which statement could be represented by the expression 10g - 5?

Answer:

\($1,800\)

He can wear 8 different outfits to school.

We have,

The boy can choose one pair of pants, one shirt, and one tie can be written as an expression as:

= 1 × 1 × 1

= 1 way.

He can choose one jacket in 8 ways.

Therefore, he can wear can be written as an expression as:

= 1 × 1 × 1 × 8

= 8 different outfits.

Thus,

He can wear 8 different outfits to school.

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Answer:

%25 of customers ordered ice tea.

Step-by-step explanation:

To find percentage = Part/Whole x 100

35/140 x 100 = 0.25 x 100 = %25

Answer:

A function that changes the same way can be a linear function.

y = a*x + b.

Where the rate of change (this is, how much changes y when x increases or decreases) is defined by the coefficient a, that is constant.

for example, suppose that when x = x0, we have y = y0

y0 = a*x0 + b.

Now x0 increases by one unit, to (x0 + 1)

y = a*(x0 + 1) + b = (a*x0 + b) + a = y0 + a.

Then if x increases (or decreases) 1 unit, y increases (or decreases) a units.

Now, we can define the rate of change of a function as it's derivate with respect to some variable.

In this case, if we derive with respect to x, we have:

y' = a

Then the rate of change is constant.

Answer:

Ok, sabemos que:

Las medidas de cada mayólica tipo A son 45 cm x 45 cm.

Las mayólicas son cuadradas, y el área de un cuadrado de lado L es:

A = L^2.

Entonces el área de una mayólica tipo A es:

A = (45cm)^2 = 2,025cm^2.

Ahora, sabemos que en el patio 1 Víctor coloca 9 de estas en cada lado.

Entonces cada lado de este patio mide 9 veces 45cm

9*45cm = 405cm

El patio 1 es de 405cm x 405cm

el área es:

A1 = 164,025 cm^2

Ahora vamos al patio 2.

Acá usa mayólicas de tipo B, que son 30cm x 30cm

Y usa 12 en cada lado, entonces cada lado de este patio mide 12 veces 30 cm

12*30cm = 360cm

El patio dos es de 360cm x 360cm.

El área es:

A2 = 129,600 cm^2

Entonces:

Patio 1 tiene mayor área, y la diferencia entre las áreas es:

D = A1 - A2 = 164,025 cm^2 - 129,600 cm^2 = 34,425cm^2

Usando la fórmula para el área de un cuadrado, tiene-se que:

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

El área de un cuadrado de lado l es dado por:

\(A = l^2\)

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

\(A_{A} = 4.05^2 = 16.40 \text{m}^2\)

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

\(A_{B} = 3.6^2 = 12.96 \text{m}^2\)

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

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EXPLANATION

Given the system of equations:

(1) 3x + 5y = -17

(2) 2x + 4y = 6

Multiplying (1) by 2 and (2) by 3:

(1) 6x + 10y = -34

(2) 6x + 12y = 18

Subtracting (2) to (1):

(2) 6x + 12y = 18

-

(1) 6x + 10y = -34

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

2y = 52

Dividing both sides by 2:

y = 52/2

Simplifying:

y = 26

Simplify:

Divide both sides by 6:

Simplify:

The solutions to the system of equations are:

The tree is 34 feet tall.

Ratio of length of the stick to the length of the shadow = 6 : 4.5 = 4:3

Ratio of length of the tree to the length of its shadow   = x : 25 = 4:3

x / 25 = 4 / 3

x = 25 x 4 / 3 = 100/3 = 33.33

Therefore, the length of the tree to the nearest foot is 34 feet (approximately).

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If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.



To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).

Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.

Number of individuals in each group = dftotal / number of treatment conditions

Number of individuals in each group = 32 / 3

Number of individuals in each group ≈ 10.67

Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.

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Answer:   y = -x + 2

Step-by-step explanation:

Point slope form is y - y = m(x - x)

m = the slope of the line

Slope-intercept form is y = mx + b

m = the slope of the line

b = y-intercept

So because the - is in the m spot in the point-slope form, that means that is the slope of the line meaning it will also be in the m spot in slope-intercept form. The y-intercept of the line is found when x is 0.  When we look at the two coordinates provided you can see that one of them shows when x is 0.  We see that when x is 0, y is 2  which means that the y-intercept is 2.

So when you put the 2 in place of b,  you get   y = -x + 2

Given,

The ratio of QR to ST in the triangle is 5/7

Three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles defined as congruent.

To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five condition for two triangles to be congruence,  according to  the trials. The congruence qualities are SSS, SAS, ASA, AAS, and RHS.

PQR and PST are congruent

So PQ/PS=QR/ST

We know that

PQ=10

PS=14

QR/ST=10/14

QR/ST=5/7

hence, the ratio of QR to ST in the triangle is 5/7.

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The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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length: 5

width: 2

height: 3

5x2= 10

10x3= 30

your answer would be 30

Answer:

40 cm³

Step-by-step explanation:

The information we have about the volume of Prism Y is only that it is 10 cm³ greater than the volume of Prism X. So, we have to first find the volume of Prism X.

The volume of a rectangular prism is found by multiplying the length, width, and height of the figure. X has dimensions of 2 × 5 × 3, so we will multiply these together.

2 · 5 · 3 = 30

The volume of prism X is 30cm³.

Prism Y is 10 cm³ greater than this.

30 + 10 = 40

Prism Y has a volume of 40 cm³.

Good luck :)

Answer:

1) x = 80

2) x = 95

3) x = -7

4) x= 32

5) No

Step-by-step explanation:

1) 180 - 60 - 40 = 80

2) 180 - 35 - 50 = 95

*Those two questions you use 180 (the total degrees of a triangle) to figure out the missing angle.*

3) 180 - 76 - 41 = 63

x + 70 = 63 (subtract 70 to get -7)

*You are trying to find x not the angle. So you need to find the angle (the first part) and plug in to find what x needs to be*

4) 180 - 122 = 58

*Those two angles are supplementary*

180 - 90 - 58 = 32

5) No because the three angles don’t add up to 180

85 + 45 + 45 = 175 Needs to be 180

Answer:

b. y = 5/3x

Step-by-step explanation:

i hope this helps :)

Answer:

\(y=42\)

Skills needed: Rhombus Geometry

1) We need to understand a property of rhombi (plural of rhombus) that is important in this problem.

---> \(\overline{AC}\) is a diagonal in the rhombus.

---> \(\overline{BD}\) is also a diagonal in the rhombus.

- In a rhombus, the diagonals are always perpendicular to each other.

---> Let's make the point of intersection of the diagonals as Point E.

\(\angle BEC=90\)

---> This angle is needed to solve the problem for y.

2) Using triangle properties:

---> The sum of interior angles of a triangle equal 180.

- Take \(\triangle{BEC\), which has 3 angles:

\(\angle{BEC}, \angle{ECB}, \angle{CBE}\)

\(\angle{BEC+\angle{ECB + \angle{CBE=180\)

\(\angle{BEC=90\) due to rhombus diagonal property

\(\angle{ECB=48\) which is given

\(\angle{EBC=y\) (what we are trying to solve for)

Let's plug in!

3) \(90+48+y=180 \\ 138+y=180 \\ y=42\)

y equals 42

Answer:

y = 42°

Step-By-Step Explanation:

since it is a rhombus, the 4 angles next to the line AC are going to be the same (48°)

Since those 4 angles are 48°,

48° × 4 = 192°

Since all quadrangles (quadrilaterals) have combined angle of 360°,

360° - 192° = 168°

Since the 4 other angles must add up to 168°,

168° ÷ 4 = 42°

Since the 4 angles around the line BD are 42° each,

y = 42°

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The probability it will have a sample mean life of greater than 48 days is  96%.

The probability that it will have a sample mean life of greater than 48 days is calculated as follows;

The mean stadard error is calculated as follows

M.S.E = σ / √n

where;

M.S.E = 6.2 / √30

M.S.E = 1.13

The z-score of the data set is calculated as follows;

z = (x - μ) / M.S.E

where;

z = (48 - 46) / 1.13

z = 1.77

From normal distribution table, z-score of 1.77 corresponding to probability of 0.96 = 96%

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Answer:

x=-1

Step-by-step explanation:

Step 1: Factor

\(x^{2} +2x+1\) => \((x+1)(x+1)\)

Step 2: Solve for x.

\(x+1=0\)

   \(-1\)     \(-1\)

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

\(x=-1\)

The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:

Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.

Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)

Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)

Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.

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a. The statement is a statistic as it represents a numerical summary of a sample of 50 nurses.

b. The statement is a parameter as it describes a characteristic of the entire population of students at ECC.

In statistics, a parameter is a numerical value that describes a characteristic of a population. On the other hand, a statistic is a numerical value that summarizes a sample of data drawn from a population.

In example (a), the statement is referring to a sample of 50 nurses who have an average salary of $6000 per month. Since the statement is based on a sample, it represents a statistic. The average salary of these 50 nurses is a summary of the data in the sample.

In example (b), the statement is referring to a characteristic of the entire population of students at ECC, specifically, the percentage of students who love math. This represents a parameter, as it describes a characteristic of the entire population, rather than just a sample. Therefore, the statement in example (b) is a parameter.

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Step-by-step explanation:

26 is 355 plus the product of 265 and p

26 = 355 + 265p

Answer:

-32

Step-by-step explanation:

-32/-4 = 32/4 = 8

8 - 5 = 3

Therefore, 5x - y = 5(4) - (-2) = 22.

The answer of Linear Equation is (e) 22.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain variables, constants, and operators such as addition, subtraction, multiplication, and division.

To find the value of 5x - y, we need to first solve the system of equations given:

\(3x + 5y = 2 ...(1)\\2x - 6y = 20 ...(2)\)

We can solve this system of equations by either substitution or elimination. Here, we will use the elimination method:

Multiplying equation (1) by 2 and equation (2) by 3, we get:

\(6x + 10y = 4 ...(3)\\6x - 18y = 60 ...(4)\)

Subtracting equation (4) from equation (3), we get:

28y = -56

Dividing both sides by 28, we get:

y = -2

Now substituting this value of y in either equation (1) or (2), we can solve for x. Let's use equation (1):

\(3x + 5(-2) = 23x - 10 = 2\)

3x = 12

x = 4

Therefore, \(5x - y = 5(4) - (-2) = 22.\)

Hence, the answer is (e) 22.

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Answer:

b = -(4a + c)/4

Step-by-step explanation:

sum of a, b, and c is five times the sum of a and b,

a + b + c = 5(a + b)

which of the following expresses the value of b in terms of a and c?

a + b + c = 5(a + b)

a + b + c = 5a + 5b

a + c - 5a = 5b - b

-4a + c = 4b

b = -(4a + c)/4

The value of x and y in the algebra (3x - y, 2) = (2, x + y) ​ are 1 and 1 respectively.

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Given the algebra:

(3x - y, 2) = (2, x + y) ​

Therefore, equation:

3x - y = 2        (1)

Also:

x + y = 2        (2)

From both equations, solving simultaneously:

x = 1, y = 1

The value of x and y are 1 and 1 respectively.

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Answer:

C

Step-by-step explanation:

7x + 3y = 30 (equation 1)

-2x + 3y = 3 (equation 2)

9x = 27 (subtract the two equations to eliminate y)

x = 3 (divide by 9)

7 * 3 + 3y = 30 (Substitute x = 3 into equation 1, it doesn't matter which equation you substitute into)

21 + 3y = 30 (7 * 3 = 21)

3y = 9 (Subtract 21)

y = 3 (divide by 3)

Answer is (3, 3)

Answer:

(3,3)

Step-by-step explanation:

7x + 3y = 30

-2x + 3y= 3

Multiply the second equation by -1 and add together to eliminate y

7x + 3y = 30

2x - 3y= -3

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

9x + 0y = 27

Divide by 9

9x/9 = 27/9

x = 3

Now find y

-2x+3y = 3

-2(3) +3y =3

-6 +3y = 3

Add 6 to each side

3y = 3+6

3y=9

Divide by 3

y = 3

The least common factor of the two integers is 1 212.

The greatest common factor is the greatest integer that can divide two integers. The greatest common factor can be rewritten as a product of prime numbers:

6 = 2 × 3

Besides, we know that the product of the two numbers:

a × b = 1 212 = 2² × 3 × 101

Then, by algebra properties we find that the integers are: (please notice that there are more than a solution

a = 2 × 3

a = 6

b = 101 × 2

b = 202

Finally, the least common multiple of the two numbers is:

LCM = 2² × 3 × 101

LCM = 1 212

The least common multiple is 1 212.

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The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

The two angles coterminal with π/10 are 21π/10 and -19π/10

Step-by-step explanation:

To find a two angles that are coterminal with π/10, we add and subtract 360°(that is 2π) from π/10.

So, the first angle coterminal with π/10 is

A = π/10 + 2π

taking the L.C.M which is 10, we have

A = (π + 20π)/10

A = 21π/10

The second angle coterminal with π/10 is

B = π/10 - 2π

taking the L.C.M which is 10, we have

B = (π - 20π)/10

B = -19π/10

So the two angles coterminal with π/10 are 21π/10 and -19π/10