Simplify the expression.

Percentage of bags that weigh more than 9.25 ounces is 19.3%.

Given:

Mean μ = 9.12

standard deviation σ = 0.15

z = x - μ / σ

= 9.25 - 9.12 / 0.15

= 0.13/0.15

= 0.867

P(x>Z)  = 0.193

= 0.193/100

= 19.3%

Therefore Percentage of bags that weigh more than 9.25 ounces is 19.3%.

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The total segment AE is 46.

"SAS" is when we know two sides and the angle between them.

To solve an SAS triangle we use "The Law of Cosines" to calculate the unknown side.

The Law of Cosines = a² = b² + c² − 2bc cosA

where

'b' and 'c' are two given sides

'A' is the angle between side 'b' and 'c' and

a' is the unknown side which we have to find.

In ΔABC , b=21, c=20, a= AC

By the Cosine law

a² = 21²+20² - 2*21*20 cos90°

a² =441 + 400 - 0 (∵cos 90° =0)

a² = 841

a=√841

a=29= AC.

Now, in ΔCDE, b=8, c=15 and a = CE

By the Cosine law

a² = 8² + 15²- 2*8*15cos90°

a² = 64 + 225 - 0 (∵cos 90° =0)

a²= 289

a = 17 = CE.

AE = AC + CE

AE = 29+17= 46.

Therefore, the total segment AE is 46.

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Check the picture below.

[tex]18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}[/tex]

Answer:

12

Step-by-step explanation:

12*12=144

Answer: 12 is the correct answer

Step-by-step explanation:

144 = a × a = 122

Then a = √144 = √(12 × 12)

12 × 12 = 144 or -12 × -12 = 144

The square root of 144 is +12 or -12

This shows that 144 is a perfect square.

Answer:

======================

(a) f(-7)

(b) f(0)

(c) f(4)

Answer:

Step-by-step explanation:

a) f(-7) = ?

→ f(x) = 8 - 4x

→ f(-7) = 8 - 4(-7)

→ f(-7) = 8 + 28

→ f(-7) = 36

Hence, f(-7) = 36.

b) f(0) = ?

→ f(x) = 8 - 4x

→ f(0) = 8 - 4(0)

→ f(0) = 8 - 0

→ f(0) = 8

Hence, f(0) = 8.

c) f(4) = ?

→ f(x) = 8 - 4x

→ f(4) = 8 - 4(4)

→ f(4) = 8 - 16

→ f(4) = -8

Hence, f(4) = -8.

Answer: The answer to this question is: the mass of the metal in pounds is 1.5 grams.

Step-by-step explanation: Search a free gram to pounds calculator and input your given input or output into there for further help if needed.

Hope this helps

The mass of the metal in pounds is 1.5 pounds.

A unit conversion expresses the same property as a different unit of measurement.

Given that, a scientist measures the mass of a metal to be 682 grams

682 grams = 0.682 kg

0.682 kg = 0.682*2.2 = 1.5 pounds.

Hence, The mass of the metal in pounds is 1.5 pounds.

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Using the fraction concept, we can say that The number of beads each friend will get is 4.

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

Number of bead = 32 bead;

Total number of friends = 8;

So,

we need to find how many beads will one friend get:

So,

The number of beads each friend will get : [tex]\frac{32}{8}[/tex]

The number of beads each friend will get is 4.

Hence,

using the fraction concept, we can say that The number of beads each friend will get is 4.

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well, we know the first $25,000 is taxed at 8%, wait a second!!!!! Chris didn't make 25,000 bucks, he only made $17,000, so he'd be in the range of $0 - $25,000 because $17,000 is in that range, that means he owes 8% of 17,000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 17000}}{\left( \cfrac{8}{100} \right)17000}\implies 1360[/tex]

The amount Chris owes in tax is $1360.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The first $25,000 is taxed at 8%.

This means,

Amount from 0 to $25000 is taxed at 8%.

Now,

Chris earned = $17,000

Tax amount.

= 8% of 17,000

= 8/100 x 17,000

= 8 x 170

= $1360

Thus,

The tax amount is $1360.

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Her situation can be modeled by the linear equation (in standard form):

x*$0.25 + y*$0.79 = $2.50

The variables that we will use here are:

x =  number of apples that she can buy.

y = number of bananas that she can buy.

We know that she has $2.50 to spend, that each apple costs $0.25 and each banana costs $0.79, then the cost of the x apples and y bananas is:

x*$0.25 + y*$0.79

and that must be equal to the amount she has to spend, then we can write the linear equation:

x*$0.25 + y*$0.79 = $2.50

That is the linear equation in standard form that represents her situation.

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The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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 y = -3/5x - 123/5 is slope-intercept form .

What is an explanation of the slope-intercept form?

Point = ( 1,24 )

slope = -3/5

the equation in standard form of the line that passes through the point

               y - y₁ = m ( x - x₁)

                y - 24 = -3/5 ( x - 1)

             5 (y - 24) = -3( x - 1 )

                5y -    120 = -3x + 3

                 5y = -3x + 3 + 120

                 5y = -3x + 123

                 y = -3/5x - 123/5

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Explanation:

Let x = depth of the gutter

then

14-2x = width of the gutter

:

Cross section area:

A = depth * width

A = x(14-2x)

A = 14x - 2x^2

:

Axis of symmetry will give x value for max area: x = -b/(2a)

x = -14/2 * -2

x = -14/-4

x = +3.5 inches is the depth for max area

:

:

Max area: 3.5 * 9 = 31.5 sq/in

Answer:

It says right there that he bought a pound of turkey for $5.50.

One pound of turkey is $5.50?

Step-by-step explanation:

This is extremely confusing

Answer:

y-(-2)= -5(x-4)

= -5x-y+18

Step-by-step explanation:

y-(-2)= -5(x-4)

y+2= -5x +20

y= -5x+18

-5x-y+18= 0

It will take 300 days to get to 2000 dollars.

According to the question,

We have the following information:

One gets paid every 12 days and one puts back $80 every 12 days.

Now, the total amount of dollars is $2000.

Now, we have the following progression:

80, 160, 240, ...

This is an arithmetic progression.

an = a+(n-1)d where a is the first term and d is the common difference

2000 = 80+(n-1)80

2000 = 80+80n-80

2000 = 80n

n = 2000/80

n = 25

Now, the number of days one is paid is after 12 days.

So, the number of days to get 2000 dollars:

25*12

300 days

Hence, it will take 300 days to get to 2000 dollars.

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Let's say we have blue and red balls

Blue : Red

3 : 5

Now we can add another ratio for the whole.

Blue : Red : Total

Total is Blue + Red = 3 + 5 = 8

So

Blue : Red : Total

3 : 5 : 8

Then the part : whole ratio for Blue is...

Blue : Total

3 : 8

The equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0 which can be found out from slope intercept formula.

It is given to us that -

The point is P(-8,0)

The line is represented as y=-3

The point P is perpendicular to the given line.

We have to find out the equation of the line passing through P which is perpendicular to the given line.

We know that the equation of a line is given by -

y = mx + c

where, (x, y) = coordinates of the point

m = slope of the line

c = a constant

Comparing this with the equation of the given line, we have

m=0 and c =-3

This implies that the slope of the perpendicular is also equal to 0.

The slope intercept formula for the perpendicular line can be represented as -

y = mx + c

Using the coordinates of P(-8,0), we have

0 = 0*(-8) +c

=> c = 0.

Thus, the equation of line passing through the point P(-8,0) that is perpendicular to the line y=-3 is y=0.

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There are 19/9 ounces in each sprinkle of sundae

From the question, we have the following parameters that can be used in our solution:

Number of sundaes = 4

Ounces of sprinkles = [tex]8\frac49[/tex] ounces

From the above parameter, we can calculate the amount of sprinkles using the constant of proportionality formula

This is represented as

Ounces per sprinkle = Ounces of sprinkles/Number of sprinkles

Substitute the known values in the above equation

So, we have the following equation

Ounces per sprinkle = [tex]8\frac49[/tex]/4

Evaluate the quotient

Ounces per sprinkle = 19/9

Hence, the ounces per sprinkle is 19/9 ounces

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Traingle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The sum of the three angles is equal to 180 degrees.

The value of angle W is 47.67

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

In this triangle:

angle W = (3x-24) degrees.

angle C = (4x-11) degrees.

angle T = 2x degrees.

Now,

The sum of the three angles is equal to 180 degrees.

3x - 24 + 4x - 11 + 2x = 180

9x - 35 = 180

9x = 215

x = 215/9

Now,

The angle W.

= 3x - 24

= (3 x 215/9) - 24

= 215/3 - 24

= 71.67 - 24

= 47.67

Thus,

The value of angle W is 47.67

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The transformations to function f(x) that results in function g(x) are described as follows:

5. Reflection over the x-axis, vertical stretch by a factor of 2.

6. Shift right of 6 units, shift up of 4 units.

7. The rule for g(x) after the transformation is given as follows:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

For item 5, the functions are given as follows:

The transformation is a multiplication by -2, which means that the function was:

For item 6, the functions are given as follows:

Then the transformations are explained as follows:

For item 7, the parent function is:

[tex]f(x) = \sqrt[3]{x}[/tex]

Then the transformations and their effects are given as follows:

Hence the function is:

[tex]g(x) = \sqrt[3]{-x + 7}[/tex]

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The slope of the line -1 and the y-intercept is 3.

From the question, we have

x+y = 3

y = -x+3

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

m = -1

c = 3

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

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The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

Given that,

y forms a circle of radius r

y=2[tex]\pi[/tex]r

r=y/2[tex]\pi[/tex]

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = [tex]\pi[/tex]r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4[tex]\pi[/tex]+(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4[tex]\pi[/tex] + 2(y-2)/16 =0

y/2[tex]\pi[/tex] + (y-2)/8 =0

y = 2[tex]\pi[/tex]/[tex]\pi[/tex]+4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/[tex]\pi[/tex]+4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/[tex]\pi[/tex]+4

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Answer:

23/20

Step-by-step explanation:

110% of 20 is 22/20, so 23/20 is more.

Step-by-step explanation:

23/20 = 1,15

110% = 1,1

1,15 > 1,1

⇒ 23/20 > 110%

The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Given data ,

The angles of the triangle ABC are

∠A = ( 2x + 10 )°

∠B = ( 4x + 2 )°

Let angle ∠C be y

The sum of ∠A + ∠B + ∠C = 180°  

So ,

( 2x + 10 )° + ( 4x + 2 )° + y = 180°   be equation (1)

Now , we can see that AD is a straight line and C is a point on the line AD

The total angle of C on the line AD is 180°

So , ( 5x + 27 )° + y = 180°

y = 180° - ( 5x + 27 )°   be equation (2)

Substituting the value of equation (2) in equation (1) , we get

( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°

On Simplifying , we get

( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0

( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0

x - 15 = 0

Adding 15 on both sides , we get

x = 15°

Substituting the value of x in the ∠A , ∠B and ∠C equation , we get

∠A = ( 2x + 10 )°

     = 40°

∠B = ( 4x + 2 )°

     = 62°

∠C = 180° - ( ∠A + ∠B )

     = 180° - 102°

     = 78°

Therefore , the angles of the triangle ABC are 40° , 62° and 78°

The measure of ( 5x + 27 )° is

= ( 5 x 15 + 27 )°

= 102°

Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

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Answer:

y = 2x + 3

Step-by-step explanation:

The slope

As the y changes by 2, the x changes by 1.  2/1 is 2

The y intercpet is 3.  This what y is when x is 0.

Inequality represented by the given graph is equal to 5x -3y > 9.

As given in the question,

For the given graph,

Consider two points on the line represented on the graph ,

( x₁ , y₁) = (0,-3)

(x₂ , y₂) = ( 3,2)

Equation of the line given by two points on the graph,

( y - y₁)/ (x -x₁) = ( y₂ - y₁)/ (x₂ -x₁)

⇒(y +3)/(x-0) = ( 2 + 3)/(3 -0)

⇒(y + 3) / x = 5/3

⇒3(y+ 3) = 5x

⇒3y + 9 = 5x

⇒5x -3y = 9

As per shaded region inequality of the graph is given by,

5x -3y > 9

Therefore, inequality represented by the given graph is equal to 5x -3y> 9.

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Answer:

26x/7

Step-by-step explanation:

If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

In the question ,

it is given that ,

From the hobby shop , Joe bought 2 model sportscars for $8.95 each

the cost for 2 sports car = 8.95*2 = 17.9

the total amount spent by Joe at the shop = $23.65

let the cost of the paint be "$x" .

the above situation can be represented by the equation .

total cost = cost for 2 model cars + cost of paint

substituting the values from above ,

we get ,

23.65 = 17.9 + x

x = 23.65 - 17.9

x = 5.75

Therefore , If Joe spent a total of $23.65 , then the cost of the paints is $5.75  .

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Answer:

y = 3x + 2

Step-by-step explanation:

The slope is the rate of change.  The y intercept is the y value when x is 0.