The Rodriguez family spends 18% of their monthly income on going out to eat. What is the equivalent fraction of the family’s budget that is spent going out to eat? ​

The unknown value from the given linear expression is 1/4

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.

When an equation is given in this format, finding both intercepts is rather simple (x and y).

Given the equation below;

6 = 12k * 2

6 = 24k

Divide both sides by 24

24k = 6

k = 6/24

k = 1/4

Hence the value of k from the given expression is 1/4

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Answer:

Two Thousand Two Hundred and Fifty

The values of the length of the missing sides of triangle is x = 7√2 and y = 7.

Special right triangles are right triangles with three determined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°-90° triangle and the 30°- 60°-90° triangle are other names for the two unique right triangles. Before going further, let's review the fundamental characteristics of a right triangle.

One of the angles of a right triangle is 90 degrees, and the total of the other two angles is also 90 degrees. The triangle's hypotenuse, which is the longest side, is the side that faces the right angle.

From the given figure we observe that the two angles are 45 degree and 90 degree.

Using the angle sum property we have:

45 + 90 + third angle = 180

third angle = 45 degrees.

The triangle is thus a 45-45-90 triangle.

The sides of 45-45-90 triangle correspond to the lengths as x : x : x√2.

Here, the angle corresponding to 45 is 7.

Thus, y = 7 and x = 7√2.

Hence, the values of the length of the missing sides of triangle is x = 7√2 and y = 7.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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The probability that the first card is a 4, the second card is a club, and the third card is a 2 is equals to 6/5,525.

We have a standard deck has 52 cards. Three cards are dealt randomly from a standard deck. It is assumed that the cards are not changed after the transaction. Since there are four 4s in the deck of cards, the probability of rolling a 4 = 4/52. Now, the second dealt card is "club". The probability that the second card will be a club is = 13/52.

However, we have already drawn 1 card, which was a 4. This means that out of 51 cards, only 12 club cards remain. Thus the probability of club cards = 12/51. The third card can now be a 2. Therefore, the probability of falling third card will be a 2 = 3/50 (since two cards already dealt so total = 50 and one drawn card is a 4 then remaining= 3).

So, the overall probability = 4/52 x 12/51 x 3/50 =144/132,600 = 6/5,525.

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Complete question:

Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a club, and the third card is a 2?

Answer:

  a) 45/4

  b) 3

  c) 12

  d) 24

  e) no; rate of change varies

Step-by-step explanation:

The average rate of change on interval [a, b] is given by ...

  m = (f(b) -f(a))/(b -a)

The function values are read from the table.

__

a) m = (f(4) -f(0))/(4 -0) = (48 -3)/(4 -0) = 45/4

b) m = (f(1) -f(0))/(1 -0) = (6 -3)/(1 -0) = 3

c) m = (f(3) -f(2))/(3 -2) = (24 -12)/(3 -2) = 12

d) m = (f(4) -f(3))/(4 -3) = (48 -24)/(4 -3) = 24

e) Not a linear function. The rate of change is not constant.

An appropriate format to use to display the given data is: Line Chart or Histogram

A line chart (also called a line plot or line graph) makes use of points that are connected by line segments from left to right to show changes in values. The horizontal axis represents a continuous trend (often a trend over time) and the vertical axis shows the value of the metric of interest for that trend.

A histogram is defined as a type of graph that shows the frequency distribution of data points over a continuous range of numbers. Values ​​are grouped into bins or buckets and arranged sequentially along the horizontal X-axis at the bottom of the chart.  

Now, the data to be represented visually is the U.S. divorce rate (a continuous, interval-ratio level variable) for the last 50 years.

Since each year will be displayed alongside the divorce rates, then it is appropriate to make use of a line chart or a histogram

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Answer:

14 is the answer

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the square formula, the value of (1+i)^4 is -4.

The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.

The given expression can be rewritten as binomial with exponent:

((1 + i)^2)^2

Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,

(1 + i)^2 = 1 + 2i + i^2

As 'i' iota is the square root of negative 1, i^2 = -1

1 + 2i -1 = 2i

Therefore,

(2i)^2 = 4i^2 = 4*-1 = -4

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The initial amount is worth $ 1538.46

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.

Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.

The formula to calculate simple interest is:

Simple Interest = Principal x Rate x Time/ 100

Here we have

You are going to receive $2,000 in 6 years from now

The annual simple interest rate is 5%

Let 'P' be the initial or principal amount

Using the formula, I = PTR/100

Simple interest will gain on 'P' at 5% for 6 years

=> I = P(6)(5)/100  

=> I = 0.3P

And total amount = P + 0.3P = 1.3P

It is given that after 6 years we get $ 2000

=> 1.3P = 2000

=> P = 1538.46

Therefore,

The initial amount is worth $ 1538.46

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Answer:

\(\boxed{x = 251.4 cm}\)

Step-by-step explanation:

Part 1: Sketching the triangle

We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.

We can then sketch this triangle out to visualize it (attachment).

Part 2: Determining what trigonometric ratio can solve the problem

Now, we need to refer to our three trigonometric ratios:

\(sin = \frac{opposite}{hypotenuse}\)

\(cos = \frac{adjacent}{hypotenuse}\)

\(tan = \frac{opposite}{adjacent}\)

Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.

Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.

By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.

Part 3: Solving for the unknown variable

Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.

The cosine function is provided: \(cos( \alpha) = \frac{adjacent}{hypotenuse}\), where \(\alpha\) is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.

\(cos (70) = \frac{86 cm}{x}\), where x is the unknown side/the hypotenuse.

\(x * cos (70) = \frac{86 cm}{x} * x\) Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.

\(\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}\), Evaluate the second fraction because the first one cancels down to just the unknown, x.

\(\frac{86}{cos(70)} = 251.4\), round to one decimal place.

Your final answer is \(\boxed{x=251.4cm}\).

Answer:

The factors of 12 are 1, 2, 3, 4, 6, 12

Step-by-step explanation:

Basically what numbers can be multiplied to equal to 12

Example:

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

The factors of the given expression will be 7, x, x, y, and ( x + 2y²- y).

We have the expression,

7x³y+ 14x²y³-7x²y²

What is a factor?

A factor is a number that divides another number completely.

Let us take '7x²y' as common in the above expression.

7x²y( x + 2y²- y)

7. x.x.y ( x + 2y² - y)

Further, we cannot make any factor.

Therefore, the factors of the given expression will be 7,x, x, y, and ( x + 2y²- y).

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Answer:

B

Step-by-step explanation:

best choice :)

Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:

\(5-8=-3\)

\(2-5=-3\)

\(-1-2=-3\)

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:

\(f(n)=a+(n-1)d\), for \(n\geq 1\)

Where, a is the first term and d is the common difference.

Putting \(a=8,d=-3\), we get

\(f(n)=8+(n-1)(-3)\)

\(f(n)=8-3(n-1)\)

\(f(n)=-3(n-1)+8\), for \(n\geq 1\)

Therefore, the correct option is A.

Answer:

Step-by-step explanation:

x=0

\(-8 \le x < 3 \text{ and } 4 \le x < 8\)

=======================================================

Explanation:

Place your pencil on the curve. Then draw a straight vertical line either up or down until you reach the x axis. If you were to start at the left endpoint, and work your way to the right, you'll eventually shade the interval \(-8 \le x < 3 \text{ and } 4 \le x < 8\) along the x axis.

We have two separate intervals being shaded in. There's a small gap from 3 to 4 that isn't shaded in.

Refer to the diagram below.

Answer:

use microsoft maths solver

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Answer:

1.3 liters

Pls leave good rating and also like it

Thank you.

Have a nice day.

Answer:

let the third side be x

Using pythagoras theorem we get,

(58)^2 = (42)^2 + (x)^2

3364=1764+x^2

x^2=3364-1764

x^2= 1600

x=√(1,600)

x=40

\(\pink{\sf Third \: side \: of \: the \: triangle = 40}\)

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

Here,

In given triangle,

Now, by Pythagoras' theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

\( \sf : \implies (58)^{2} = (42)^{2} + P^{2}\)

\( \sf : \implies 58 \times 58 = 42 \times 42 + P^{2} \)

\( \sf : \implies 3364 = 1764 + P^{2}\)

\( \sf : \implies P^{2} = 3364 - 1764\)

\( \sf : \implies P^{2} = 1600\)

By squaring both sides :

\( \sf \sqrt{P^{2}} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{(40)^{2}}\)

\( \sf : \implies P^{2} = 40 \)

\(\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 40}\)

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During the month of May, there were 130 births, of which the newborn death rate is 38.4615.

According to the question,

There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.

In order to find the newborn death rate we have the formula:

=  \(\frac{number of death under 28 days of age }{Total live births in the same year}\)  × 1000

= \(\frac{5}{130}\) × 1000

=\(\frac{5000}{130}\)

=38.4615

Hence, the new born death rate is 38.4615.

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\(y {}^{2} + 3 {}^{2} = 5 {}^{2} \)

\(y {}^{2} = 25 - 9 = 16\)

\(y = \sqrt{16} = 4\)

\(x ^{2} = {y}^{2} + 7 {}^{2} \)

\(x {}^{2} = 4 {}^{2} + 7 {}^{2} \)

\(x {}^{2} = 16 + 49\)

\(x {}^{2} = 65\)

\(x = \sqrt{65} \)

The equation total amount of flour (f) for making n number of cakes is given by f = 3n

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Let f represent the total amount of flour and n represent the number of cakes. Hence:

f = kn

where k is the constant of proportionality.

The baker uses 3 pounds of flour to make cupcakes. Hence:

3 = k(1)

k = 3

f = 3n

The equation is given by f = 3n

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Answer:

\(\sqrt{100}+\sqrt{36}=16\)

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

Solution:-

\(\sqrt{100}+\sqrt{36}\)

\(\sqrt{100} =10}\)

\(\sqrt{36} =6\)

\(=10+6\)

\(=16\)

✩✩✩✩✩✩✩

hope it helps...

have a great day!!

Answer:

hope it is helpful to you

Step-by-step explanation:

The value after solving the expression will be equal to 6.5.

The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

From the data in the question,

The expression is,

2 - (-4.5)

⇒ 2 + 4.5

= 6.5

Therefore, the result for the expression is 6.5.

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Answer:

41

\(3 {x}^{2} - 2x + 1\)

\(now \: \: x = 4\)

\(3 {(4)}^{2} - 2(4) + 1\)

\(3(16) - 8 + 1\)

\(48 - 8 + 1 = 41\)

41 is the answer