The height of a tower on a scale drawing is 14 centimeters. The scale is 2 cm : 13 m. What is the actual height of the tower?

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Answer:

the rate of change is constant

Step-by-step explanation:

Combining similar terms:

Answer:

89

Step-by-step explanation:

178/2=89

9514 1404 393

Answer:

  [[-14][-1]]

Step-by-step explanation:

Row m of the first matrix is multiplied term-by-term by column n of the second matrix to get term (m,n) of the product matrix.

  \(\left[\begin{array}{cc}2&-4\\3&-1\end{array}\right]\times\left[\begin{array}{c}1&4\end{array}\right] =\left[\begin{array}{c}(2)(1)+(-4)(4)&(3)(1)+(-1)(4)\end{array}\right] =\left[\begin{array}{c}-14&-1\end{array}\right]\)

Answer:

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

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 \(s = \sqrt{\frac{p(1-p)}{n}}\)

Suppose 49% of American singers are Grammy award winners.

This means that \(p = 0.49\)

Sample of size 502

This means that \(n = 502\)

Mean and standard deviation:

\(\mu = p = 0.49\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.49*0.51}{502}} = 0.0223\)

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%?

Proportion below 49% - 4% = 45% or above 49% + 4% = 53%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 45%

p-value of Z when X = 0.45. So

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

By the Central Limit Theorem

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

\(Z = \frac{0.45 - 0.49}{0.0223}\)

\(Z = -1.79\)

\(Z = -1.79\) has a p-value of 0.0363.

2*0.0363 = 0.0726

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Answer:

a. The population is represented by the registered voters of the Raleigh city

b. The population size is 9,500

c. The sample size is 350

d. The proportion of people that voted for Brown was 32% >> (112 x 100) / 350 = 32%

e. The expected number of Brown's voters is 3,040 >>  (32 x 9,500) / 100 = 3,040

Step by step explanation:

In statistics, a population includes all the dataset from the study, while a sample is represented by one or more observations obtained from this dataset. The proportion can be represented by two fractions (ratios) which are equivalent to each other. Finally, the estimated size of the total population can be estimated by multiplication of the observed ratio in the sample and the size of the population (32 % x 9,500), and then dividing this number by the total ratio value.

Answer:

Hence the true proportion is (0.388, 0.492).

Step-by-step explanation:

Given n=250,

\(p= 110/250 =0.44\)

\(a=0.1, |Z(0.05)|=1.645\) (check standard normal table)  

So 90% CI is

\(p ± Z*√[p*(1-p)/n]\\0.44 ± 1.645*sqrt(0.44*(1-0.44)/250)\\ ( 0.388, 0.492)\)

For question 12, if you put the $629.63 toward reducing your credit card debt of $2,856.74 at a 14.75% APR, then you would save in interest in 1 full month is  $7.75

what is  interest ?

Interest is the cost of borrowing money. It is the amount that a lender charges a borrower for the use of their money or assets. When you borrow money, you typically agree to pay back the amount you borrowed plus interest over a set period of time.

In the given question,

Yes, your calculation is correct. If your realized income is $3,167.89 per month and your fixed expenses are $954.32 every 2 weeks (so $1,908.64 per month), then your monthly discretionary income is:

$3,167.89 - $1,908.64 = $1,259.25

If you save 50% of this discretionary income each month, you would save:

50% x $1,259.25 = $629.63

For question 12, if you put the $629.63 toward reducing your credit card debt of $2,856.74 at a 14.75% APR, then you would save in interest in 1 full month:

$629.63 x (14.75%/12) = $7.75

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Answer:

Step-by-step explanation:

Blue is 1 and a quarter.

Brown is Half

Answer:

-13w + 3

Step-by-step explanation:

Answer:

w=3/13

Step-by-step explanation:

(-7w+13)-(6w+10)=

-7w+13-6w-10=

reduce

-13w+3=

13w=3

w=3/13

Answer:

A = Length × breath

A = 3 × 7

A = a × 4

A = m × m

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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Answer:

          ______

x  =  − 0.  142857

Step-by-step explanation:

Answer:

c. 25°

Step-by-step explanation:

Sum of angles in a triangle:

The sum of the measures of the angles of a triangle is 180º.

In this question:

Angles of 3x, 2x-13 and 5x + 3.

The sum is 180º. So

\(3x + 2x - 13 + 5x + 3 = 180\)

\(10x - 10 = 180\)

\(10x = 190\)

\(x = \frac{190}{10}\)

\(x = 19\)

Measure of each angle:

3x = 3(19) = 57º

2x - 13 = 2(19) - 13 = 38 - 13 = 25º

5x + 13 = 5(19) + 3 = 95 + 3 = 98º

The smallest angle is 25º, and the correct answer is given by option c.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

the last one

Step-by-step explanation:

there is no rhythm

Answer:

Sure, I'd be happy to help you with that!

To calculate Dan's earnings with simple interest, we can use the following formula:

I = P * r * t

where:

I = interest earned

P = principal amount (initial investment)

r = interest rate (as a decimal)

t = time period (in years)

We know that Dan invests £2500 and receives 5% simple interest per year, so:

P = £2500

r = 0.05

t = 2 years

Plugging these values into the formula, we get:

I = £2500 * 0.05 * 2

I = £250

This means that Dan will earn £250 in interest over the 2-year period.

To calculate Dan's total earnings, we simply add the interest earned to the initial investment:

Total earnings = £2500 + £250

Total earnings = £2750

Therefore, Dan will have £2750 in his bank account after 2 years.

Answer:

this is your answer.

when x=2

y=2-16=-14

and similarly other.

Answer:

16.25 acres

Step-by-step explanation:

If corn is 1/4 of the land and we have 65 acres, we merely multiply 1/4 to 65.

You get 16.25 acres.

Answer:

16.25acres

Step-by-step explanation:

65/4=16.25 or 16 and 1/4

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.

Given data:

From the figure:

m∠RST  = m∠QST + m∠QSR

Put the values

70 = 2x + 3x - 10

5x = 80

x = 16

Thus,

m∠QSR = 3x - 10  = 3(16) - 10

m∠QSR = 38

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

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Complete question:

If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.

The figure is attached:

16

48

32

38

The situation that could not be represented by the algebraic expression b + 5 is given as follows:

If there are b ounces of water in a bottle, b + 5 could represent the amount of water after you drink 5 bottles.

The algebraic expression for this problem is defined as follows:

b + 5.

Meaning that an unknown amount b is increased by a value of 5.

For the answer of this problem, the correct expression would be of b - 5 instead of b + 5, hence it is the option that could not be represented by the algebraic expression b + 5.

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Answer: line: To represent straight objects in geometry, mathematicians introduced the concept of line or straight line

rays: vector, a ray is a vector from a point to a point. In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and taken to be at infinity

segments: The term line segment refers to a section of a line bounded by two distinct points. It is comprised of all points on the line between its endpoints. A closed line segment includes both endpoints, whereas an open line segment excludes both endpoints.

Step-by-step explanation:

Using the normal approximation to the binomial, it is found that there is a 0.0041 = 0.41% probability that at most 10 of them married their first love.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

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

In this problem:

For the approximation, the mean and the standard deviation are given by:

\(\mu = np = 50(0.4) = 20\)

\(\sigma = \sqrt{np(1-p)} = \sqrt{50(0.4)(0.6)} = 3.4641\)

Using continuity correction, the probability that at most 10 of them married their first love is \(P(X \leq 10 + 0.5) = P(X \leq 10.5)\), which is the p-value of Z when X = 10.5.

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

\(Z = \frac{10.5 - 20}{3.4641}\)

\(Z = -2.74\)

\(Z = -2.74\) has a p-value of 0.0041.

0.0041 = 0.41% probability that at most 10 of them married their first love.

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Answer:

- 2

Step-by-step explanation:

f(1) = - 2

Answer:

Step-by-step explanation:

==

Answer:

triangle

Step-by-step explanation:

i dont know if there should be picture attached

The value of the expression is 1.766.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given the expression,

2\(e^{3x}\) = 400

divide by 2 into both sides

\(e^{3x}\) =  400/2

\(e^{3x}\) = 200

converting the expression in form of a log,

ln(\(e^{3x}\))= ln(200)

log(aⁿ) = n log(a)

3x ln(e) = ln(200)  [ln(e) = 1 and ln(200) = 5.2931]

3x = 5.2931

x = 1.766

Hence Option B is correct.

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