 years ago

Suppose two parallel lines are cut by a transversal. Which angles MUST be supplementary?

Fittoniya [83]

6 7, angle 6 is congruent to angle 7. At each of the parallel lines adjacent angles are supplementary. The angles have special names identifying their positions with respect to the parallel lines and transversal. They are corresponding angles, alternate interior angles, or alternate exterior angles.

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3 years ago

Read 2 more answers

The national average for the math portion of the College Board’s Scholastic Aptitude Test

Alex73 [517]

Answer:

a) 0.1587

b) 0.023

c) 0.341

d) 0.818

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 515

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(score greater than 615)

P(x > 615)

$P( x > 615) = P( z > \displaystyle\frac{615 - 515}{100}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,

$P(x > 615) = 1 - 0.8413 = 0.1587 = 15.87\%$

b) b) P(score greater than 715)

$P(x > 715) = P(z > \displaystyle\frac{715-515}{100}) = P(z > 2)\\\\P( z > 2) = 1 - P(z \leq 2)$

Calculating the value from the standard normal table we have,

$1 - 0.977 = 0.023 = 2.3\%\\P( x > 715) = 2.3\%$

c) P(score between 415 and 515)

$P(415 \leq x \leq 515) = P(\displaystyle\frac{415 - 515}{100} \leq z \leq \displaystyle\frac{515-515}{100}) = P(-1 \leq z \leq 0)\\\\= P(z \leq 0) - P(z < -1)\\= 0.500 - 0.159 = 0.341 = 34.1\%$

$P(415 \leq x \leq 515) = 34.1\%$

d) P(score between 315 and 615)

$P(315 \leq x \leq 615) = P(\displaystyle\frac{315 - 515}{100} \leq z \leq \displaystyle\frac{615-515}{100}) = P(-2 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -2)\\= 0.841 - 0.023 = 0.818 = 81.8\%$

$P(315 \leq x \leq 615) = 81.8\%$

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