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jonny [76]
3 years ago
12

Can someone help me one this? Will mark brainlist!

Mathematics
1 answer:
pshichka [43]3 years ago
6 0
Because there are 4 cards and you’re trying to find the probability of drawing number 6, it’s would be 1/4
You might be interested in
4. Two savings accounts each start with a $200 principal and have an interest rate of 5%. One account earns simple interest and
slega [8]

Answer:

The compounded annually account will earn more interest over 10 years

Step-by-step explanation:

The rule of the simple interest is I = Prt, where

  • P is the original value
  • r is the rate in decimal
  • t is the time

The rule of the compounded interest is A = P(1+\frac{r}{n})^{nt}, where

  • A is the new value
  • P is the original value
  • r is the rate in decimal
  • n is the number of periods
  • t is the time

The interest I = A - P

∵ Each account start with $200

∴ P = 200

∵ They have an interest rate of 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ One account earns simple interest and the other is compounded  

   annually

∴ n = 1 ⇒ compounded annually

∵ The time is 10 years

∴ t = 10

→ Substitute these values in the two rules above

∵ I = 200(0.05)(10)

∴ I = 100

∴ The simple interest = $100

∵ I = A - P

∵ A = 200(1+\frac{0.05}{1})^{1(10)}

∴ A = 325.7789254

∵ I = 325.7789254 - 200

∴ I = 125.7789254

∴ The compounded interest = $125.7789254

∵ The simple interest is $100

∵ The compounded interest is $125.7789254

∵ $125.7789254 > $100

∴ The compounded annually account will earn more interest

   over 10 years

6 0
3 years ago
A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40
bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. How large was the sample used in this survey?

We have that s = 25, \sigma = 400. We want to find n, so:

s = \frac{\sigma}{\sqrt{n}}

25 = \frac{400}{\sqrt{n}}

25\sqrt{n} = 400

\sqrt{n} = \frac{400}{25}

\sqrt{n} = 16

(\sqrt{n})^2 = 16^2[tex][tex]n = 256

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0
3 years ago
In Amy’s backyard, there are also chickens and rabbits. There are 5 more chickens than rabbits. The total number of legs is 130.
Butoxors [25]

Answer:

There are 25 chickens and 20 rabbits

Step-by-step explanation:

Let

x-----> the number of chickens

y ----> the number of rabbits

Remember that

1 chicken has two legs

1 rabbit has four legs

so

2x+4y=130 -------> equation A

x=y+5 -----> equation B

Substitute equation B in equation A and solve for y

2(y+5)+4y=130

2y+10+4y=130

6y=120

y=20 rabbits

Find the value of x

x=y+5

x=20+5=25 chickens

3 0
3 years ago
Thx u if u get the answer
trapecia [35]
So the man's age is divisible by 3, 5, and 7 but not by 2, 4, 6, or 8.

3 * 5 * 7 = 105
105 is not divisible by 2, 4, 6, or 8.
Not sure if any lower ages are there, but since the man is 105 years old, you would receive $105.
5 0
3 years ago
Read 2 more answers
A square has side length (x+5) units. What is it’s area
daser333 [38]

The area of square is x^{2}+10 x+25 square units

<h3><u>Solution:</u></h3>

Given that square has side length (x+5) units

To find: area of square

<em><u>The area of square is given as:</u></em>

\text {Area of square }=\mathrm{a}^{2}

Where "a" is the length of side

From question, length of each side "a" = x + 5 units

Substituting the value in above formula,

\text {Area of square }=(x+5)^{2}

{\text {Expanding }(x+5)^{2} \text { using the algebraic identity: }} \\\\ {(a+b)^{2}=a^{2}+2 a b+b^{2}}\end{array}

\begin{array}{l}{\text {Area of square }=x^{2}+2(x)(5)+5^{2}} \\\\ {\text {Area of square }=x^{2}+10 x+25}\end{array}

Thus the area of square is x^{2}+10 x+25 square units

7 0
3 years ago
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