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3 years ago

The quotient of two numbers is 4 and their difference is 39. What is the smaller number of the two?

Mathematics

1 answer:

MatroZZZ [7]3 years ago

3 0

Answer:

Step-by-step explanation:

x/y = 4

x=4y

x - y = 39

4y - y = 39

3y = 39

y= 13

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3 years ago

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A sample of students from an introductory psychology class were polled regarding the number of hours they spent studying for the

Anni [7]

Answer:

$8.68,13.16$

Step-by-step explanation:

Hint- First we have to calculate the mean and standard deviation of the sample and then applying formula for confidence interval we can get the values.

Mean of the sample is,

$\mu=\dfrac{\sum _{i=1}^{24}a_i}{24}=\dfrac{262}{24}=10.92$

Standard deviation of the sample is,

$\sigma =\sqrt{\dfrac{\sum _{i=1}^{24}\left(x_i-10.92\right)^2}{24-1}}=5.6$

The confidence interval will be,

$=\mu \pm Z\dfrac{\sigma}{\sqrt{n}}$

Here,

Z for 95% confidence interval is 1.96, and n is sample size which is 24.

Putting the values,

$=10.92 \pm 1.96\cdot \dfrac{5.6}{\sqrt{24}}$

$=10.92 \pm 2.24$

$=8.68,13.16$

Confidence interval is used to express the degree of uncertainty associated with a sample.

95% confidence interval means that if we used the same sampling method to select different samples and calculate an interval, we would expect the true population parameter to fall within the interval for 95% of the time.

5 0

3 years ago

Find the Area. Simplify your answer.

Vaselesa [24]

Answer:

Area = $9x^2$ square units

Step-by-step explanation:

<u>Key skills needed: Area of a parallelogram</u>

1) This shape is a parallelogram, and the way to find the area of a parallelogram is:

$A = bh$

A = area

b = base (the side at the bottom

h = the height ( the length that runs from one side to another and makes a right angle)

2) The base (b) would be 3x. The height (h) would also be 3x

3) This means A = $3x(3x)$

3 times 3 is 9 --> and x times x is $x^2$

Therefore the area is --> $9x^2$

<em>Hope you understood and have a nice day!! :D</em>

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3 years ago

In the above figure (not drawn to scale), Find ∠AEC.

n200080 [17]

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

$m\angle AEC=\frac{110^o+40^o}{2}$