In how many ways can the digits in the number 7,400,000 be arranged?

Answer:

785.204

Step-by-step explanation:

700+80+5+.2+.004

785.204

Answer:

(-5,-9)

Step-by-step explanation:

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14   let's call this equation 1.

x-2y=-12   let's call this equation 2.

-x+Зу-2z =13  let's call this equation 3.

USING EQUATION 1 AND EQUATION 3.

2х+5y-3z-=14   (EQUATION 1)

-x+Зу-2z =13  (EQUATION 3)

LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.

2х+5y-3z-=14   (EQUATION 1) * 2

-x+Зу-2z =13  (EQUATION 3) * 3

4х+10y-6z-=28   let's call this equation 4.

-3x+9у-6z =39  let's call this equation 5.

TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).

4х+10y-6z-=28   (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11  let's call this equation 6.

USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.

x-2y=-12  (EQUATION 2)

x + y = -11  (EQUATION 6)

x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.

We will subtract equation 6 from equation 2. Take note of the signs.

x-2y=-12  (EQUATION 2)

- (x + y = -11)  (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

Divide both sides by -3.

-3y/-3 = -1/-3

y = 1/3

LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.

x-2y=-12  (EQUATION 2)

x-2(1/3)=-12  

x -2/3 = -12

Add 2/3 to both sides.

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.

2х+5y-3z-=14   (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14  

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

Add 21 to both sides.

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

Divide both sides by -3.

-3z/-3 = 35/-3

z = -35/3 or  

Therefore, x = -34/3, y = 1/3, and z = -35/3

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(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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Table 1: 1.683 Table 2: 9

The missing values in the table will be 11.452.

Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.

The given data from the table;

\(\rm f(x)=b^x\)

For the first function;

\(\rm b^(0.683)= 3 \\\\ b= 4.995\)

The blank data is found as;

\(\rm b^x = 8 \\\\ \rm (4.995)^x = 8 \\\\ x \ log \ 4.995 =8 \\\\ x=11.452\)

Hence the missing values in the table will be 11.452.

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Answer:

75%

Step-by-step explanation:

To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.

According to the information provided:

55% of the team does not like to run.

Of those who do not like to run, 70% enjoy cycling.

Of those who enjoy running, 80% also enjoy cycling.

To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.

Percentage of athletes who do not like to run and enjoy cycling:

= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)

= 55% * 70% = 38.5%

Percentage of athletes who enjoy running and enjoy cycling:

= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)

= (100% - 55%) * 80% = 45% * 80% = 36%

Total percentage of athletes who enjoy cycling:

= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling

= 38.5% + 36% = 74.5%

Therefore, the correct answer is:

74.5%

Answer:

----------------------------

Find the composition of the functions f(x) and g(x), which is written as f(g(x)).

Given functions:

Find f(g(x)):

Evaluate f(g(2)):

So, (f·g)(2) = 14.

Answer:

Each boxed lunch costs $11.20

Step-by-step explanation:

29 boxed lunches = $324.80

divide by 29 on each one

1 boxed lunch = $11.20

The unit cost of each boxed lunch would be; 11.20 dollars.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that company orders 29 boxed lunches from a deli for $324.80. If each boxed lunch costs the same amount, then;

29 boxed lunches = $324.80

Now divide by 29 on each one to get the unit cost;

1 boxed lunch = $11.20

Each boxed lunch costs = $11.20

Hence, the unit cost of each boxed lunch would be; 11.20 dollars.

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Answer:

Ok

Step-by-step explanation:

Answer:

US basketball legend Kobe Bryant and his daughter Gianna were among nine people killed in a helicopter crash in the city of Calabasas, California. Bryant, 41, and Gianna, 13, were travelling in a private helicopter when it came down and burst into flames. The LA county sheriff said there were no survivors.

Answer:

y=4

x=3

Step-by-step explanation:

2y-4=y

y=4

4x=x+9

3x=9

x=3

The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

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9514 1404 393

Answer:

  62°

Step-by-step explanation:

If x is the largest angle, the sum of angles in the triangle is ...

  x + (x -3) +(x -3) = 180

  3x -6 = 180 . . . . . simplify

  x -2 = 60 . . . . . . . divide by 3

  x = 62 . . . . . . . . . .add 2

The largest angle is 62°.

Answer:

72 minutes

Step-by-step explanation:

You need to set up 2 fractions and set them equal to one another to be able to solve this.

Equation: 4km/18min = 16km/x min

You need to find x. In order to do this you can use that butterfly method/cross multiplication. You do 4 times set equal to 18*16.

Next, you get 18*16=288 and you must divide the other side (4x) to get your final answer. So, 288/4= 72 minutes.

Hope this was helpful!

Answer:

Scale factor = 2 for C

Scale factor = 2 for D

Scale factor = 2 for B

Step-by-step explanation:

Shape C has the dimensions of 2 x 6

Shape A has the dimensions of 1 x 3

Shape C is exactly 2 times an englargement of A because:

multiply 1 (dimension of A) times 2 (scale factors) = 2 (dimension of C)

multiply 3 (dimension of A) times 2 (scale factors) = 6 (dimension of C)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Shape D has the dimensions of 2 x 6

Shape A has the demensions of 1 x 3

Shape D is exactly 2 times an englargement of A because (same as C):

multiply 1 (dimension of A) times 2 (scale factors) = 2 (dimension of D)

multiply 3 (dimension of A) times 2 (scale factors) = 6 (dimension of D)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Shape B has the dimensions of 3 x 9

Shape A has the demensions of 1 x 3

Shape B is exactly 3 times an englargement of A because:

multiply 1 (dimension of A) times 3 (scale factors) = 3 (dimension of B)

multiply 3 (dimension of A) times 3 (scale factors) = 9 (dimension of B)

Solving log12 20,736 is 3

To solve for log12 20,736, we need to determine what power of 12 is equal to 20,736.

We can do this by repeatedly dividing 20,736 by 12 until we get a quotient less than 12:

20,736 / 12 = 1,728

1,728 / 12 = 144

144 / 12 = 12

So we can write 20,736 as 12 raised to the power of 3 (since we divided by 12 three times):

20,736 = 12^3

Now we can take the logarithm of both sides, using the rule that log a b^c = c log a b:

log12 20,736 = log12 12^3

log12 20,736 = 3

Therefore, log12 20,736 = 3.

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Solution:

Luisa's method is given below as

Sam's method is given below as

To score a point correctly will take a positive sign, while to get an incorrect point will take a negative sign and hence be substracted

Luisa's method subtracted directly the incorrect points from the correct points to get the remaining scores

While,

Sam's method added the correct score to the incorrect score while introducing a negative sign in front of the 400

Answer: 2x+35

Step-by-step explanation:

distribute -7

9x-7x+35

like terms

2x+35

Answer:

2x+35

Step-by-step explanation:

Multiply 7 with 5

Combine 9x with the x which would be 10x

10 divided by 1/2 which is 5- 2x

Answer:

5 over 12

Step-by-step explanation:

Given:

Required:

To complete the square that leads to the equivalent equation (x +__ )^2 = __.

Explanation:

Consider

Final Answer:

Answer:

105cm squared

Step-by-step explanation:

I put my answer here before, but somehow it got deleted, so I'm typing it again.

A square-based pyramid is made up of one square and four triangles.

We know that one side of the square is 5cm. And since all four sides of the square are the same, we know that the base is 5 x 5.

5 x 5 = 25

Therefore, the area of the base is 25cm squared.

Now, we need to find the area of one triangle. To find the area of a triangle, we multiply the base by the height, then halve it. We know that base of the triangle is 5cm as it shares a side with the square. We also know that the height of the triangle is 8cm.

5 x 8 = 40

40 / 2 = 20

Therefore, the area of one triangle is 20cm squared.

But wait! There are 4 triangles, not just one. Which means we have to multiply the area of one triangle by 4.

4 x 20 = 80

Add everything together:

25 + 80 = 105

Therefore, the total surface area of the square-based pyramid is 105cm squared.

Deepa makes use of the geometric property of similar triangles formed by

incident and reflected rays to determine the height of the goalpost.

Reasons:

When an object is reflected on a mirror, the angle of incidence, θ₁ is equal

to the angle of reflection, θ₂.

θ₁ = θ₂

Given that the angle, ∅₁, the incident ray of light and the angle, ∅₂, the

reflected light make with horizontal are both complementary angles, to the

angle of incident and reflection, respectively, we have;

θ₁ + ∅₁ = θ₂ + ∅₂

θ₁ = θ₂

Therefore, by subtraction property of equality, we have;

∅₁ = ∅₂

The vertical line from the top of the goalpost to the base of the goalpost

and the the vertical line from Deepa's eyes to the ground on which her feet

is standing are both perpendicular to the ground, therefore, the light from

the top of the goalpost to the mirror and to her eyes form similar triangles

by Angle Angle similarity postulate, which gives;

\(\displaystyle \frac{6.95}{9.35} = \frac{1.35}{The \ height \ of \ the \ goalpost}\)

6.95 × Height of the goalpost = 1.35 × 9.35

\(\displaystyle Height \ of \ the \ goalpost = \frac{1.35 \ m \times 9.35 \ m}{6.95 \ m} \approx 1.82 \ m\)

The height of the goalpost is approximately 1.82 meters.

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Answer:

it call enlargement and similarities and for the boxes they are showing u that u will work for scale factor and it with the boxes

Answer:

E

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

slope = rise / run = 7 / 1 = 7

m = 7

y-intercept = 0

So:

y = 7x + 0

y = 7x

Answer:

7 cups

Step-by-step explanation:

1/2 * 2 times per day * 7 days per week = 7