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3 years ago

On the grid draw the graph of x + 2y =7

Mathematics

1 answer:

Elena-2011 [213]3 years ago

5 0

Answer:

See attachment for graph

Step-by-step explanation:

Given

$x + 2y = 7$

Required

Draw the graph

First, we identify at least 2 possible values of x and y

Let $x = 1$

Solve for y

$x + 2y = 7$

$1 + 2y = 7$

$2y = 6$

$y = 3$

So, a point is: $(1,3)$

Let $x = 3$

Solve for y

$x + 2y = 7$

$3 + 2y = 7$

$2y = 7 -3$

$2y = 4$

$y = 2$

So, another point is: $(3,2)$

Plot $(1,3)$  and  $(3,2)$  on the graph, then draw a straight line through both points

See attachment for graph

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Pi/24 is the solution for 4cos2 (4x) - 3 = 0 True or false

inessss [21]

Answer:

True.

Step-by-step explanation:

Given,

4cos2 (4x) - 3 = 0

Now, 4π/24 = π/6

Or, cos π/6 = √3/2

Or, cos^2 π/6 = 3/4

Or, 4 cos^2 π/6 = 3

Now, Left Hand Side= 4cos2 (4x) - 3

= 3-3 =0 = Right Hand Side (Proved)

Here, Left Hand Side= Right Hanad Side. So, 4cos2 (4x) - 3=0 is true.

5 0

2 years ago

Read 2 more answers

Roberto wants to display his 18 sports cards in an album . Some pages hold 2 cards and others hold 3 cards .

nexus9112 [7]

Answer:

Step-by-step explanation:

Assuming Roberto wants to completely fill each page that he puts cards in, this function describes the number of 2-card pages, a, and 3-card pages, b.

2a + 3b =18

Ricardo can fill up 9 2-card pages, and 6 3-card pages.

a=9, b=0

We must add 2 3-card pages at a time,so that we have an even number for the 2-card pages:

a=6, b=2

Add 2 to b once more:

a=3, b=4

One more time:

a=0, b=6:

Thus, Ricardo can display his figures in the following page combinations:

a=9, b=0

a=6, b=2

a=3, b=4

a=0, b=6

Remember that a= number of 2-card pages and b=number of 3-card pages

There are 4 different ways that Ricardo can arrange his figures in terms of what kind of pages he uses.

3 0

3 years ago

In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th

marysya [2.9K]

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}$

Where:

$\hat{p}$ is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

$z_{\alpha /2}$ is the critical value needed to find the tails of distribution related to the confidence level,

$n$ is the sample's size.

First we compute the $\hat{p}$ value:

$\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625$

Next we find the z-score at any z-distribution table or app (in this case i've used StatKey):

$z_{\alpha /2}=2.576$

Now we can replace in the formula with the obtained values to compute the confidence interval:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)$

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3 years ago

Comparing Leaking Pool Problem

Blababa [14]

Answer:

Pool 1 leaks faster than pool 2.

Step-by-step explanation:

Rates of change

The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.

We are given two rates of change for two pools that are leaking. The first one loses 2/3 gallon in 15 minutes, and the other loses 3/4 gallon in 20 minutes.

To compare them, we are required to express time in hours. Recall one hour has 60 minutes, or equivalently, one minute has 1/60 hours. Converting both times, we have:

15 minutes = 15/60 = 1/4 hours

20 minutes = 20/60 = 1/3 hours

Now compute both rates of change:

Pool 1:

$\displaystyle ROC_1=\frac{2/3}{1/4}=\frac{8}{3}\approx 2.67\ gal/h$

Pool 2:

$\displaystyle ROC_2=\frac{3/4}{1/3}=\frac{9}{4}= 2.25\ gal/h$

Comparing both ratios, it's clear pool 1 leaks faster than pool 2.

8 0

3 years ago

Tamara was asked to write an example of a linear functional relationship. She wrote this example:

Llana [10]

Answer:

Tamara's example is in fact an example that represents a linear functional relationship.

This is because the cost of baby-sitting is linearly related to the amount of hours the nany spend with the child: the more hours the nany spends with the child, the higher the cost of baby-sitting, and this relation is constant: for every extra hour the cost increases at a constant rate of $6.5.

If we want to represent the total cost of baby-sitting in a graph, taking the variable "y" as the total cost of baby-sitting and the variable "x" as the amount of hours the nany remains with the baby, y=5+6.5x (see the graph attached).
The relation is linear because the cost increases proportionally with the amount of hours ($6.5 per hour).
See table attached, were you can see the increses in total cost of baby sitting (y) when the amount of hours (x) increases.

8 0

3 years ago