Solve the system of equations below. Enter your answer in the boxes.8a + 12b = 926a – 4b = 4

Answer:

increased by 10%

Step-by-step explanation:

The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the values of the parameters are given as follows:

n = 6, p = 0.5.

The probability that fewer than 3 of them are boys is given by:

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156\)

\(P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938\)

\(P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344\)

Then:

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438\)

0.3438 = 34.38% probability that fewer than 3 of them are boys.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

Answer:

Step-by-step explanation:

you have to add 8 in both sides

x-8<-1

x-8+8<-1+8

x<7

Answer:x<7

Step-by-step explanation:

Step 1: Add 8 to both sides.

x−8+8<−1+8

x<7

Answer:

0.0066

Step-by-step explanation:

The x has a distribution that is approximately normal. For normal distribution the probability of x will be,

u = 12 and 18

P (12 \(\leq\) \(x\) \(\leq\) 18)

P (- 2.3  \(\leq\) \(x\) \(\leq\) 2.85 )

P (0.9912 - 0.9978)

= 0.0066

The value of x is equal to: A. 7.2 units.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

LM/MO = LN/NO

18/x = 10/4

By cross-multiplying, we have the following:

10x = 72

x = 72/10

x = 7.2 units.

Read more on basic proportionality theorem here: brainly.com/question/3213812

#SPJ1

Complete Question:

LO bisects ∠NLM, LM=18, NO=4, and LN=10

What is the value of x?

A. 7.2

B. 45

C. 5.43

D. 2.22

Answer:

\( \frac{5}{9} \times \frac{3}{9} \\ = \frac{5 \times 3}{9} \\ = \frac{15}{9} \\ = \frac{5}{3} \\ thank \: you\)

Answer:

15/9

Step-by-step explanation:

Answer:

1st

Step-by-step explanation:

-400 degrees can also be seen as positive 40 degrees

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

Answer:

3:20

Step-by-step explanation:

6000:40,000

find HCF (2000)

divide both sides by 2000

3:20

The image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)

The given parameters are

Point = (1, -4)

Transformation: 180∘ counterclockwise about the origin

The rule of 180∘ counterclockwise about the origin is

(x, y) = (-x, -y)

When this rule is applied to the given point, we have the image to be

Image = (-x, -y)

This gives

Image = (-1, 4)

Hence, the image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)

Read more about transformation at

https://brainly.com/question/4289712

#SPJ1

3990

Step-by-step explanation:

57*70=3990

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Answer:

b(a+c) this is answer okay

Answer:

Step-by-step explanation:

ab+bc

b(a+b)

u can add two term only if they have same base.

Answer:

BRAINLIEST PLEASE!?!

you will follow PEMDAS

Please- Parenthesis

Excuse- Exponents

My- Multiplication

Dear- Division

Aunt- Addition

Sally- Subtraction

10^8 is

10x10x10x10x10x10x10x10=100,000,000

then

62x4=248

OR

62+62+62+6=248

now you have

100,000,000 divided by 248=

403225.806

Step-by-step explanation:

Answer:

403,225.80

Step-by-step explanation:

Check the other guy's answer, I originally answered wrong but after seeing his answer and rechecking my work, I changed the answer.

From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic,  and use this to reach a conclusion.

This is a two-sample test, thus, it is needed to understand the central limit theorem and subtraction of normal variables.

Doing this:

-------------------

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

-------------------------------------

Proportion 1: Jet-ski users

86.5% out of 400, thus:

\(p_1 = 0.865\)

\(s_1 = \sqrt{\frac{0.865*0.135}{400}} = 0.0171\)

Proportion 2: boaters

92.8% out of 250, so:

\(p_2 = 0.928\)

\(s_2 = \sqrt{\frac{0.928*0.072}{250}} = 0.0163\)

------------------------------------------------

Hypothesis:

Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

At the null hypothesis, it is tested that the proportions are the same, that is, the subtraction is 0. So

\(H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2\)

At the alternative hypothesis, it is tested that the proportions are different, that is, the subtraction is different of 0. So

\(H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2\)

------------------------------------------------------

Test statistic:

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis.

This means that \(\mu = 0\)

From the samples:

\(X = p_1 - p_2 = 0.865 - 0.928 = -0.063\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0171^2 + 0.0163^2} = 0.0236\)

The value of the test statistic is:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.063 - 0}{0.0236}\)

\(z = -2.67\)

The value of the test statistic is z = -2.67.

---------------------------------------------

p-value of the test and decision:

The p-value of the test is the probability that the proportion differs by at at least 0.063, which is P(|z| > 2.67), given by 2 multiplied by the p-value of z = -2.67.

Looking at the z-table, z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076.

The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

A similar question is found at https://brainly.com/question/24250158

Step-by-step explanation:

CFB reads as twenty five degrees

complementary angle  will add to it to sum 90 degrees  = sixty five degrees

   angle CFD is sixty five degrees

Using compound interest, it is found that the account that has about the same annual interest rate as Meg's current savings account is given by:

\(S = 50(1.0025)^y\)

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, considering yearly interest, we have that the equation is:

\(S(y) = 50(1.0304)^y\)

Hence r = 0.0304.

Considering monthly interest, we have that:

\(r_m = \frac{0.0304}{12} = 0.0025\)

Hence, the desired account has the equation given by:

\(S = 50(1.0025)^y\)

You can learn more about compound interest at https://brainly.com/question/25781328

Answer:

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

Step-by-step explanation:

Mutually exclusive:

If two events are mutually exclusive, if one events happen, the other cannot happen, and vice-versa.

Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4}

A die has the following outcomes: 1,2,3,4,5,6

Even numbers: 2,4,6

Greater than 4: 5, 6

6 is an outcome of both events A and B, so they are not mutually exclusive.

Picking a card; A= {Selecting a 7}, B={Selecting a Heart}

Cards numbered from 1 to 13, each number with 4 types. So we can have a card of hearts numbered 7, which means that these events are not mutually exclusive.

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

If you get no heads, the probability of at least 1 head is 0.

If you get at least 1 head, the probability of no heads is 0.

This means that this is the answer, that is, these events are mutually exclusive.

Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

(3,1) or (1,3) has a sum of 4 and a 3 on one die, which means that these events are not mutually exclusive.

Step-by-step explanation:

please give me full question

The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

------------------

Given:

Add up the two equations:

Substitute the value of A and find B:

Find the product of the two numbers:

Answer:

so simple! n÷4=remainder 3.

2n÷4=3×2=6.

HOPE THIS HELPS AND PLSSS PLSSS MARK AS BRAINLIEST

THNXX :)

The value of iⁿ is -1 \(i^n\) = \(-i\).

Complex numbers are numbers which are of the form \(a + ib\), where a and b are real numbers and i is the imaginary number called iota whose value is \(i^2\) = -1.

We have to find the value of iⁿ if the remainder of  n/4 is 3.

The remainder of n/4 is 3 means that the value of n is 1 less than the multiple of 4.

When 1 is taken less to any of the multiple of 4, then the number will be an odd number.

So n is an odd number.

Now, the value of \(i^2\) = -1.

\(i^3\) = \(i^2\) × \(i\) = \(-i\)

\(i^4\) = \(-i\) × \(i\) = \(-i^2\) = 1

From the pattern it is seen that any number, n which is 1 less than the multiple of 4 will have, \(i^n\) = \(-i\).

Hence the value of \(i^n\) = \(-i\).

Learn more about Complex Numbers here :

https://brainly.com/question/11230333

#SPJ2

common difference=d=43-39=4

We need first term a

\(\\ \sf{:}\dashrightarrow a_5=43\)

\(\\ \sf{:}\dashrightarrow a+4d=43\)

\(\\ \sf{:}\dashrightarrow a+4(4)=43\)

\(\\ \sf{:}\dashrightarrow a+16=43\)

\(\\ \sf{:}\dashrightarrow a=27\)

We know that she put a principal of $400, the interest rate is 1.5% each year, and the time is 5 years. Using the simple interest formula, we have

Answer:

B) >

Step-by-step explanation:

We can convert the fractions into decimals to see which is greater.

3/5 = 0.6

5/10 = 0.5

From this, we can see that 3/5 is greater than 5/10, so the sign is >.

hope this helps :)

Using Monotone Convergence Theorem,  {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent

To show that the sequence {aₙ} defined by a₁ = 1 and aₙ₊₁ = 3 - (1/aₙ) is increasing, we need to prove that aₙ < aₙ₊₁ for all n.

Let's first prove that aₙ < 3 for all n by induction:

Base case: For n = 1, a₁ = 1 < 3.

Inductive step: Assume aₙ < 3 for some arbitrary n. Then we have:

aₙ₊₁ = 3 - (1/aₙ) < 3 - (1/3) = 8/3

Since aₙ₊₁ is positive (because aₙ < 3), we can also write:

aₙ₊₁ = 3 - (1/aₙ) > 3 - 1 = 2

Therefore, we have:

2 < aₙ < 3 < aₙ₊₁

This shows that {aₙ} is an increasing sequence that is bounded above by 3, and thus it is convergent by the Monotone Convergence Theorem.

To find the limit of {aₙ}, we can take the limit of both sides of the recursive definition:

limₙ→∞ aₙ₊₁ = limₙ→∞ (3 - (1/aₙ))

Since {aₙ} is convergent, we can replace limₙ→∞ aₙ with a to get:

a = 3 - (1/a)

Multiplying both sides by a, we get:

a² = 3a - 1

This is a quadratic equation that can be solved using the quadratic formula:

a = (3 ± √(3² + 4))/2

a = (3 ± √13)/2

Since aₙ < 3 for all n, we have:

a = (3 - √13)/2

Therefore, the limit of {aₙ} is (3 - √13)/2.

Learn more on convergence of series here;

https://brainly.com/question/30761859

#SPJ1