Noor wants to spend less than $20 on condiments. Each kilogram of salt costs $1.50, and each kilogram of pepper costs 2.50.

Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1); dot(w); dot(x); dot(y); do

grandymaker [24]

Answer:

a=7

Step-by-step explanation:

The image is rendered and attached below.

Triangle WXY is an Isosceles right triangle, since WX=XY.

First, we determine the length of WY using Pythagoras Theorem.

$WY=\sqrt{4^2+4^2}\\WY=\sqrt{32}$

Since triangle WXY is Isosceles, $\angle XYW=45^\circ$

$\angle XYZ=\angle XYW+\angle WYZ\\135^\circ=45^\circ+\angle WYZ\\\angle WYZ=135^\circ-45^\circ=90^\circ$

Therefore:

Triangle WYZ is a right triangle with WZ as the hypothenuse.

Applying Pythagoras Theorem

$WZ^2=WY^2+YZ^2\\9^2=(\sqrt{32})^2+a^2\\a^2=81-32\\a^2=49\\a^2=7^2\\$Therefore: a=7$

3 0

2 years ago

Mr. Walker asked his students to use the associative property to find an expression that is equivalent to (13 + 15 + 20) + (20 +

kaheart [24]

Answer:

The correct option is four.

Step-by-step explanation:

The associative property implies that the values are added however we want, i.e. the numbers can be grouped in any way and the answer would still be the same.

The associative property of addition is:

$(a+b)+c=a+(b+c)$

The expression provided is:

(13 + 15 + 20) + (20 + 47 + 18)

The answer provided by four students are:

Jeremy : (20 + 13 + 15) + (20 + 47 + 18)

Layla : (20 + 47 + 18) + (13 + 15 + 20)

Keith : (13 + 20) + (20 + 47 + 18) + 15

Melinda : (13 + 15 + 20 + 20) + (47 + 18)

So, all the four students correctly applied only the associative property to rewrite the expression.

The correct option is four.

6 0

1 year ago

Read 2 more answers

A belt and a wallet cost $42 while 7 belts and 4 wallets cost $213. Calculate the cost of each item.

Fittoniya [83]

Let, the cost of a belt = x
cost of a wallet = y

Then, system of equations would be:
x + y = 42
7x + 4y = 213

Multiply 1st equation by 4,
4x + 4y = 168
Substitute it from 2nd equation,
3x = 45
x = 15

Now, substitute it in 1st equation,
15 + y = 42
y = 42 - 15 = 27

In short, Belt costs $15 and wallet costs $27

Hope this helps!

3 0

2 years ago

Read 2 more answers

A production line operates with a mean filling weight of 16 ounces per container. Overfilling or underfilling presents a serious

Dominik [7]

Answer:

Part1) $z=\frac{16.32-16}{\frac{0.8}{\sqrt{30}}}=2.191$

$p_v =2*P(Z>2.191)=0.0284$

Readjustment is needed

Part 2) $z=\frac{15.82-16}{\frac{0.8}{\sqrt{30}}}=-1.232$

$z=\frac{15.82-16}{\frac{0.8}{\sqrt{30}}}=-1.232$

$p_v =2*P(Z$

No readjustment is needed

Step-by-step explanation:

Data given and notation

Part 1

$\bar X=16.32$ represent the sample mean

$\sigma=0.8$ represent the population standard deviation

$n=30$ sample size

$\mu_o =16$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to apply a two tailed test.

What are H0 and Ha for this study?

Null hypothesis: $\mu =16$

Alternative hypothesis : $\mu \neq 16$

Compute the test statistic

The statistic for this case is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{16.32-16}{\frac{0.8}{\sqrt{30}}}=2.191$

Give the appropriate conclusion for the test

Since is a two tailed test the p value would be:

$p_v =2*P(Z>2.191)=0.0284$

Using the value of $\alpha =0.05$ we see that $pv$ and we have enough evidence to reject the null hypothesis.