sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?

The equation of the line in fully simplified slope - intercept form is 5x + y = 8 .

In the question ,

a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .

to find the equation , we need minimum two points ,

So , from the graph

we can see that

when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 8 ,

the first point is (0 [tex],[/tex] 8) .

when x [tex]=[/tex] 2 , the value of y [tex]=[/tex] -2 ,

the second point is (2 [tex],[/tex] -2) .

the slope can be calculated by

slope = (-2-8)/(2-0)

= -10/2

= -5

So , the equation of the line passing through point (2,-2) with slope -5 , in the slope intercept form is

(y -(-2)) = -5(x-2)

y + 2 = -5x + 10

Simplifying further , we get

5x + y = 10 - 2

5x + y = 8

Therefore , The equation  line in fully simplified slope - intercept form is 5x + y = 8 .

The given question is incomplete , the complete question is

Write the equation of the line in fully simplified slope-intercept form, the line graph is shown below .

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The value of the expression in the form of k² will be (T²/4π²)-h²).

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 T² = 4π² (h² + k²). The expression for the value of k² will be calculated as,

T² = 4π² (h² + k²)

(h² + k²) = T² / 4π²

k² =  (T² / 4π²) - h²

Therefore, the value of the expression in the form of k² will be (T²/4π²)-h²).

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Answer: 0.04536

Step-by-step explanation:

well, we know WXYZ is a kite, so is a quadrilateral, namely it has 4 sides, and it has two congruent angles, so

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 94+94+112+\measuredangle ZYW=360\implies \implies \measuredangle ZYW=60[/tex]

Check the picture below.

The equation of the line that passes through the point (8, 6) and has a slope of 0 is  y = 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through the point (8, 6) and has a slope of 0.

Therefore,

m = 0

Hence, let's find the y-intercept using the (8, 6)

y = mx + b

6 = 0(8) + b

b = 8

Therefore, the equation is y = 8

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Answer:

Here ,

sigma x=50+60+65+70+70+80+90=485

N=7

now,

Mean =sigma x÷N

=485÷7

=69.28

Answer:

May be helpful.

thx.......

Answer:22.5

Step-by-step explanation:

A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.

Therefore,

let x = the first piece and x+14 is the second.

2x + 8 = 36

2x = 28

x = 14, the other piece is 22

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Answer: C. 100,000 gallons

Step-by-step explanation:

10,000 gallons a minute.

10 minutes.

10,000 x 10 = 100,000.

Gallons:  10,000     20,000     30,000     40,000     50,000     60,000    

Minutes:       1               2               3                4               5                6              

... 70,000     80,000     90,000     100,000

...      7                8                9              10

8.08 percent of babies are born prematurely .

We have following information,

lengths of pregnancy of humans are Normally distributed.

mean of distribution ( μ ) = 268 days

standard deviations of distribution = 15 days

We shall find out the pecent of babies are born. prematurely.

Using the Normal distribution formula ,

Z = ( X - μ ) /σ

where X---> sample mean

μ --> poplution mean

putting the possble values of variables we get,

if a baby born three weaks early then he is considered as premature.

X = 21 , μ = 268 , r =

Z = ( 21-268)/ 15 = - 247/15 = - 16.4

Now, p-value corresponding to Z-value= -16.4 is

8.08..

thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.

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Answer:

4 hostel rooms

Step-by-step explanation:

okay so for this all you need to do is read the chart

Answer: 65°

Step-by-step explanation:

You can determine the total degree within a shape by using the formula 180°(n-2), where n is the number of sides of the shape. Thus, the total degree within the parallelogram is 360°.

Angles sum up to the total degree, meaning we need to add up all the angles we see and set them equal to the total degree. We have two (2x-15) and two x's.  

2(2x-15) + 2x = 360

Distribute the 2 to (2x-15), you will get 4x - 30.

4x - 30 + 2x = 360

Add like terms, 4x + 2x to get 6x.

6x - 30 = 360

Add both sides by 30 to isolate the 6x, because we are trying to determine the value of x, we need to isolate the term.

6x = 390

Divide both sides by 6, and you are left with the value of x being 65°

The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

Given,

In the question:

Use distributive property to remove parenthesis.

-9(-3w + 3u - 4)

Now, According to the question:

First, we know:

What does parentheses mean distributive property?

The distributive property allows us to multiply all terms in a parentheses by a number outside of it. a(b +c) = ab + ac.

We have:

-9(-3w + 3u - 4)

Solve by Distributive Property :

-9(-3w + 3u - 4)

Open the bracket:

27w - 27u +36

Hence, The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

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A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

So we know that the perimeter of rectangle is

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

As we know the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

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The translated absolute value function graphed is defined as follows:

y = |x - 3| + 5.

The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:

In this problem, the coordinates of the vertex are given as follows:

Hence the vertex is given by the following point:

(3,5).

Then the equation graphed is defined by the rule presented as follows:

y = |x - 3| + 5.

Which is a translation of 3 units right and 5 units up of the standard absolute value function.

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Answer:  how

Step-by-step explanation: love

Student B has raised the least amount of money after walking for 7 miles.

A unit rate means a rate for one of something.

Given that, three students are participating in a walkathon,

Student A's money is represented by the equation y = 13x, where y is money raised for walking x miles.

Student B raised $36 money for 3 miles and Student C has raised  $52 and $65 money for 4 and 5 miles respectively.

Money raised by each of them for a mile =

Student A = $13

Student B = $12

Student C = $13

Money raised by them by walking 7 miles =

Student A = $13*7 = $91

Student B = $12*7 = $84

Student C = $13*7 = $91

Hence, Student B has raised the least amount of money after walking for 7 miles.

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The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

f)Having distinct digits and even are 337

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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Answer:

The equation for the slope-intercept form is y = 4x - 10

Hope this helps!

Step-by-step explanation:

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]   Equation = y = mx + b

The two points given are ( -5, 10 ) and ( 0, -10 ).

Putting in the values gives you [tex]\frac{-10-10}{0-(-5)} = \frac{-20}{5} =-4[/tex].

y = 4x + b, to find b, insert one of the points:

-10 = 4(0) + b    ->   -10 = 0 + b,    b = -10

Putting it all together gives you y = 4x - 10

40 freezers could be shipped in the container.

What is a variable?

A variable is a quality that may be measured and take on several values.

We are given that

A railroad container can hold weight=42,000 pounds

Total number of ovens for ship=90

Weight of each oven=200 lbs

Weight of each freezer=600 pounds

We have to find the number of freezers that can be shipped in the container.

Let x be the number of freezers that can be shipped in the container.

According to the question,

42000=90(200)+600x

42000=18000+600x

600x=42000-18000=24000

x=24000/600=40

Hence, 40 freezers can be shipped in the container.

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Answer:

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

The six frequent factors between 72 and 90 are 1, 2, 3, 6, 9, and 18.

Consequently, 18 is the number that links 72 and 90 most frequently.

Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.

The central limit theorem is one reason they are significant.

This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size.

Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.

Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance.

Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.

The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line.

Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.

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x = 2/7

see explanation in image

Now we have to,

→ find the required value of c.

Formula we use,

→ (AC)² = (BC)² + (AB)²

Then the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

Each bag got 2 pieces of gums and 4 pieces of candies.

Given, that

Ana is making treat bags to give to her 10 students.

She puts x number of gum and 4 pieces of candy in each bag.

She had used a total of 60 pieces.

Now, as she puts 4 pieces of candy in each bag and she prepare total 10 bags.

So, She used total 4×10 = 40 candies

Now, if she used 60 pieces out of which 40 pieces are of candies

Then, 60 - 40 = 20 pieces

20 pieces will be of gums.

So, she puts total 20 pieces of gums in 10 bags

Hence, in each bag she puts 20/10 pieces of gums i.e. 2 pieces of gums

So, each bag got 2 pieces of gums 4 pieces of candies.

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Answer:

x-intercept(s): (−5,0)

y-intercept(s): (0,−5)

Explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Im also in K12 so Ez Good Luck

Hope this helped!