Which equation has the variable, or missing number, in the correct place to match the given situation?

The Lerch family drove a total of 482 miles, starting on Friday and ending on Sunday. They drove 138 miles on Friday and 225 miles on Saturday. How many miles did they drive on Sunday?

Kittens without black markings to kittens with black markings: 2:5

Kittens without black markings to total kittens: 2:7

Kittens with black markings to total kittens: 5:7

Answer:

a

Step-by-step explanation:

i ink

The value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

We are given the functions:

f(x) = x + 3

g(x) = x² − 2

Now,

(f + g) (−8) × (f + g)(−8)

= [ (f + g) (−8) ]²

Substituting the values of the functions, we get that:

=(x + 3 + x² - 2)² ,   where x = -8

= ( -8 + 3 + 64 - 2 )²

= ( -5 + 62)²

= (57) ²

= 3249

So, the value of the function  (f + g)(−8) (f + g)(−8) for f (x) = x + 3 and g (x) = x² - 2 is 3249.

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Answer:

3.24x10^-5,    5.48x10^-2,    1.2x10^1,      4.68x10^6,         8.34x10^6

Step-by-step explanation:

3.24 x 10^-5 = 0.0000324

5.48 x 10^-2 = 0.0548

1.2 x 10^1 = 12

4.68 x 10^6 = 4680000

8.34 x 10^6 = 8340000

If Max is building a set of shelves and he buys a board that is 4 yards long and he wants to cut as many pieces of board that are 3/4 yards long as he can, then the no of pieces he can cut is 5 and he will have 0.25 yards of board left over.

3/4 is a fraction which can be represented as,

3/4 = 0.75

The number of pieces of board that Max can cut that is 4 yards long can be determined by the division of the length of the board by the length of the cut pieces. Therefore,

number of pieces cut = length of the board ÷ length of a cut piece

number of pieces cut = 4 ÷ 0.75

number of pieces cut = 5.33, that is round off to 5

Thus he can cut 5 pieces of 3/4 yards.

As 5 × 3/4 = 3.75 yards

The remaining yards of the board can be calculated by subtraction.

Board leftover = 4 - 3.75 = 0.25 yards

Hence, Max can cut 5 pieces of 3/4 yards and will have 0.25 yards of the board left over.

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The midpoint is at ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

In the given statement is

To find the midpoint of the line segment joining the pair of points

B(√3, 2,2√2) and C(-2√3, 4,4√2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2} ,[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points B(√3, 2,2√2) and C(-2√3, 4,4√2)

Solving for the midpoint , we have,

m = ([tex]\frac{\sqrt{3}+(-2\sqrt{3} ) }{2}, \ \frac{2+4}{2}, \frac{2\sqrt{2} +4\sqrt{2} }{2}[/tex])

m = [tex]\frac{-2\sqrt{3} }{2} ,\frac{6}{2},\frac{6\sqrt{2} }{2}[/tex]

m = ([tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

Therefore, the midpoint is at( [tex]-\sqrt{3} , 3 ,3\sqrt{2}[/tex])

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Using a system of equations, it is found that there were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

There were 639,000 French Creole speakers, hence:

f = 639,000.

There were 186,000 more Arabic speakers than French Creole speakers, hence:

a = 186,000 + f = 186,000 + 639,000 = 825,000.

There were a total of 825,000 Arabic speakers, and the diagram is completed as follows:

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Option c is the correct answer. Sam's total earning for the day is equal to

E(n) = 2.5n + 24

Given data

Sam earning per hour = $6

Sam earning on tips per person = $2.5

Sam's total hour per day =4

Sam's daily earning excluding tips = Sam earning per hour * Sam's total hour per day

= $6 * 4 hours = $24

If n represents the number of people Sam serves that day, then Sam's earnings on tips in a day = $2.5 * n = $2.5n

The function for Sam's total earning is given by  E(n)

E(n) = Sam's daily earning excluding tips +  Sam's earnings on tips in a day

E(n) = $24 + $2.5n

this is re arranged as

E(n) = 2.5n + 24

Therefore we can say that Sam's total earning for the day is equal to

E(n) = 2.5n + 24

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Complete question

Sam is a waiter at a local restaurant where he earns wages of $6 per hour. Sam figures that he also earns about $2.50 in tips for each person he serves. Sam works 4 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E, his total earnings for the day?

A. E(n) = 2.5n

B. E(n) = 4n + 10

C. E(n) = 2.5n + 24

The following set of numbers, 10, 12, and 23, cannot be the measures of the sides of a triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 10, b = 12, and c = 23

a + b > c     10 + 12 > 23     22 > 23     False

a + c > b     10 + 23 > 12     33 > 12     True

b + c > a     12 + 23 > 10     35 > 10     True

If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.

Hence, the set of numbers 10, 12, and 23 can not be the measure of the sides of a triangle.

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The two consecutive odd integers are less than 76 is the numbers are 37 and 39.

Any integer's reverse and sum are both equal to zero.

A positive sum results from adding two positive numbers, whereas a negative sum results from adding two negative integers.

Take the absolute value of each integer, then subtraction, to obtain the total of a positive and a negative integer.

Let two consecutive odd numbers be x and x+2

According to question

⇒ x........... equation (1)

⇒ x+2........equation (2)

by adding equation 1 and 2

⇒ x+x+2=76

⇒ 2x+2=76

⇒ 2x=76-2

⇒ 2x=74    

⇒  x=74/2

⇒ x=37

We apply the value of x=37 in equation (2)

⇒ x+2

⇒ 37+2

⇒ 39

so, the numbers are 37 and 39.

Therefore, the two consecutive odd integers are less than 76 is the numbers are 37 and 39

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The transformation rule for the triangle P by translating the vector (2, -7) is ( x , y ) <=> ( x + 2 , y - 7 )

Transformation rule says that, if a translation occurs then each point of the shape will be shifted in the same direction with the same distance.

According to the rule , the translation for the triangle P using the vector (2,-7) is ( x + 2 , y - 7 ).

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The fish population will be the same as on January 1, 2002 on January 1, 2017 and all the fish in the lake will have died by 2019

The function is given as:

F(t) = 1000(30 + 15t - t^2)

Start by calculating F(0) --- population in 2002

So, we have:

F(0) = 1000(30 + 15(0) - 0^2)

F(0) = 30000

Substitute 30000 for F(t) in F(t) = 1000(30 + 15t - t^2)

1000(30 + 15t - t^2) = 30000

Divide by 1000

30 + 15t - t^2 = 30

Simplify

t^2 - 15t = 0

Divide through by t

t - 15 = 0

Solve

t = 15

This means that

Year = 2002 + 15

Year = 2017

Hence, the fish population will be the same as on January 1, 2002 on January 1, 2017

This means  that F(t)= 0

So, we have:

1000(30 + 15t - t^2) = 0

Divide by 1000

30 + 15t - t^2 = 0

Rewrite as

t^2 - 15t - 30 = 0

Using a graphing calculator, we have

t = 17 (approximated)

This means that

Year = 2002 + 17

Year = 2019

Hence, all the fish in the lake will have died by 2019

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The measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ =  8. and the triangle XYZ must be an acute triangle

In this questions we have been given the the coordinates of the triangle XYZ.

X(-4, -2), Y(-3, 7), Z(4, -2)

We need to find  the measures of the sides of ΔXYZ .

We find the the measures of the sides using distance formula.

XY = √[(7 + 2)² + (-3 + 4)²]

XY = √[9² + 1²]

XY = √(81 + 1)

XY = √(82)

XY = 9.1

Now side YZ

YZ = √[(-2 - 7)² + (4 + 3)²]

YZ = √[(-9)² + (7)²]

YZ = √81 + 49

YZ = √130

YZ = 11.4

And the length of side XZ would be,

XZ = √[(-2 + 2)² + (4 + 4)²]

XZ = √0 + 8²

XZ = 8

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 8² + 9.1²

= 64 + 82.81

= 146.81

= 12.12²

And 11.4² = 129.96

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, the measures of the sides of ΔXYZ are XY = 9.1, YZ = 11.4, XZ =  8. and the triangle XYZ must be an acute triangle

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The probability that she makes no more than 20 of them is 0.394

We use Binomial Distribution in solving this question.

The discrete probability distribution known as the binomial distribution only offers two outcomes for an experiment: success or failure.

Sum of independent Bernoulli trials is binomial distribution; a random Variable x is said to be following binomial distribution if it's density is given as

P(X=x) = (nCx) px (1−p)n−x    where x=0,1,2…n

Let x denotes the number of throws that makes a free throw so here

x follows Binomial distribution with n=28 and p=0.603

Thus, we calculate

P(X≤20) =∑_(k=0)^1▒1= (28Ck)0.603k (1−0.603)28−k =0.3144

=0.394

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Answer:

Step-by-step explanation:

B) is correct

Answer:

6

Step-by-step explanation:

Let's call the bands by numbers :

So we have Band 1,2 and 3

The orders can be :

1,2,3

2,3,1

3,1,2

1,3,2

3,2,1

2,1,3

so there must be 6 different orders

Another method of doing this is to called product rule of counting :

3 × 2 × 1 = 6

Hope this helped and have a good day

The equation of the line in standard form with slope equal to 2/3 and y -intercept (0 , 5) is 2x - 3y = -15.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the slope-intercept form, plug in the values of the slope and the point to set up the equation.

y = mx + b

where m = 2/3 and y-intercept, b = 5

y = 2/3 x + 5

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y = 2/3 x + 5

2/3 x - y = -5

Multiply both sides by 3 to have integer coefficients.

3(2/3 x - y) = -5(3)

2x - 3y = -15

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Answer:

0

Step-by-step explanation:

Substitute x for 1 and solve.

2(1) -2

2-2

0

Answer:

0 I belive

Step-by-step explanation:

f(x) =2x-2

f(1)= 2(1)-2

2-2

f(1)= 0

As per latent heat, size of 11.61 BTUH is required to complete the whole action.

Let's assume the ice was at 32° F. So, 144 BTU/lb is required as latent heat. To melt ice and make it 32°F water required BTU is:

10 × 144 = 1440 BTU ( m× l = H where m is the mass and l is the latent heat )

To, convert 10°F ice to 32°F ice required heat is,

10×0.5035× ( 32° - 10°) = 110.77 BTU ( H = msΔt, m= mass, s = specific heat of ice, and Δ t = difference in temperature which is, 32° - 10° = 22°)

Now, to convert 32°F water to 212°F water required heat is:

10×1×180 = 1800 BTU ( SPECIFIC HEAT OF WATER IS 1 and Δt = 212-32 = 180°F )

To covert 212°F water to 212°F steam the required heat is,

10 × 970 = 9700

Now, to convert 212°F steam to 400°F steam, the required heat is ;

10 × .47 × 188 = 883.6 BTU ( The specific heat if steam is .47, Δt = 188°F )

Now total heat is, 883.6 BTU +9700 BTU + 1800 BTU + 110.77 BTU + 1440 BTU = 13934 BTU

Required power to convert it within 20 min. or 1200 sec is,

13934/1200 = 11.61 BTUH.

We can now say that, if 10 pounds of ice starts at ten degrees and is changed to steam at 400 degrees in twenty minutes, 11.61 BTUH is required.

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Answer: x = 3

Step-by-step explanation:

From the diagram above , the area of a triangle especially a right angled triangle

A = 1/2 X b X h where b is the base and h is the height.
Now,

h = x + 3

b = x + 1

Now , substitute for those values in the formula provided vide

A = 1/2 x (x+ 3)( x + 1 ) and equated it to 12

= (x+3)(x+1)

—————. = 12

2

Now, multiply both side a by 2 to make it a linear equation or better put , cross multiply

= (x+3)(x+1) = 2 x 12

= (x+3)(x+1) = 24

Then open the bracket by multiplication

= x2 + x + 3x + 3 = 24

= x2 + 4x + 3 = 24

= x2 + 4x + 3 - 24 = 0

By solving this quadratically,

= x2 + 7x - 3x - 21 = 0 ,

( x2 + 7x) - ( 3x - 21 ) = 0

x( x + 7 ) - 3( x + 7 ) = 0

Therefore

( x+ 7 )( x - 3 ) = 0

Solving this gives

x = -7 or x = 3

Therefore x = 3 since x can’t be negative, x can’t be = -7

Using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units

Given,

The points = A(0,0) and B(15,20)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(15-0)^{2}-(20-0)^{2} }[/tex]

[tex]=\sqrt{15^{2}+20^{2} } \\=\sqrt{225+400}\\ =\sqrt{625}[/tex]

=25 units

Hence, using the distance formula, the distance between the pair of points A(0,0) and B(15,20) is 25 units.

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Using system of three equations, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

The standard form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Substituting the values of the x and y coordinates of each point to the standard form of the equation of a circle, the three system of equations are:

(x - h)^2 + (y - k)^2 = r^2

(0 , 0) : (0 - h)^2 + (0 - k)^2 = r^2

(6 , 8) : (6 - h)^2 + (8 - k)^2 = r^2

(7 , 7) : (7 - h)^2 + (7 - k)^2 = r^2

Expanding these equations,

(0 , 0) : h^2 + k^2 = r^2     (equation 1)

(6 , 8) : 36 - 12h + h^2 + 64 - 16k + k^2 = r^2     (equation 2)

(7 , 7) : 49 - 14h + h^2 + 49 - 14k + k^2 = r^2     (equation 3)

Subtracting equation 1 from equation 2 and 3.

36 - 12h + h^2 + 64 - 16k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

36 - 12h           + 64 - 16k           = 0

100 - 12h - 16k = 0

12h + 16k = 100

Dividing both sides by 4,

3h + 4k = 25     (equation 4)

49 - 14h + h^2 + 49 - 14k + k^2 = r^2

-                (h^2 +                 k^2 = r^2)

49 - 14h            + 49 - 14k          = 0

98 - 14h - 14k = 0

14h - 14k = 98

h + k = 4     (equation 5)

h = 7 - k

Substitute h = 7 - k to equation 4 and solve for k.

3h + 4k = 25     (equation 4)

3(7 - k) + 4k = 25

21 - 3k + 4k = 25

k = 25 - 21

k = 4

Substitute the value of k to equation 5 and solve for h.

h = 7 - k     (equation 5)

h = 7 - 4

h = 3

Substitute the value of h and k to equation 1 and solve for r.

h^2 + k^2 = r^2     (equation 1)

3^2 + 4^2 = r^2

9 + 16 = r^2

r^2 = 25

r = 5

Hence, the equation of the circle that contains the points (0 , 0), (6 , 8), and (7 , 7) is (x - 3)^2 + (y - 4)^2 = 25.

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The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 0 and (x1 , y1) = (4 , -2)

(y - -2) = 0(x - 4)

(y + 2) = 0

y = -2

In slope-intercept form, the equation of the line is:

(y + 2) = 0

y = -2

In standard form, the equation of the line is:

y = -2

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Answer:-5/4

Step-by-step explanation:

The solution of the above equation y/5 + y/2 = 7 for y is 10.

According to the given question.

We have an equation y/5 + y/2 = 7.

Since, we have to solve the above equation y/5 + y/2 = 7 for y.

Therefore, the solution of the above equation for the above equation y/5 + y/2 = 7 is given by

y/5 + y/2 = 7

⇒ (2y + 5y)/10  = 7

⇒ 7y /10 = 7

⇒ 7y = 70

⇒ y = 70/7

⇒ y = 10

Hence, the solution of the above equation y/5 + y/2 = 7 for y is 10.

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(a) 2.1°C per minute

(b) 1.9°C per minute

(a)

(b)

Answer:

£41.20

Step-by-step explanation:

Pack of 10 x 8 = 80

(I got the 8 from 84)

80 divided by 2 = 40

then all you need are 4 pencils = 1.20

40 + 1.20 = 41.20

Hope this makes sense aha, if it doesn't just contact me :) xx

The number of packs of markers Mr. Sowers can purchase is 6.4 packs.

According to the task content, it is required that an inequality should be written and solved for the number of packs of markers Mr. Sowers can purchase.

5.49x ≤ 35

x ≤ 35 / 5.49

x ≤ 6.375227686703096

Approximately

x ≤ 6.4

Therefore, the number of packs of markers Mr. Sowers can purchase is 6.4 packs

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