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3 years ago

Irunt

Mathematics

1 answer:

natita [175]3 years ago

8 0

Answer:

30 = 2x + 3y

Step-by-step explanation:

x is the number of pens bought and y is the number of notbooks bought you graph this and you get a graph that shows you all the combinations.

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the length of diagonal of a rectangular field is 23.7 m and one of its sides is 18.8 m. find the perimeter of the field.

katen-ka-za [31]

Answer:

Approximately 66.4 Meters

Step-by-step explanation:

So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.

$a^2+b^2=c^2$

Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.

$(18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}$

Therefore, the length is 14.4 meters. Now, find the perimeter:

$P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}$

7 0

3 years ago

In a spelling bee, Anish's placement is both the 11th highest and the 25th lowest among all the spellers who participated. How m

Vlad [161]

Answer: There are 35 spellers participated in the spelling bee.

Step-by-step explanation:

Since we have given that

Rank of Anish's placement at the highest = 11 th

Rank of Anish's placement at the lowest = 25 th

We need to find the number of spellers participated in the spelling bee.

So, Number of spellers participated in the spelling bee is given by

Highest + Lowest - 1

= 11 + 25 - 1

= 36 - 1

= 35

Hence, there are 35 spellers participated in the spelling bee.

4 0

3 years ago

In the diagram, JOK and MON are straight lines. Angle NOP and Angle NOQ are complimentary angles. Calculate the value of x - y.

Pepsi [2]

Answer:

x - y = 118

Step-by-step explanation:

Since ∠ NOP and ∠ NOQ are complimentary then ∠ POQ = 90°

Since JOK is a straight line then

∠ JOP + ∠ POQ + ∠ QOK = 180 , that is

76 + 90 + y = 180

166 + y = 180 ( subtract 166 from both sides )

y = 14

Since MON is a straight line then

∠ MOK + ∠ KOQ + ∠ QON = 180, that is

x + 14 + 34 = 180

x + 48 = 180 ( subtract 48 from both sides )

x = 132

Thus

x - y = 132 - 14 = 118

5 0

3 years ago

An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

3 years ago

A gum ball machine has 6 red gum balls, 3 green gum balls, and 5 blue gum balls. What is the probability that the next gum ball

lord [1]

Answer:

Step-by-step explanation:

P(red gum ball)= 6/14=3/7

6/14 can be simplified to 3/7 by dividing by 2. 6/2=3. 14/2=7.

P(red gum ball)=3/7

7 0

3 years ago