Need some help pls. Amanda needs 3 quarters for the washing machine and 2 quarters for the dryer for a complete load at the laundromat. Which function shows the relationship between the number of complete loads of laundry (x) and the total number of quarters needed (y)?

1 .y= x + 5
2.y= 3/2x
3.y= 3x + w
4 y= 5x

Answer:

Rosemary worked 12 hours at the bookstore and 16 hours driving around for pizza delivery.

Step-by-step explanation:

Let x be the number of hours spent working at the bookstore where she makes 8.25 an hour. Her pay from the bookstore is in total, 8.25x.

Likewise, let's let y = the number of hours working at the pizza place. Her total pay there would be 9.25y.

Her all together over all pay would be:

bookstore$ + pizza$

8.25x + 9.25y

= 247

8.25x + 9.25y = 247

here is one equation. It tells us her total pay from both jobs is 247.

Also, her hours totaled 28. So,

x + y = 28

Solve the system of equations:

8.25x + 9.25y = 247

x + y = 28

You could use substitution or elimination. If you are learning matrices or a graphing program you could use that.

Here is the substitution work.

x + y = 28

y = 28 - x

8.25x + 9.25y = 247

substitute. y = 28-x

8.25x+9.25(28-x)=247

use distributive property.

8.25x+259 - 9.25x=247

combine like terms.

259 - x = 247

subtract 247, add x

12 = x

This means that Rosemary worked 12 hours at the bookstore. And since 28 - 12 = 16.

She works 16 hours at the pizza delivery

12 + 16 is 28, the number of hours she worked.

Also, 8.25(12)+9.25(16)

= 99 + 148

= 247

So these number check out.

By Angle-Angle-Side (AAS) triangle congruence theorem we know that two triangles are congruent if they have two sets of congruent angles and a set of non-included congruent sides.

Since no figure is given in the question we employ the reflexive characteristic to demonstrate that the overlapping sections are congruent in order to demonstrate that overlapping triangles are congruent.

If two triangles are precisely the same size and shape—that is, if they have the same side lengths and angle measurements—they are said to be congruent. If we are aware that two triangles have all the same sides and angles, we can conclude that the triangles are congruent.

To demonstrate that two triangles are congruent, however, we don't necessarily need to know that all of their sides and angles are congruent.

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The sum can be written in logarithms as 6z log 6

What is logarithm ?

The word "logarithm" comes from the combination of the Greek words "logos," which means "principle or concept," and "arithmos," which means "number." A logarithm is the power that must be increased to obtain a given number. It is shown by a number's log.

Use of property

log (ab) = log a + log b

log a^b = b log a

Given that,

log 6^8 + log 6^z

=log 6^8 + log 6^z

=log (6^8*6^z)

=log (6^6z)

=6z log 6

Therefore, the sum can be written in logarithms as 6z log 6

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Opposite of an integer on the number line is the same integer with opposite sign

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

The number line's opposite of the integer "a" is "-a"; hence, the opposite of the integer "-a" is "a" on the number line, but on the other side of 0.

For example,

The number line's opposite of the integer "4" is "-4"

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The solutions for all three questions regarding the Fibonacci sequence are given below.

The Fibonacci sequence can be defined as a set of integers that form a sequence that follows one rule ie., every number is the sum of the preceding two numbers. The first six numbers of the Fibonacci sequence are =  1, 1, 2, 3, 5, 8.

The 63rd term of the Fibonacci sequence is  4052739537881. The 12th number in this sequence is 144. This can be found out using the formula -

= [tex]F_{n-1}[/tex] +  [tex]F_{n-2}[/tex]

Here, if we know the values of the preceding two numbers, we can easily find out the value of any number in the Fibonacci sequence.

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a)The value of  ∠b=64°.

b)The values of angles q, r, s, t are ∠q= 65°, ∠r=65°, ∠s=50°, ∠t=65°.

c)The value of  ∠B=72 degrees.

The same-side interior angles are additional if a transversal connects two parallel lines. Alternate interior angles are equivalent if a transversal connects two parallel lines. Corresponding angles are equal.

a) Given line PQ is parallel to ST.

   One of the theorems of parallel lines is, Corresponding angles are equal.

Here the corresponding angles are ∠a, ∠b.

so, ∠a=∠b

∴∠b=64°

b) It is given that lines B and C are parallel, according to one of the theorems of parallel lines, vertically opposite angles are equal. So, the angle opposite to 65° is also equal to 65°. Sum of the angles suspended by a line on another line is 180°. Therefore the other angle in the triangle is 180°-130°=50°.

Since the sum of interior angles in a triangle is 180°, the angle q will be:

   ∠q= 180°-(65°+50°)

    ∠q= 65°.

Vertically opposite angles are equal, therefore ∠q=∠r=65°.

∠s=180°-(65°+65°)

∠s=50°.

Corresponding angles are equal, therefore

130°=65°+∠t

∠t=65°.

c) Given lines A, and B are parallel. We know that the Corresponding angles are equal, therefore

3m=4m-24

⇒m=24

Therefore ∠B=4(24)-24

∠B=72 degrees.

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The 95% confidence interval for the true population mean textbook weight is given by 63.133< X< 70.866.

The value of Z for a 95% confidence interval, is 1.960

According to the question, It is given:

Sample size (n) = 37

Mean weight (X) = 67 ounces

Standard deviation (s) = 12 ounces

A 95% confidence interval is described by the relationship:

x±1.960* [tex]8/\sqrt{n}[/tex]

Substituting the values given in the question to find the value of x:

The lower limits and upper limits are:

U= 67+1.960* [tex]12/\sqrt{37}[/tex]

U= 70.866

L=67-1.960* [tex]12/\sqrt{37[/tex]

L=63.133

Thus, the 95% confidence interval for the true textbook mean weight is 63.133< X< 70.866.

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The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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Answer:

Step-by-step explanation:

answer is a

Answer:

The answer is b!

Step-by-step explanation:

the answer is A .

the open end of the arrow points to the bigger variable. When the variable is included there will be a line under the arrow

The given confidence interval is correct and it is between 22% to 38%.

The formula for calculating the confidence interval of population proportion is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Here the sample proportion is represented by [tex]\bar{p}[/tex].

It is given that,

The 95% confidence interval has a sample size of n = 120 and the number of successes = 36.

So, the sample proportion [tex]\bar{p}[/tex] = 36/120 = 0.3

For the 95% confidence interval, α = 1 - 0.95 = 0.05

And α/2 = 0.05/2 = 0.025

Then, the z-score for α/2 = 0.025 is [tex]z{\alpha/2|=1.96[/tex].

And the standard deviation, [tex]\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }=\sqrt{\frac{0.3(1-0.3)}{120} }[/tex] = 0.0418

So, the interval is in between

C.I = 0.3 ± 1.96 × 0.0418

Upper limit = 0.3 + 1.96 × 0.0418 = 0.38 = 38%

Lower limit = 0.3 - 1.96 × 0.0418 = 0.218 = 0.22 = 22%

Therefore, the given confidence interval is correct.

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A coin rolls a distance of 33 cm in 5 rotations is nickel coin.

A straight line that runs through the middle of a body or figure from the sideways particularly a circle or sphere is called as a diameter of a circle or sphere.

Given that a coin rolls a distance of 33 cm in 5 rotations.

So that the circumference of the coin is,

33/5 = 6.6 inch.

And the formula for circumference is π 2r, where 2r is the diameter of coin.

Now we will check the diameter of given coins and match with the required coins.

Given coins penny, nickel, dime and quarter have the diameter 1.9 cm, 2.1 cm, 1.8cm and 2.4 cm respectively.

For the coin nickel,

π (2.1) = 6.6

And every coin have different diameter.

Therefore, a coin rolls a distance of 33 cm in 5 rotations is nickel coin.

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The measure of the spread of scores within a set of data is termed as standard deviation. Usually, we are interested in the standard deviation of a population. since, we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation.

When to use the sample or population standard deviation ?

Population standard deviation is of great intrest because our population contains all the values we are interested in. Therefore, we would normally calculate the population standard deviation In two cases first when we have the entire population or second we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize our findings to the population. but, in statistics, a sample is presented from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this.

Thus it can be concluded that, if we have all is a sample, but we wish to make a statement about the population standard deviation from which the sample is drawn, we need to use the sample standard deviation. There a Confusion can often arise as to which standard deviation to use due to the name "sample" standard deviation incorrectly being interpreted and not the estimate of the population standard deviation based on the sample.

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the interest will be $1000 IBM corporation bank.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

So simple interest will be = 10000*10*1 /100 = $1000

Hence, the interest will be $1000 IBM corporation bank.

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Hence, the amount of dividends in arrears that is still owed to preferred stockholders is $ [tex]50000[/tex].

What are the dividends?

The dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.

The dividend is one of the four important parts of the division process. It is the whole which is to be divided into different equal parts.

Here given that,

Cumulative preferred stockholders of Rale Company receive $ [tex]80[/tex]per share. The company has [tex]70,000[/tex] shares outstanding. For the last [tex]9[/tex] years, Rale paid no dividends. This year, Rale paid $[tex]400,000[/tex] in dividends.

They are receiving $ [tex]80[/tex]per share and total amount they are receiving $ [tex]875[/tex].

So, when the Rale paid  $[tex]400,000[/tex] in dividends then the amount they are receiving is

[tex]\frac{400000}{80}=50000[/tex]

Hence, the amount of dividends in arrears that is still owed to preferred stockholders is $ [tex]50000[/tex].

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A pair of dice is thrown the sum of the 2 scores calculated can be 5,6,7,8

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

The Three Kinds of Probability

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

The value of dice is 1,2,3,4,5,6

Hence the sum of the 2 dice when rolled together can vary from 2 to 12

since 5,6,7,8 lies between 2 and 12

all of them are correct.

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Answer:

correct answer is option b i think...

Answer: K=10

Step-by-step explanation:

To begin, you should multiply out the terms in front of the parentheses. This results in: 47=2k+6+3k-9

Next, we can combine like terms: 47=5k-3

Add 3 to both sides: 50=5k

Divide both sides by 5: 10=k

k=10

a) The average weight is 195 pounds b)The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40% c) The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.

In statistics, the standard deviation measures how widely distributed or how much a group of values can vary. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Normal Probability Distribution:

The z-score formula can be used to address problems with normal distributions.

The zscore of a measure X in a set with mean and standard deviation can be calculated as follows:

Z=[tex]\frac{x-u}{\alpha }[/tex]

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.

(a) If 46 people are on the elevator, and their total weight is s 8970 pounds, what is their average weight?

This is s 8970  divided by 46, that is s 8970 /46 = 195pounds.

Their average weight is 195 pounds.

Z=[tex]\frac{x-u}{\alpha }[/tex]

=> Z=195-177/70

=>Z=0.25 pvalue of 0.5160

1 - 0.5160 = 0.4840

(b) If a random sample of 46 adult men ride the elevator ,the probability that the maximum safe weight will exceed or not

The weights of adult U.S. men have mean 177 pounds and standard deviation 71 pounds, which means that

Z=[tex]\frac{x-u}{\alpha }[/tex]

=> Z = 195 -177/71

=> Z=0.25 pvalue of 0.6461

=> 1-0.6461=0.3539

Therefore a) The average weight is 195 pounds b)The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40% c) The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.

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Answer:

Below

Step-by-step explanation:

231469.335329 to the nearest thousand.     '1' is the thousand position

the '4' next to it says leave the '1' alone to get

231000      rounded to nearest thousand.

According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).

A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.

This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.

A simple example of a system of polynomial equations is

x²+y²- 5 = 0

      xy-2 = 0.

Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.

Based on above description, we can say that:

(x+1) must be 0.

(x+1)=0

x=-1

Thus, If (x-1)=0 then x is 1 instead of -1 in question.

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Binary Variable is  a variable that can only be 1 or 0. Binary variables are categorical variables that can take only one of two values, are usually represented as Boolean (True or False) or integer variables (0 or 1), and usually have no attributes indicates that it exists.

Binary variables have only two states, such as 0 or 1. 0 defines the variable does not exist, 1 defines the variable exists. For example, for the patient-defining variable Smoker , 1 means the patient smokes and 0 means the patient does not smoke. Binary variables can be viewed as if they were scaled by intervals, which can lead to misleading clustering results. Therefore, a method that defines binary data is essential for computing dissimilarities.

Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics.

Binary data is used to represent one of two conceptually opposite values. "correct" or "incorrect".

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The valid conclusion is  A. We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

The confidence interval used by the student researcher refers to the probability that the university's population parameter (average amount that students spent on sporting events last year) will fall between $217 and $677 for 90% of the time.

Thus, the interval measurement gives the researcher some degree of certainty that the calculated sample mean falls within the population mean most of the time.

Hence ,we can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

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Answer:

Two dimensions.

Straight sides.

Congruent (equal-length) sides.

An interior and exterior.

Equal interior angles.

Equal exterior angles.

Step-by-step explanation:

The value of that guarantees the equation has exactly one real root is Zero

A quadratic equation has exactly one real number solution, then the value of its discriminant is always zero.

Quadratic

The word Quadratic is derived from the word Quad which means square. In other words, a quadratic polynomial is a polynomial function of degree 2.There are many scenarios where quadratic polynomials are used. When a rocket is launched, its path is described by the zero of a quadratic polynomial.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a ≠ 0.

In the case of one real solution, the value of discriminant b2 - 4ac is zero.

For example, x2 + 2x + 1 = 0 has only one solution x = -1.

Discriminant = b2 - 4ac = 22 - 4 (1) (1) = 0

Thus,  a quadratic equation has exactly one real number solution, then the value of the discriminant is always zero.

The value of that guarantees the equation has exactly one real root is Zero.

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The integers in the set S:{-79, 80, 39, 40) that will make the inequality 1/0.4(m - 0.4) ≤ 1/21(m - 39) false are: S:{39, 40}​.

Determine the integers

In order to determine which integers are true and false with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-80, 79), we have:

1/0.4(m - 0.4) ≤ 1/21(m - 39)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39)

1/3(-39) ≤ 1/6(-40)

-39.6 ≤p< -40 (True).

For integers (-80, 79), we have:

1/0.4(m - 80) ≤ 1/21(m - 39)

1/3(24 - 3) ≤ 1/21(24 - 12)

1/3(27) ≤ 1/6(36)

79.6 ≤ p < 80 (False).

For integers (-40, -39), we have:

1/3(27) ≤ 1/6(36)

1/3(24 - 3) ≤ 1/21(24 - 12)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39)

-39.6 ≤ -40 (True).

For integers (-80, 79), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

For integers (12, 24), we have:

1/3(m - 3) ≤ 1/6(m - 12)

1/3(12 - 3) ≤ 1/6(12 - 12)

1/3(9) ≤ 1/6(0)

3 ≤ 0 (False).

1/3(m - 3) ≤ 1/6(m - 12)

1/3(24 - 3) ≤ 1/6(24 - 12)

1/0.4(-80 - 39) ≤ 1/21(-40 - 39))

79.6 ≤ p < 80  (False)

1/0.4(m - 0.4) ≤ 1/21(m - 39) false are: S:{39, 40}​.

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Gracie shay must add $11,873 to buy that new hammer with its initial investment.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the given information in the question,

The price of hammer =$28,000

The annual rate of interest = 6%

Total number of years = 5

Principal investment = $12,000

The equation for annual compound interest, with the principal amount included, is :

A = [tex]P(1+\frac{r}{n} )^(^n^t^)[/tex]

Substitute all the values from above in the equation,

A = 12,000(1+0.06/2)⁽²⁾⁽⁵⁾

A = 12,000 × 1.03¹⁰

A = $16127

After five years, Gracie won't be able to be the hammer and will have to pay more money:

28000 - 16127 = $11,873.

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For the given expression the value of x must be 11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is h(x) = 11. The value of x will be calculated as,

h(x)=11

h(x) = x

Compare the above equations and find the value of x,

x = 11

Therefore, for the given expression the value of x must be 11.

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When a mass of 3 kg is hanged to it, the string will stretch 7.5 cm.

Given,

The length of the spring attached to the ceiling = 10 cm

The quantity of the mass hanged in the spring = 2 kg

The amount of stretching happened in the spring = 15 cm

We have to find the stretching of string when a mass of 3 kg is hanged to it;

Here,

Given that the force applied to the spring by the 2.0 kg is equal to the mass's weight:

F = mg = 2 kg × 9.8 m/s² = 19.6 N

Additionally, the stretching of:

Δx = 15 cm - 10 cm = 5 cm

So, applying Hooke's law:

F = kΔx

To determine the spring constant, k;

k = F/Δx = 19.6/5 = 3.92  N/ cm

The spring is now coupled to a new mass of m = 3.0 kg; the force this mass exerts on the spring equals

F = mg = 3 kg × 9.8 m/s² = 29.4 N

Thus, we may apply Hooke's law once more to determine the new stretching:

Δx = F/k = 29.4/3.92 = 7.5 cm

Therefore,

The string will be stretched 7.5 cm when a mass of 3 kg is hanged to it.

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