There are 4 bananas and 5 apples in a bag. If Peter picks a fruit at random from the bag, then what is the probability of picking a banana?
A. 4/9
B.1/9
C.2/9
D.5/9

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

The 95% confidence interval for the population proportion is approximately 0.3573 to 0.7141. None of the given options (A, B, C, D) match the calculated interval.

To construct a confidence interval for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± critical value * standard error

Where the sample proportion (p-hat) is calculated by dividing the number of successes (x) by the total sample size (n). In this case, n = 56 and x = 30, so the sample proportion is 30/56 = 0.5357.

The critical value is determined based on the desired degree of confidence. For a 95% confidence level, which is given in this case, the critical value can be obtained from a standard normal distribution. For a two-tailed test, the critical value is approximately 1.96.

The standard error is calculated by taking the square root of (p-hat * (1 - p-hat) / n). Plugging in the values, we get sqrt(0.5357 * (1 - 0.5357) / 56) = 0.0907.Now, we can construct the confidence interval:Confidence Interval = 0.5357 ± 1.96 * 0.0907Calculating the upper and lower bounds of the interval:

Lower bound = 0.5357 - (1.96 * 0.0907) ≈ 0.3573

Upper bound = 0.5357 + (1.96 * 0.0907) ≈ 0.7141\

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Given:

Steven wrote this equation:

\(4\times 18=418\)

To find:

The error in Steven's reasoning and then find the correct product.

Solution:

We have,

\(4\times 18=418\)

This statement is incorrect because we cannot write product directly as Steven wrote.

We need to multiply the place values of each digit of first number with the place values of second number and then we need to add the resulted values.

\(4\times 18=4\times (10+8)\)

\(4\times 18=4\times 10+4\times 8\)

\(4\times 18=40+32\)

\(4\times 18=72\)

Therefore, the correct product is 72.

Answer:

17.96 mph is the answer to this question

Answer:

Step-by-step explanation

the diving board is 2 ft then mike jumps 2 more ft off the diving board how high was mike off the ground after he jumped

The present value of $10,000 if interest is paid at a rate of 4% per year is $7,888.10.

To find the present value of $10,000 if interest is paid at a rate of 4% per year, compounded weekly, for 5 years, we can use the formula for present value of a lump sum:

PV = FV / \((1+r/n)^{nt}\)

where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.

In this case, FV = $10,000, r = 0.04 (4% expressed as a decimal), n = 52 (52 weeks in a year), and t = 5.

Plugging in the values, we get:

PV = $10,000 / \((1+0.04/52)^{52*5}\)

PV = $7,888.09

Rounding up to the next cent, the present value of $10,000 is $7,888.10.

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Using it's concept, the experimental probability that the next boat to dock will be from North Carolina is given by: 5/13.

A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials.

In this problem, there are 13 boats, of which 5 were from North Carolina, hence the experimental probability that the next boat to dock will be from North Carolina is given by: 5/13.

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According to the percentage,There are the three(3) odds that you would receive no money after pushing it 300 times.

According to the statement

we have to find that the odds that you would receive no money after pushing it 300 times.

So, For this purpose, we know that the

A percentage is a number or ratio expressed as a fraction of 100.

From the given information:

There is a 1% chance of giving you a dollar every time you pushed it

And the times we push the button is a 300 times.

Then

the odds that you would receive no money after pushing it 300 times

And for this

The chances that we would not receive money = 1/100*300

The chances that we would not receive money = 0.01*300

The chances that we would not receive money = 3.

So, According to the percentage,There are the three(3) odds that you would receive no money after pushing it 300 times.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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This shows that the difference between the eigenvalues of x for vector A and B is related to the commutator [A, B] and the eigenvector of x for matrix B.

To show that if x is an eigenvector of matrix A belonging to an eigenvalue λ, then x is also an eigenvector of matrix B belonging to an eigenvalue μ, we can start with the eigenvector equation for matrix A:

A x = λ x

Multiplying both sides by matrix B, we get:

B (A x) = B (λ x)

Using the associative property of matrix multiplication, we can rewrite the left side as:

(B A) x = (A B) x

Substituting the eigenvector equation for matrix A, we get:

(λ B) x = (A B) x

Since x is nonzero, we can divide both sides by x:

λ B = A B

This shows that if x is an eigenvector of matrix A belonging to eigenvalue λ, then it is also an eigenvector of matrix B belonging to eigenvalue μ = λ.

The matrices A and B are related through the commutator [A, B] = AB - BA. We can rewrite the equation λ B = A B as:

λ B - A B = [A, B] B

Since x is nonzero, we can multiply both sides by x:

λ B x - A B x = [A, B] B x

Using the eigenvector equation for matrix A and the fact that x is an eigenvector of matrix A, we get:

λ x - μ x = [A, B] B x

Simplifying, we get:

(λ - μ) x = [A, B] B x

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Answer: 18

Step-by-step explanation:

32-14=18

To check your answer 18+14=32

The zero product property tells us that if the product of two terms is 0, then one of the terms must be equal to 0.

Polynomial functions can be written in intercept form:

\(y=x(x-r)(x-s)(...)\)

In this form, according to the zero product property, r and s are zeros of the function. The first 'x' term also signifies that 0 is also a zero of the function (x = 0).

We're given:

\(y=x(x-2)(x+6)^2\)

In this case, r and s are equal to 2 and -6.

However, there is an x written in the front, indicating that 0 is also a zero of the function.

-6, 0 and 2

Answer:

It is False

Hey bro Good Luck for exams!

Step-by-step explanation:

I think it's answer is false

Answer:

  ∠B ≈ 30.0°

Step-by-step explanation:

The law of sines can be used to solve a triangle when two sides and an angle opposite one of them are given.

__

  sin(B)/b = sin(C)/c

  sin(B) = (b/c)sin(C) . . . . solve for sin(B)

  sin(B) = (14/28)sin(91°) ≈ 0.49992385

The angle is found using the inverse sine function:

  B = arcsin(0.49992384) ≈ 29.99496°

Rounded to tenths, the angle is ...

  m∠B ≈ 30.0°

_____

Additional comments

Many triangle solver apps and web sites are available if all you want is an answer.

When using your calculator, be sure the angle mode is set to "degrees."

The Law of Sines can also be used to solve a triangle when two angles and one side are known.

Answer:

X: 45° Y:16°

Step-by-step explanation:

by help of teacher

Answer:

4x+2=18

18-2=16

16÷4=4

x=4

Step-by-step explanation:

Hope this help!

Answer:

7600

Step-by-step explanation:

Answer:

7, 4

Step-by-step explanation:

Answer:

(A), 21, 22,and 26

Step-by-step explanation:

gakzbzkxvuxnsslvzixvdkdbdjxvshhzvskdvxy dgsjzvsks ysjdbdudvsk jdkdbdb

Answer:

6 and 7

Step-by-step explanation:

Based on the ratio, 5¹/₂ : 1¹/₂, the unit rate can be found to be so the statement is TRUE.

To find the unit rate of a ratio, you should divide the first number in the ratio by the second number in the ratio.

When given the ratio, 5¹/₂ : 1¹/₂, therefore, the unit rate is:

= 5¹/₂ ÷ 1¹/₂

= 11/2 ÷ 3/2

= 11/2 x 2/3

= 22 / 6

= 3.6667

= 3²/₃

In conclusion, the unit rate of 5¹/₂ : 1¹/₂ is 3²/₃.

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Answer:

y+6 = 16 (x+1)

Step-by-step explanation:

Point slope form of an equation is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y- -6 = 16 (x- -1)

y+6 = 16 (x+1)

Answer:

I have no idea if you are saying that x=16. If it does the answer is 8/5

Answer:

x-8=5x-80

8+80=5x-x

88=4x

x=88/4

x=22

Answer:

D. 104

Step-by-step explanation:

After taking the square root of all possible answers 104 gives you 10.19 in decimal form which is the closest and most accurate number to 10.2 where the point is closely located to.

Answer + Step-by-step explanation:

(a)

Check the attached image.

(b)

Range of sample means : 7.5 - 5.75 = 1.25

(c)

The closer the range of the sample means is to 0 ,

the more confident they can be in their estimate . \(\huge \checkmark\)

The farther the range of the sample means is from 0 ,

the more confident they can be in their estimate . 

The mean of the sample means will tend to be a better estimate

than a single sample mean . \(\huge \checkmark\)

A single sample mean will tend to be a better estimate

than the mean of the sample means .

Real number \($x^2+y^2= \boxed{158}$\)

Let's start by using the formulas for arithmetic mean and geometric mean:

Arithmetic mean:

\($\frac{x+y}{2}=7 \Rightarrow x+y=14$\)

Geometric mean:

\($\sqrt{xy}=\sqrt{19} \Rightarrow xy=19$\)

Now, we can square the equation for the arithmetic mean:

\($(x+y)^2=14^2 \Rightarrow x^2+2xy+y^2=196$\)

Substituting\($xy=19$\), we get:

\($x^2+y^2+2(19)=196$\)

Simplifying:

\($x^2+y^2= \boxed{158}$\)

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Answer:

\(( - 0.5 , - 4.5 )\)

Step-by-step explanation:

Rewrite the equation in vertex form.

Complete the square for

\(2 {x}^{2} + 2x - 4\)

Use the form

\(a {x}^{2} + bx + c\)

to find the values of a, b, and c.

a = 2

b = 2

c = −4

Consider the vertex form of a parabola.

\(a(x + d) ^{2} + e\)

Find the value of d using the formula

\(d = \frac{b}{2a} \)

\(d = \frac{1}{2} \)

Find the value of e using the formula

\(e = c - \frac{ {b}^{2} }{4a} \)

\(e = - \frac{9}{2} \)

Substitute the values of a, d, and e into the vertex form

\(2(x + \frac{1}{2} ) ^{2} - \frac{9}{2} \)

Set y equal to the new right side.

\(y = {2(x + \frac{1}{2}) }^{2} - \frac{9}{2} \)

Use the vertex form, 

\(y = a(x - h) ^{2} + k\)

to determine the values of a, h, and k.

a = 2

h = -1/2

k = -9/2

Find the vertex (h,k).

\(( - \frac{1}{2} , - \frac{9}{2} )\)

0.99999028444 is the probability that at most 22 heads occur.

What does the maths term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probability of different outcomes if we are unclear of how an event will turn out. Probability is a measure of how likely or likely-possible something is to happen.

                               For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

probability of getting head,  P = 1/2 = 0.5

        q = 1 - p  = 1 - 0.5 = 0.5   and n = 25

 P(X ≤ 22)

 P(X = x ) = ⁿCₓ (q)ⁿ⁻ˣ (p)ˣ

      = 1 - P(x = 23) - P(24) - P(25)

  = 1 - ²⁵C₂₃(0.5)²⁵⁻²³ (0.5)²³ - ²⁵C₂₄ (0.5)²⁵⁻²⁴ (0.5)²⁴ - ²⁵C²⁵ (0.5)²⁵⁻²⁵ (0.5)²⁵

        = 0.99999028444

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Answer:

E, A, F, A

Step-by-step explanation:

A,A

B,A

C,A

D,A

E,A

F,A