:
Ethan needs to add together two whole numbers
and wants to estimate the answer first.
He rounds both numbers to 1 significant figure,
which gives him 300 and 600, and adds them
together to get an estimate of 900.
What is the greatest possible difference
between his estimate and the true answer to the
addition?

A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.

The power function is a function that links the true value of a parameter to the probability of rejecting a null hypothesis about the value of that parameter.

A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. (A number that multiplies a variable raised to an exponent is known as a coefficient.) As an example, consider functions for area or volume.

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The equation of the line is y = 7x + 6 when  the line crooses the y-axis at the point (0,6) and has a slope of 7

The line crosses the y-axis at the point (0,6)

The slope of the line is 7

The equation of a line in slope point form is

y - y' = m(x - x')

Where m stands for the slope of the line and x' y' are the coordinates of the point through which the line passes.

So, the point x',y' is 0, 6 and the slope m is 7

y - y' = m(x - x')

y - 6 = 7 (x - 0)

y - 6 = 7x

y = 7x + 6

Therefore, the equation of the line which  crosses the y-axis at the point (0,6) and has a slope of 7 is y = 7x + 6

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Answer:

y -1 = -1/3 (x -6)

Step-by-step explanation:

Answer:

2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

simplifying

[tex]\sqrt{45}[/tex]

= [tex]\sqrt{9(5)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex]

Then

[tex]\sqrt{45}[/tex] - [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex] - [tex]\sqrt{5}[/tex]

= 2[tex]\sqrt{5}[/tex]

Answer:

16

Step-by-step explanation:

You have to know which theorem applies. This theorem only works because we know line m and line n are parallel.

Alternate Exterior Angles theorem says 111 degrees and 7x-1 are congruent.

This means we can set them equal to each other:

7x - 1 = 111

Solve for x:

7x = 112

112 / 7 = x

x = 16

It will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline

Given that: Chad is planning a 672–mile road trip

Chad’s car can travel 308 miles with 11 gallons of gas. We can use this information to calculate the miles 1 gallon can cover. Thus:

Number of miles per gallon =   308/11 = 28 miles per gallon

Also, Chad plans to drive 168 miles every 3 hours. We can use this information to calculate Chad's speed. Thus:

Speed = 168/3 =  56 miles per hour

To determine how many hours it will take Chad to drive 672 miles:

Speed = distance/time

=> time = distance/speed    

Speed = 56 miles per hour and distance =  672 miles

time = 672/56 = 12 hours

Number of gallons = distance / Number of miles per gallon

Number of gallons = 672/28 = 24 gallons

Therefore, it will take Chad 12 hours to drive 672 miles and he will need 24 gallons of gasoline

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The probability of a bill exceeding $300 is 0.0091.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

For normal distribution z score = (X-μ)/σ

here mean= μ = 196

std deviation  = σ = 44.0000

probability of a bill exceeding

$300  = P(X>300)

          =P(Z>(300-196)/44)  

          =P(Z>2.36)

          =0.0091

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The true Statements are : π is the area of the circle of radius 1 and π is the circumference of diameter 1.

What is Area of a Circle ?

The area of a circle is pi times the radius squared (A = π r²)

Putting r =1 ,we get

A = π×(1)² = π

What is Circumference of a Circle ?

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

C = π×D

putting D =1 , we get

C = π

Hence,  π is the area of the circle of radius 1 and π is the circumference of diameter 1.

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The minimum score required for recruitment is 669

The normal distribution is expressed as

z = (x - µ)/σ

Where

x = SAT Mathematics scores.

µ = mean score

σ = standard deviation

From the question, we have

µ = 518

σ = 113

The probability value for the top 9% would be (1 - 9/100) = (1 - 0.09) = 0.91

the z score corresponding to the probability value is 1.34

1.34 = (x - 518)/113

1.34 × 113 = x - 518

151.42 = x - 518

x = 151.42 + 518

x = 669 to the nearest whole number.

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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After solving, her total finance charge was $11.65.

In the given question we have to find her total finance charge.

Mrs. stevens bought identical gifts for her children = 5

Each gift value = $80

So, Total cost = $80×5

Total cost = $400

She paid total 1/2 cost.

Financed the remaining balance through her credit union for 18 months at 9 % interest.

the money is paid 1/2

The rest amount is converted into EMIs.

P = $200

r= 9% = 0.09

n =18 months

[tex]\text{EMI}=P\times\frac{r}{n}\left [ \frac{(1+\frac{r}{n})^n}{(1+\frac{r}{n})^n-1} \right ][/tex]

Put the values.

[tex]\text{EMI}=200\times\frac{0.09}{18}\left [ \frac{(1+\frac{0.09}{18})^{18}}{(1+\frac{0.09}{18})^{18}-1} \right ][/tex]

After solving

EMI = $11.65

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The ladder is 26ft far up to the wall if the bottom of a 10-foot ladder is 2 ft closer to the wall.

A unit of length is any arbitrarily defined and agreed reference standard for measuring length.

The measurement or extent of something from end to end is defined as its length. In other words, it is the larger of two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and width dimensions.

Distance on the ground = 10 feet

Length of the  ladder (hypotenuse) = x      

Height on the wall =  x-2

According to the  Pythagorean theorem of a right angle,

a²+b²=c²

100  + (x-2)²  =x²

100 + x² -4x + 4 =  x²      

100 -4x + 4 = 0              

104 - 4x = 0                  

-4x = -104              

x = 26ft

The ladder is 26ft far up to the wall.

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The correct notation for the 8th term of the expansion (3x – 5)12 would be (3x)^(-5)8.

The term "expansion" describes the process of expanding or expanding. It can be used to describe actual expansion, such as when an organism gets bigger or a gas expands to fill a container. It can also relate to abstract notions such as the development of thoughts or knowledge. Extension in economics refers to growth in the size of the economy or in a specific sector of the economy, such as a rise in goods and services output. The process of conquering or occupying additional areas, such as when a nation extends its borders by conquest or settlement, is another definition of expansion. The act of growing larger or more extensive is generally referred to as expansion.

How to solve?

(3x – 5)12 = (3x)12 – 12(3x)11(5) + 66(3x)10(5^2) – 220(3x)9(5^3) + ... + (-5)12

The 8th term of the expansion (3x – 5)12 is (-5)8(3x)4, which can be written as (3x)^(-5)8.

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The model assumption are satisfied in histogram, residuals vs order of collection and residuals vs fitted values.

HIstogram

We can see from the histogram that the residuals are normally distributed, so the assumption that the errors are normally distributed is met.

residuals vs. the fitted values

We find a circular pattern where the errors are concentrated based on the residuals vs. the fitted values. indicating a breach of the assumption of equal variance (homoscedasticity). There is another nonlinear pattern that should be investigated.

Residuals vs. Order of collection

: Because the residuals are randomly distributed, the assumption of equal variance of the residuals is not violated.

Residuals vs. gestational length

A The gear concentration of the residuals in the shape of an oval indicate additional signals from the data that have not been modelled. As a result, the assumption of equal variance of the residuals is violated, and it may also indicate a nonlinear relationship between the dependent and independent variables. This problem can be solved by taking the log of the independent variable and normalising the data.

Parity vs. residuals

Because this is a binary variable, the plot provides no clear indication.

Residuals vs. mother's height

There is a clear oval pattern visible, indicating that the variable is violated.

Residuals vs. mother's weight

There is a clear oval pattern visible, indicating that the variable is violated.

Smoking vs. Residuals

Because this is a binary variable, the plot provides no clear indication.

Overall, this is the next step. We must examine the variables for multicollinearity. Because the residuals histogram is normally distributed, but the residuals vs fitted values has a violation.

We must determine whether the independent variables are correlated with one another. If they are correlated, we must discard the one that is least correlated with the target variable.

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The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

The slope intercept form is used to calculate the y-intercept and slope of a straight line.

We know that the equation of the line is, y= mx +b

4x+y-1=0 is the same as y= -4x+1

For this equation, b=1, but for a line with slope -4 passing through the point (1,2), the y-intercept changes.

y= -4x+b

The above line is passing through the point (1, 2)

2=-4(1)+b

Now, we have to solve for b value we get b=6.

The equation that we get is,

y= -4x+6 or 4x+y-6=0.

The equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0 is  4x+y-6=0.

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Negative one-sixth times the quantity 3 minus 15 times the quantity one-third squared end quantity is C. negative two ninths.

Fractions: A fraction can represent any number of equal parts or a portion of a whole. A fraction is a word used in everyday English to indicate the number of parts of a given size, such as one-half, eight-fifths, or three-quarters.

we will compute the expression,

The expression will be, based on the information provided:

= 1/6 ×( 3 - 15 ) × (1/3)²

= -1/6 × -12 × 1/9

= -2 × 1/9

= -2/9

thus, we can conclude that a negative two-ninth is the correct answer to the expression.

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In the Marital Instability Over the Life Course project, when men were asked to indicate the cause of their divorce, the most common response from the men was incompatibility. And the most common response from the women was infidelity.

Marital instability is described as including the range of activities from thinking about and discussing divorce to actually filing for either separation or divorce. There are a lot of causes of marital instability, but the most common causes are money problems and lack of intimacy.

Marital Instability Over the Life Course project is a nationwide longitudinal study started in 1980 with funding from the Social Security Administration's Office of Research and Statistics and the National Institute on Aging. This study measures predicting marital instability and divorce and assessing marital quality were developed.

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The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given that,

Principle amount P = $2000

Rate of interest R = 12%

Compounded quarterly n = 4

Time period T = 3 years

Total amount = P{1 + R/n]^(nT)

Total amount = 2000[1 + 0.12/4]^(4×3)

Total amount = $2851.52

Hence "The total amount owed after 3 years with the given rate of interest compounded quarterly will be $2851.52".

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The 3 ways to prove two triangles are similar are AA, SSS and SAS Similarity Postulate.

In the given question we have to explain the 3 ways to prove two triangles are similar.

Similar triangles are described as having the same shape but varying sizes. Examples of related objects include squares with any side length and all equilateral triangles. Alternatively put, if two triangles are similar, their corresponding sides will be proportionately equal and their corresponding angles will be congruent.

The 3 ways to prove two triangles are similar are:

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We apply permutation formula to the number of participants considering that there are no ties and find out that there are 60 different outcomes possible if there are no ties.

It is given to us that -

There are 5 participants - Abe, Bobby, Charles, Devin, and Edwin

We have to find out the number of different 1st - 2nd - 3rd place outcomes that are possible if there are no ties.

Considering that there should be no ties,

If we select one person, say Abe, then there are 4 different ways remaining for the second place in the race.

Similarly, assuming that Abe ranked 1st in the race and Bobby ranked 2nd in the race, there are 3 different ways remaining for the third place in the race.

Continuing like this, the 5 different participants can be ranked accordingly such that there are no ties.

For this situation, we have to find the permutation where -

Total number of objects (in this case, participants) = n = 5

and, total number of objects selected = r = 3

We know that the formula for permutation is -

[tex]P = \frac{n!}{(n-r)!}\\[/tex]

Substituting the values of 'n' and 'r' in the above equation, we have

[tex]P = \frac{n!}{(n-r)!}\\= > P = \frac{5!}{(5-3)!}\\= > P = 60[/tex]

Thus, by applying permutation formula, we find out that there are 60 different outcomes possible if there are no ties.

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4s2 4p1 - electronic configuration corresponds to gallium

Periodic table has 4 different blocks, which are s block, d block, p block, and f block. Each block has corresponding elements which gives its electron configuration

What is group and period?

Prediction of Period ⟶ In electronic configuration of an atom, principal quantum number (n) of valence electrons represents the period of an element.

Prediction of Block ⟶ The orbital out of s,p,d and f which receives last electron represents block of an element

Prediction of Group ⟶ The group prediction occurs with help of block as:-

(1) For s block: Group Number = Number of valence e-

(2) For d block: Group Number = Number of e- in (n−1)d subshell + number of e- in ns subshell

(3) For p block: Group Number = Number of valence

e- + 10

(4) For f-block: Group Number = 3

Lets take an ex of chlorine ( Z= 17 )

Electronic configuration = 1s2 2s2 2p6 3s2 3p5

Since the last e- enters in p - subshell:

(i) Therefore Block will be "p "

(ii) For group we have element in p-block

∴ Group number = 10 + Valence e- in s subshell + Valence e- in p subshell

Group Number = 10+2+5=17

(iii) For period

Quantum number of valence e- =3

∴ Period number = 3

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The inequality that represents the number of quarters in the jar is [tex]y \geq 24[/tex].

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Tyler filled a little container with quarters and dimes and gave it to his school's foundation club. The club party getting the container inquired, "Do you end up realizing how much is in the container?" Tyler said, "I know it's something like $8.50, yet I don't have a clue about the specific sum."

Let x be the number of dimes and y be the number of quarters. Then the inequality is given as,

0.10x + 0.25y ≤ 8.50

The inequality that represents the relationship will be 0.10x + 0.25y ≤ 8.50.

The inequality that represents the number of quarters in the jar, can be get by solving the above inequality for y, 0.10x + 0.25y ≤ 8.50.  can be written as [tex]y \geq \frac{8.5 - 2.5}{0.25}[/tex]  or  [tex]y \geq \frac{8.5}{0.25}[/tex]  or [tex]y \geq 24[/tex] .

Hence, the inequality that represents the number of quarters in the jar is   [tex]y \geq 24[/tex] .

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Disinfection of dental impressions should last b)15 minutes. So, correct option is b.

Disinfection of dental impressions is an essential routine that actually aims to protect the dental personnel, who handle impressions or casts, against exposure to diseases brought about by the contact with microorganisms such as the viruses; hepatitis B, hepatitis C, herpes, and HIV, and Mycobacterium tuberculosis (Hemalatha & Ganapathy, 2016).

Impression materials that have been exposed to the infected saliva and blood provides a significant source of such infectious agents. Dental checkups are increasing now a days very frequently.

Hence, option b is correct.

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(Complete question) is:

disinfection of dental impressions should last minutes. a)5 b)15 c)30 d)60

The length of fence  is 170feet if a rectangular garden measures 60 feet by 25 feet. Fencing is used to cover the garden from any unwanted animals.

A fence is defined as the structure that encloses an area, typically outdoors, and is usually constructed from the posts that are connected by boards, wire, rails or netting.

We know very well that the length of the fencing can be found by the perimeter of rectangle.

Perimeter of rectangle is given by =2×(length + breadth) or

=>P=2L +2W

if L is the length of rectangle and W is the width of rectnagle

Now, here we have length of rectangular garden as 60 feet and width as 25 feet

=>P=2×60+2×25

=>P=120+50

=>P=170feet

Hence, required length of fence is 170 feet.

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The solution for this system of linear equation is (-16, -5 1/3)

What in mathematics is a linear equation?

From the first equation, x = 3y

Substituting the expression on the right for the value of x on the second equation,

                                  -2(3y) + 3y = 16

Solving for the value of y gives y = -5 1/3

With this value of y, solving for x gives x = -16

Thus, the solution for this system of linear equation is (-16, -5 1/3)

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The complete question is -

What is the solution to this system of linear equations? x − 3y = −2 x + 3y = 16

Answer: -15

Step-by-step explanation:

do 17-32= -15

Answer:

D

E

Step-by-step explanation:

Prime factorize 252.

252 = 2 * 2 * 3 * 3 * 7

[tex]\sf \sqrt{252}=\sqrt{2*2*3*3*7}[/tex]

        [tex]\sf = 2*3\sqrt{7}\\\\=6\sqrt{7}[/tex]

D

[tex]\sf \text{The exponent form of } \ \sqrt{252}=252^{\frac{1}{2}}[/tex]

E

Step-by-step explanation:

so, first, let's see the factors of 252 :

252 / 2 = 126

126 / 2 = 63

63 / 2 no

63 / 3 = 21

21 / 3 = 7

so, 252 = 2×2×3×3×7 =

= 4×9×7 =

= 36×7 =

= 42×6 =

= 18×14

and others. but these are closest to the given answer options.

A. is wrong. 126^(1/2) is the same as sqrt(126). that is of course not the same as sqrt(252).

B. is wrong. to leave 6 in the square root, the remaining factor is 42. and sqrt(42) is not 7.

C. is wrong. to leave 7 in the square root, the remaining factor is 36. and sqrt(36) is not 18.

D. is correct. see C. sqrt(36) = 6. so, sqrt(252) = sqrt(36×7) = 6×sqrt(7).

E. is correct. 252^(1/2) is exactly the same as sqrt(252). an exponent of 1/n means the nth root.

the linear regression equation that represents this set of data rounding all coefficients to the nearest tenth is ŷ = 0.23571X + 75.24762

Sum of X = 120

Sum of Y = 1157

Mean X = 8

Mean Y = 77.1333

Sum of squares  = 280

Sum of products (SP) = 66

Regression Equation = ŷ = bX + a

b  = 66/280 = 0.23571

a = 77.13 - (0.24*8) = 75.24762

ŷ = 0.23571X + 75.24762

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20%(20 percent) of the people  are 25 or older according to the line plot that shows the ages of people taking a driving test at a certain station one day.

Percentage signifies a fraction of a total amount and means "per 100." For instance, 45% denotes 45 out of 100. Finding the percentage of a whole in terms of 100 is what percentage calculations are all about. It can be computed manually or with the use of internet calculators.

A % is a relative figure that represents one tenth of a quantity. One percent is a hundredth part; consequently, 100 percent denotes the complete amount and 200 percent specifies twice the supplied number. percentage

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth.

The total number of people we have are 25

From the line plot given, we see that fived people are 25, or older

Then,

5 / 25

=  1 / 5  

= 20 %

Hence, 20% of the people  are 25 or older according to the line plot that shows the ages of people taking a driving test at a certain station one day.

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Answer:

14

Step-by-step explanation:

-2(-12)/3-(-2+(-4))

=24/3-(-2+(-4))

=8-(-2+(-4))

=8-(-2-4)

=8-(-6)

=8+6

=14