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3 years ago

The cost of a fridge has increased by 15% to £828 Work out the original price

2 answers:

6 0

Let the original price be x. Now you'll have to pay x plus 15% of x for the same refrigerator. This is equivalent to 1.15x=£828. Solve this equation for x and you'll then have your answer. Be certain to include the correct unit of measurement (<span>£).</span>

Afina-wow [57]3 years ago

4 0

Muliply .15 to 828 and get your answer the add it to 828

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Which expression is equivalent to (5^-2)(5^-1)

nadya68 [22]

The rule for multiplying similar bases with exponents:

(a^b)(a^c)=a^(b+c)

In this case we have:

(5^-2)(5^-1)

5^(-2-1)

5^(-3)

The rule for negative exponents:

a^(-b)=1/(a^b)

So in this case:

5^(-3) is equal to

1/(5^3)

1/125

5 0

3 years ago

Read 2 more answers

The volume of a cube is related to the area of s face by the formula v= a^3/2. What is the volume of a cube whose face has an ar

Sophie [7]

Answer:

1000 m³

Step-by-step explanation:

Put the number into the formula and do the arithmetic.

v = a^(3/2) = (100 m²)^(3/2) = (√100)³ m³ = 1000 m³

The volume is 1000 cubic meters.

4 0

3 years ago

Round 526.745 to the nearest hundred

Marrrta [24]

Answer:526.75

Step-by-step explanation:

Find the number in the hundredth place 4 and look one place to the right for the rounding digit 5. Round up if this number is greater than or equal to 5 and round down if it is less than 5

3 0

2 years ago

Read 2 more answers

23. A certain type of gasoline is supposed to have a mean octane rating of at least 90. Suppose measurements are taken on of 5 r

Nostrana [21]

Answer:

a) $p_v =P(Z$

b) Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

c) $P(\bar X >90)=1-P(Z$

$1-P(Z$

d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

Step-by-step explanation:

Previous concepts and data given

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".

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$\bar X=88.96$ represent the sample mean

$s=1.011$ represent the sample standard deviation

n=5 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 90, the system of hypothesis would be:

Null hypothesis: $\mu \geq 90$

Alternative hypothesis: $\mu < 90$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic 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:

$z=\frac{88.96-90}{\frac{0.8}{\sqrt{5}}}=-2.907$

Part a

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=5-1 = 4$

Then since is a left tailed test the p value would be:

$p_v =P(Z$

Part b

Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

Part c

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >90)=1-P(Z$

$1-P(Z$

Part d

For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

7 0

3 years ago

Three times the smallest of three consecutive integers is six less than the largest. Find rhe numbers.

docker41 [41]

Let the numbers be x , x+1 and x+2

Then:-

3x = x + 2 - 6

3x - x = -4

2x = -4

x = -2

So the 3 integers are -2, -1 and 0. answer

5 0

3 years ago