Objective function Z=3x+6yFind the value at each corner of the graph

Divide the numbers:

21/5 = 4.2

Answer:

y=5

Step-by-step explanation:

The curve stops at the y value of 6. And we need a horizontal line for the asymptote, so we don't need an x value only a y-value. So the y-value is 5 on the y-axis, which means your equation will be y=5.

-Hope this helped

Answer:

61.56%

Explanation:

Let the first American = A

• P(A goes) = 0.62

• P(A does not) = 0.38

Let the second American = B

• P(B goes) = 0.62

• P(B does not) = 0.38

The probability that one or both of the people chosen does not go on vacation each year

=P(A goes and B does not) or P(A does not and B does) or P(both do not)

Therefore, the probability that one or both of the people chosen does not go on vacation each year is 61.56%.

Problem: 6(3n+10)

Solution:

Applying the distributive law of natural or real numbers, we obtain:

then, the correct answer is:

Given 3 ( 3 + 4k ) = 45

So, divide both sides by 3

3 + 4k = 45/3

3 + 4k = 15

subtract 3 from both sides

3 + 4k - 3 = 15 - 3

4k = 12

divide both sides by 4

k = 12/4 = 3

So, the value of k = 3

1) In this question, we need to remember that in any boxplot the line in the middle of the box indicates the median.

Based on that, we can tell the Median is 140

2) In the Interquartile Range, we need to find the range between the lower quartile and the upper one, based on that boxplot. We can tell the IQR is:

Note that the boundaries of the box show us the lower and the upper quartile:

In the ratio of 2:6 , Lacey will get 6 cards and Martha will get 18 cards

Total number of cards = 24

Let Lacey gets "x" numbers of cards and Martha gets "y" numbers of cards

Ratio of cards given to Lacey to Martha = 2:6

x:y = 2:6

and we also know that total cards are 24

x + y = 24

x = 24 - y

putting value of x in the ratio,

[tex]\frac{24 - y}{y} = \frac{2}{6}\\[/tex]

cross multiplication,

6(24 - y) = 2y

144 - 6y = 2y

8y = 144

y = 18

Substituting value of y ,

x = 24 - 18

x = 6

Hence , Lacey will get 6 cards and Martha will get 18 cards.

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For a transformation that involves a reflection over the x-axis, it means the pre-image is reflected across the horizontal line.

For a reflection over the x-axis, the x coordinate remains the same while the y coordinate changes.

The rule that describes a transformation when an image has been reflected over the x-axis is:

(x, y) ==> (x, -y)

Using the pre-image (-x, -y), we have:

(-x, -y) ==> (-x, y)

For a triangle, we have:

A(-x, -y) ==> A'(-x, y)

B(-x, -y) ==> B'(-x, y)

C(-x, -y) ==> C'(-x, y)

Using the given ratio, we will see that we can define the proportions to find that:

Sandra gets 12 marshmallows.

Peter gets 18 marshmallows.

We know that Sandra and Peter share a packet of 30 marshmallow eggs in the ratio of 2:3.

We can find the fractions for each person by doing the following steps:

So if we add the two values in the ratio we get 2 + 3 = 5

The ratio is:

Sandra:Peter = 2:3

Then we can write the fractions as:

The fraction of the total number of eggs that Sandra gets is 2/5

The fraction of the total number of eggs that Peter gets is 3/5

Now remember that the total number of marshmallow eggs is 30, then the number that Sandra gets is:

S = (2/5)*30 = 12

And the number that Peter gets is:

S = (3/5)*30 = 18

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Answer:

5(−2)−3 y = 5 (- 2) - 3

Step-by-step explanation:

y = 5x − 3 y = 5 x - 3 Substitute −2 - 2 for x x and find the result for y y. y = 5(−2)−3 y = 5 (- 2) - 3

Given the function

First I'll rewrite it in terms of y

Next is to determine the values of y (range) for the given values of x

Now you can graph it:

Answer:

[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]

[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]

[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]

Step-by-step explanation:

Given the terminal side of an angle we can calculate the distance between the point given and the origin:

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]r=\sqrt{|(-5^2)+(-7^2)|}[/tex]

[tex]r=\sqrt{74}[/tex]

y = opposite side

x = adjacent side

r = hypotenuse

Now we have

[tex]r=\sqrt{74}[/tex]

[tex]x=-5[/tex]

[tex]y=-7[/tex]

[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]

[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]

[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]

x represents the cost of each bottle of juice. Given that he bought a pack containing 6 bottles of juice, the cost of the 6 pack juice bottles would be $6x

Given that the total cost of a bag of popcorn which costs $2.11 and a 6-pack of juice bottles is $11.41, it means that

2.11 + 6x = 11.41

6x = 11.41 - 2.11

6x = 9.3

x = 9.3/6

x = 1.55

The cost of each bottle of juice is $1.55

Answer: 2.5, 5.3

Step-by-step explanation:

[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]

The Required Sample size is 138 . Yes, this number of IQ test Score is a fairly large number.

In the given statements we have , An IQ test is designed such that

the mean of adults ( X bar ) = 100

standard deviations (σ ) = 18

Estimate the mean iq score of statistics students such that the confidence level is 95%

We know the value of Z score for given confidence level 95% is 1.96 .

Margin of error in IQ test = 3

we shall calculate the sample size here.

Using the Margin of error formula,

M.E = Z( √σ ²/n )

where, Z--> z score value

σ --> standard deviations

n ---> sample size

putting all the values in this formula we get ,

3 = 1.96 (√(18)²/n )

=> 3/1.96 = √324/n => (1.5306)² = 324/n

=> n = 324/ 2.342 = 138.29

Hence, the required Sample size is 138 .

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Complete question:

An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 3 IQ points of the true mean. Assume that σ =18 and determine the required sample size using technology.

Then determine if this is a reasonable sample size for a real world calculation.

We know that:

6 < 3r-45 < 36

We want to re arrange the inequations:

Step 1: all terms with an unkown value on one side.

We want to let 3r "be alone" in the middle side:

6 < 3r-45 < 36

6 + 45 < 3r < 36 + 45 [adding 45 in each part]

51 < 3r < 81 [6 + 45 = 51 and 36 + 45 = 81]

Step 2: we want to clear r

51 < 3r < 81

51/3 < r < 81/3 [dividing by 3 all sides]

17 < r < 27 [51/3 = 17 and 81 /3 = 27]

The range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.

Spectral lines are bright or dark lines over continuous spectrum which occur due to emission or absorption of energy.

When an electron jumps to or from one energy level to another energy level, spectral lines are produced. The range of spectral lines depends on the number of energy levels available to which the electron can jump. This depends the amount of energy gained/lost by the electron.

Thus, the range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.

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Since the slope of the soil line is a quarter of an inch per foot and the drainage line is 50 feet long, then the difference in elevation is:

Simplifying the above expression we get:

Recall that:

Therefore:

Answer: 12.5 inches= 1.04 feet.

Answer:

The angle has measure 72°.

Step-by-step explanation:

Definition:

Two angles are supplementary angles if the sum of their measures equals 180°.

Let x and y be the supplementary angles.

According to the definition above, then,

x + y = 180

We can the above equation for y:

x + y = 180

y = 180 - x

The two angles have measures:

x

180 - x

Now we look carefully at this statement:

"three times the measure of an angle is equal to twice the measure of the angle's supplement"

We translate the above statement into an equation, using x for one angle, and 180 - x for the supplement.

3x = 2(180 - x)

Solve the equation for x.

Distribute 2 on the right side.

3x = 360 - 2x

Add 2x to both sides.

5x = 360

Divide both sides by 5.

x = 360/5

x = 72

The angle has measure 72°.

We need to decide whether the given equations are always or never true for values of x .The given equations are ,

solve out for x,

[tex]\longrightarrow x -x =12+1\\ [/tex]

[tex]\longrightarrow 0 =13\\ [/tex]

This can never be true. Hence the equation is never true for any values of x.

solve out for x,

[tex]\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ [/tex]

[tex]\longrightarrow 0=\dfrac{3}{2}[/tex]

This can never be true. hence the equation is never true for any values of x.

solve out for x,

[tex]\longrightarrow 4x +12=8x+12-4x\\[/tex]

[tex]\longrightarrow 4x -8x +4x =12-12\\[/tex]

[tex]\longrightarrow 0=0[/tex]

hence this equation is true for all values of x.

solve out for x,

[tex]\longrightarrow 2x -x -x =8+8\\ [/tex]

[tex]\longrightarrow 0=0 [/tex]

hence the equation is true for all values of x.

solve out for x,

[tex]\longrightarrow 2x +10+3x =5x-25\\ [/tex]

[tex]\longrightarrow 5x -5x =-25-10\\[/tex]

[tex]\longrightarrow 0 =-35[/tex]

This can never be true. hence the equation is never true for any values of x.

and we are done!

Notice that the all estimations for each graph are correct.

The graph of g(X) = -(x+3)⁴ compares to the parent function of f(x) = x⁴ got shifted 3 units to left and reflected over x-axis.

Translation means shifting , rescaling and reflecting parents function.

Shifting the graph means to move the graph to new location

Scaling means changing it shape

and Reflecting means a mirror image of parent function across either x-axis or y-axis.

here, If we draw graph of both the function you'll see

The parent function f(x) = x⁴ have center as (0,0)

where as Center of function g(x) = -(x+3)⁴ is (-3,0)

means g(x) = -(x+3)⁴ is moves towards the left by 3 units

and also the graph is in downwards which means it has also reflected across x-axis

Hence , the g(x) = -(x+3)⁴ is shifted 3 units to the left and reflected over the x-axis compare to parent function.

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Answer:

Step-by-step explanation:

it ty

Answer:

٠٠

First write all the points on the graph

second

multiply 2 in all the numbers and write them again

Answer:

(- 7, - 10 )

Step-by-step explanation:

a translation of 1 unit right means add 1 to the x- coordinate

a translation of 5 units down means subtract 5 from the y- coordinate.

(- 8, - 5 ) → (- 8 + 1, - 5 - 5 ) → (- 7, - 10 )

Answer: Not equal to.

Step-by-step explanation: you don't get the same answer to the problem for both.

Given:

The cardboard costs 0.05 per square inch

And the surface area = 286

So, the total cost is the product of the surface area and the cost per square in.

Total cost =

So, the answer will be Total cost = $14.30

Let's label the diagram with the information provided. The diagram would look like:

This is labeled as x.

With respect to angle alpha, the side x is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "x". Shown below:

Answer: 58.23 feet

This is labeled as y.

With respect to angle beta, the side y is opposite and the antenna is the side adjacent.

Thus, we need the trig ratio tan to solve for "y". Shown below:

Answer: 77.97 feet

The distance between Anchor 1 and Anchor 2 is "x + y". We already found x and y. Let's do the sum:

Answer: 136.2 feet

Simplify the expression to obtain the value of n.

Thus value of n is -4.

Answer

The remaining board piece will be 3 (7/8) feet long

Explanation

Mia's board is 15 (1/2) feet long.

He cut three pieces off the board with each board measuring 3 (7/8) feet long.

The key to this is to first convert the values given in mixed fractions as improper fractions.

3 (7/8) = (31/8)

15 (1/2) = (31/2)

Then, the three pieces each had a length of 3 (7/8)

1 piece = 3 (7/8) feet = (31/8) feet

3 pieces = 3 × (31/8) = (93/8) feet

So, taking this out of 15 (1/2) long board will leave

[15 (1/2)] - (93/8)

= (31/2) - (93/8)

To do that, we need to take the LCM of these two denominators

The remaining board piece will be

(31/8) = 3 (7/8) feet long

Hope this Helps!!!