Henry is making a recipe for biscuits. A recipe calls for 5/10 kilogram flour and 9/100 kilogram sugar .

What is the side length, in inches, of the pets

tatiyna

Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. What is the side length, in inches, of the pet shop sign?

Answer:

the length of the sign is $4x-5$ inches

Step-by-step explanation:

Given

Area of the square of design = $16x^{2} -40x+25$

First we find the roots of equation $16x^{2} -40x+25=0$

The roots of the quadratic equation $ax^{2} +bx^{2} +c=0$ are given by

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

where $a=16, b=-40, c=25$

$x=\frac{40\pm\sqrt{(-40)^2-4\times 16\times 25}}{2\times 16}$

$x=\frac{40\pm\sqrt{1600-1600}}{32}$

$x=\frac{40\pm\sqrt{0}}{32}$

$x=\frac{40}{32}$

$x=\frac{5}{4}$

$4x=5\\4x-5=0$

That is, the factors of the polynomial $16x^{2} -40x+25$ are $4x-5$ and $4x-5$ .

So, Area of the square design = $16x^{2} -40x+25$ = $(4x-5)^{2}$

Area of a square = Length^2

Thus, the length of the sign is $4x-5$ inches

7 0

3 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

8 0

3 years ago

What is located closest to the orgin

jeka94

The zero is closed to the origin

6 0

3 years ago

Read 2 more answers

Match the function to the correct parabola

Lisa [10]

Answer:

The box to the left will have the equation p(x) = 5x² and the box to the right will have the equation n(x) = $\frac{1}{5} x^{2}$

Step-by-step explanation:

The coefficient of the x² decides how wide or narrow a quadratic graph is. If the coefficient is a fraction of 1, the smaller the fraction the wider the graph gets. If the coefficient is a number bigger than 1, the bigger the number, the narrower the graph gets.

5 0

3 years ago

Drinking 8 fluid ounces of milk provides 270.0 milligrams of calcium. How many fluid ounces of milk provide 72.5 milligrams of c

olga nikolaevna [1]

I believe this is a problem dealing with proportions, so you could cross multiply and divide. so you would do 8/270 then x/72.5 , you cross multiply 72.5x8 which equals 580. then you divide that answer by 100 which equals 5.8 (:

6 0

3 years ago