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4 years ago

9

Lin was waiting to check out at a store. She estimated her total bill to be $20. The actual total was $24.16. What is the differ

ence between Lin’s estimate and the actual total?

1 answer:

ziro4ka [17]4 years ago

4 0

Answer

$4.16

Step-by-step explanation:

24.16-20=4.16

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What is the value of x, if 105% of 90 is equal to 200% of x?

lisov135 [29]

From the given equation

105% * 90 = 200% * x

105/100 * 90 = 200/100 * x

105*90 = 200*x

x = 105*90/200

X = 21*9/4

X = 189/4

x = 47.25

Value of x = 47.25 or 47 1/4

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4 years ago

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Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

AC = 2 x XY
CB = 2 x YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x XY

CB = 2 x YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A - given

Then ∠X and ∠Z are said to becomplementary angles

Since m∠Z = 90° - m∠X -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5 seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

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2 years ago

For a normal distribution with μ=500 and σ=100, what is the minimum score necessary to be in the top 60% of the distribution?

STatiana [176]

Answer:

475.

Step-by-step explanation:

We have been given that for a normal distribution with μ=500 and σ=100. We are asked to find the minimum score that is necessary to be in the top 60% of the distribution.

We will use z-score formula and normal distribution table to solve our given problem.

$z=\frac{x-\mu}{\sigma}$

Top 60% means greater than 40%.

Let us find z-score corresponding to normal score to 40% or 0.40.

Using normal distribution table, we got a z-score of $-0.25$ .

Upon substituting our given values in z-score formula, we will get:

$-0.25=\frac{x-500}{100}$

$-0.25*100=\frac{x-500}{100}*100$

$-25=x-500$

$-25+500=x-500+500$

$x=475$

Therefore, the minimum score necessary to be in the top 60% of the distribution is 475.

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3 years ago

Which is the graph of y= [X] - 2?

Vera_Pavlovna [14]

Answer:

The third one from left

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3 years ago

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Find the midpoint of the line segment JK if j (4,6) and k(0,-4)

Snowcat [4.5K]

Answer:

$(2,1)$

General Formulas and Concepts:

Order of Operations: BPEMDAS

Midpoint Formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

<u>Step 1: Define points</u>

J (4, 6)

K (0, -4)

<u>Step 2: Find midpoint</u>

Substitute: $(\frac{4+0}{2},\frac{6-4}{2})$
Add/Subtract: $(\frac{4}{2},\frac{2}{2})$
Divide: $(2,1)$

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3 years ago