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3 years ago

Lucia draws a square and plots the center of the square. (image)

Mathematics

1 answer:

ss7ja [257]3 years ago

8 0

Answer:

Step-by-step explanation:

Lucia's claim is correct since any rotation that is a multiple of 45° carries a square onto itself

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What is 1 1/3 times 2 1/3

svp [43]

3.11 is the answer for 11/3 times 2 1/3

6 0

3 years ago

Write the equation in POINT-SLOPE FORM of the line that passes throught (5,9) and has a slope of -7.

Debora [2.8K]

Answer:

The equation of line with slope -7 passing through (5,9) in point-slope form is:

$y-9 = -7(x-5)$

Step-by-step explanation:

Given

Slope of line = m = -7

Point = (5,9)

The point slope form of equation is obtained from a point and slope. It is given by the equation:

$y-y_1 = m(x-x_1)$

We know that (x1,y1) = (5,9)

Putting the values we get

$y-9 = -7(x-5)$

Hence,

The equation of line with slope -7 passing through (5,9) in point-slope form is:

$y-9 = -7(x-5)$

4 0

3 years ago

A bank is investigating ways to entice customers to charge more on their credit cards. (Banks earn a fee from the merchant on ea

MAVERICK [17]

Answer:

$CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\$

$CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )$

The correct answer choice is a. (62.2, 113.8)

Step-by-step explanation:

Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225.

Sample size = n₁ = 500

Sample mean = x₁ = $527

Standard deviation = s₁ = $225

Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189

Sample size = n₂ = 500

Sample mean = x₂ = $439

Standard deviation = s₂ = $189

We are asked to find the 95% confidence interval for the difference between two means.

The given group of answer choices are

a. (62.2, 113.8)

b. (86.2, 120.5)

c. (10.3, 23.8)

d. (55.6, 67.8)

The confidence interval for the difference between two means is given by

$CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\$

Where $\bar{x_{1} }$ and $\bar{x_{2} }$ are the given sample means and margin of error is given by

$MoE = z_{\alpha/2} \cdot \sqrt{\frac{s_{1}^2}{n_1} + \frac{s_{2}^2}{n_2}}$

The z-score corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table at α = 0.025 the z-score is 1.96

$MoE = 1.96 \cdot \sqrt{\frac{225^2}{500} + \frac{189^2}{500}}$

$MoE = 1.96 \cdot 13.14$

$MoE = 25.75$

Finally,

$CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\$

$CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )$

Therefore, the correct answer choice is a. (62.2, 113.8)

How to use z-table?

In the z-table find the probability of 0.025

Note down the value of that row, it would be 1.9.

Note down the value of that column, it would be 0.06.

Add the two numbers together.

The z-score is 1.9 + 0.06 = 1.96

4 0

4 years ago

Is the golden ratio a coincidence or grand design

DENIUS [597]

The Golden number is one of the roots of x²-x-1=0 and x = (1+√5)/2= 1.618
It's just a mathematical constant you can come across in trigonometry, geometry, sequence like Fibonacci and others. You may find it in fractals also and in many shapes in the nature but not necessarily always true.

It might be a coincidence in some natural shapes, but definitely it is a recognized math contant useful in many math domains

3 0

3 years ago

If tñ=2ñ+3, find S10

Allisa [31]

Answer:

$S_{10}=280$