The formula F = (9/5)C + 32 can be used to convert between degrees Celsius (C) and degrees Fahrenheit (F). What number of degrees Fahrenheit corresponds to 30° Celsius?
Group of answer choices

A) 86

B) 13

C) 62

D) 22

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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Graph of ​y+6=45(x+3)​ using the point and slope is given.

The slope of a line in mathematics, usually referred to as its gradient, is a numerical representation of the steepness and direction of the line.

Standard form of the slope-intercept form;

y = mx + b,

where m is the slope and b is the y-intercept.

We have the equation,

​y+6=45(x+3)​

Simplifying,

y = 45x + 135 - 6

y = 45x + 129.

Now, comparing the equation to the slop-intercept form;

we get,

m = 45,

and b = 129

And point slope form is the slope-intercept form.

And the graph is given in the image.

Therefore, y = 45x + 129 is the required equation.

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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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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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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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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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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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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 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:

correct answer is option b i think...

To begin, let's find how much the book is including tax and the student discount.  Once we find this, we can see if Lara or Alex is correct and if they can afford it.

First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.

Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.

.35 x 28.50 = 9.975

28.50 - 9.975 = 18.525

Then he takes 10% of this number and adds it back.

.10 x 18.525 = 1.8525

18.525 + 1.8525 = 20.3775

Alex has the correct answer.

Next, we will see if Lara computed it correctly.

First she takes 65% of the normal price.

0.65 x 28.50 = 18.525

Then she computes 110% of the reduced price.

18.525 x 1.10 = 20.3775

Lara also gets the correct answer.

So, do they have enough money to purchase the book?

YES:

$20.38 < $21

Is Alex correct?

YES

Is Lara correct?

YES

Although they used different methods to get the answer, they both got the right one!

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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We can take Samanta's equation and rewrite it in such a way that we get Phil's equation, then the equations are equivalent.

Two equations are equivalent if we can rewrite one of them and get the other one.

We know that the equations are:

Samantha's equation: f(x)=(x+12)^2−16

Phil's equation: f(x)=(x+16)(x+8)

We can find the zeros of Samantha's equation by solving the quadratic equation:

(x+12)^2−16 = 0

(x + 12)^2 = 16

(x + 12) = ±√16

x + 12 = ± 4

x = ±4 - 12

Then the two zeros are:

x = (+4 - 12) = -8

x = (-4 - 12) = -16

Then we can factorize the quadratic function of Samantha as:

y = (x - (-8))*(x - (-16))

x = (x + 8)*(x + 16)

That is Phil's equation, then the equations are equivalent.

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The given expression 9x(46+70)5 - 32(40-219) is equal to = 10948.

What is mathematical expression?

A mathematical sentence that contains at least one operation, numbers, and/or variables without the equal sign is known as a mathematical expression.

Expressions does not have equal sign as the equations have.

Considering the given question as:

9x(46+70)5 - 32(40-219) = ?

At first we will solve the expressions inside of the brackets:

= 9x(116)5 - 32(-179)

Now, ,we will solve the rest of the expressions

= 9x580 + 5728

= 5220 + 5728

= 10948

Therefore, the answer of the given question is 10948

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Answer:

Step-by-step explanation:

answer is a

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

The given statement is FALSE.

Given info,

In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable.

⇒ The statement is FALSE.

Finding the degree and direction of the link between two numerical variables is made easier with the use of correlation analysis.

The value of one variable can be predicted based on the value of another using regression analysis.

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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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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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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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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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Answer:

Two dimensions.

Straight sides.

Congruent (equal-length) sides.

An interior and exterior.

Equal interior angles.

Equal exterior angles.

Step-by-step explanation:

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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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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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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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.

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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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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