Please help me identify the equation for this table

Answer:

1. x = {-3, 3}

2. a = {-12, -2}

3. v = {-7, 10}

4. m = {-8, 8}

5. k = {-11, 1}

6. y = {-13, 19}

Step-by-step explanation:

|-2x| = 6

means that

-2x = 6     or      -2x = -6

x = -3        or      x = 3

|a + 7| = 5

means that

a + 7 = 5    or      a + 7 = -5

a = -2        or      a = -12

|8v-12| = 68

means that

8v-12 = 68     or      8v-12 = -68

8v = 80        or      8v = -56

v = 10            or      v = -7

| m / -4 | + 1 = 3

| m / -4 | = 2

means that

m/-4 = 2     or      m/-4 = -2

m = -8        or      m = 8

3|k + 5| = 18

|k+5| = 6

means that

k + 5 = 6    or      k + 5 = -6

k = 1        or      k = -11

|2y - 6| / 4 = 8

|2y - 6| = 32

means that

2y - 6 = 32     or      2y - 6 = -32

y = 19        or      m = -13

On closely observing and solving the Probability it can be stated that  the batter will hit around 3 balls out of the next nine balls

What is Probability?

The ratio of the number of outcomes in an exhaustive collection of equally probable options that create a particular event to the entire number of conceivable outcomes.

Solution:

Average of Batter is 0.303 which means that the batter hits 303 shots of 1000 balls

So, in the next nine balls he will hit 9 * 303/1000 = 2.7 balls

Which means the batter will hit around 3 balls

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Answer:

x=8/9

Step-by-step explanation:

step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.

3x+-3x cancels itself out and 3x+6x=9x.

now, the equation looks like: 9x-7=1

step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.

7+-7 cancels itself out and 7+1=8.

now, the equation looks like 9x=8

step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".

9x/9= x, 8/9

so the answer is x=8/9

hope this helped!!

Answer:

Step-by-step explanation:

Answer:(x,y)=(1/3 , 4/3)

Step-by-step explanation:

The expected value and the standard error for a labor participation rate in the company's sample is 0.0043

In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.

The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).

A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.

We have to find the expected value and the standard error for a labor participation rate in the company's sample.

Working age people sample n = 120

The labor force participation rate in the United States was 66.9% = 0.669

The Expected value is μ = p = 0.669

The standard error:

SE = √p(1-p)/n

SE = √0.669(1-0.669)/120

SE = √0.669*0.331/120

SE = √0.2214/120

SE = √0.001845

SE = 0.043

Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.

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January has an overnight average temperature of 52.4°F, making it the coldest month in Tampa. The average daytime temperature increases to 90.0°F in August, the warmest month.

What's it like to live in Tampa, Florida?

This Florida city, which is a part of the Tampa Bay region, has reasonable housing options, wonderful tropical weather, easy access to the beach, and more, making it one of the greatest locations to live in the Southeast.

How far away from the beach is Tampa?

The beach lottery has been won by Tampa visitors. You can reach more than a dozen of the world's most stunning beaches in less than 30 minutes by car from downtown Tampa. You need only select one.

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Answer:

Step-by-step explanation:

I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...

The equivalent exponential expression for the radical expression [tex]\sqrt{2 + 3}[/tex]

is [tex](2 +3)^{\frac{1}{2} }[/tex].

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expression may not look the same but substituting the variables  will result to the same values.

Therefore, let's find the equivalent exponential expression for the radical expression can be found as follows:

[tex]\sqrt{2 + 3}[/tex]

Using exponential law,

[tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

Therefore,

[tex]\sqrt{2+3} = (2 +3)^{\frac{1}{2} }[/tex]

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The value of the variable 'x' is 10. Then the measure of angle ∠2 is 113°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

If angles ∠1 and ∠2 form a linear pair, m∠1 = (7x - 3) and m∠2 = (12x - 7). Then the equation is given as,

∠1 + ∠2 = 180

7x - 3 + 12x - 7 = 180

Simplify the equation, then we have

7x - 3 + 12x - 7 = 180

19x = 190

x = 10

Then the measure of angle ∠2 is calculated as,

∠2 = 12(10) - 7

∠2 = 120 - 7

∠2 = 113°

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The value of  h’(1) is = 22

How may the chain rule example be used?

Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.

Given that :

h(x) = 2f(x).g(x)

f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1

h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule

h’(1) = 2 f'(1)g(1) + g'(1)f(1)

= 2 * (4 * 2 + 1 * 3)

= 2* (11)

= 22

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

[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{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266[/tex]

ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)

steps

find the zeros JUST MEANS SOLVE FOR X

x⁴-2x²-16x-15=0

break it up

let u = x²

x⁴ = (x²)² = u²

-16x+u²-2u-15=0

hold off on -16x

u²-2u-15=0

what 2 numbers when multiplied give you -15 & when added give you -2?

-5 and 3

(u-5) (u+3)

-16x + (u-5) (u+3) = 0

go back x

-16x + (x²-5) (x²+3) = 0

factor -1 out

( looks horrible so far lol )

-1 ((- x²+ 5) (x²+3) + 16x) = 0

multiply (- x²+ 5) with ( x² + 3 )

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0

-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0

Answer:

Step-by-step explanation

The slope intercept form is M=y2-y1 over x2-x1.

The answer for the equation is 12/3. 3 goes into 12 four times, so the answer is 4.

Answer:

If the temperature cooled by 4° on the first day of the year, and then heated up 7° on the second day, the net change in temperature would be a 3° increase. This means that the temperature increased by a total of 3° over the two days.

Step-by-step explanation:

On the first day of the year, the temperature starts at a certain degree (let's call it X).

On the same day, the temperature cools by 4°. This means that the temperature becomes X - 4°.

On the second day of the year, the temperature starts at X - 4° (the temperature from the previous day).

On the second day, the temperature heats up by 7°. This means that the temperature becomes (X - 4°) + 7° = X + 3°.

The net change in temperature over the two days is X + 3° - X = 3°.

I hope this helps to clarify the example! Let me know if you have any further questions.

Adult tickets cost $8.25 and children ticket is $6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let adult tickets = a

Let children tickets = c

Since Johnny bought 4 adult tickets and 8 children tickets for $81. Leslie bought 2 adult

tickets and 2 children tickets for $28.50.

This will be:

4a + 8c = 81 ....i

2a + 2c = 28.50... ii

From equation ii a + c = 14.25

a = 14.25 - c

Put this into equation I

4a + 8c = 81 .

4(14.25 - c) + 8c = 81

57 - 4c + 8c = 81

4c = 81 - 57.

c = 6

Since a = 14.25 - c

a = 14.25 - 6.

a = 8.25

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The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.

What is linear inequality?

A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

y < -5x + 1

Substitute the points and see if they are true

(3, 6)

6 < -5*(3) + 1

6 < -15 + 1

6 < -14  

Not true not a solution

Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.

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The coordinates of the vertices after a reflection over the line y = -5 is given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

The vertices of the original quadrilateral are given as follows:

T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).

The reflection line y = -5 is an horizontal line, meaning that after the reflection:

For example, the distance of the y-coordinate of the vertex U from -2 is of:

2 units above.

Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:

U'(2,-7).

Applying this rule for all the other vertices, they will be given as follows:

T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).

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The only person that is correct with respect to the measurement of  ∠CEA of the congruent triangles is; Carlos

From the diagram attached, we are given that;

The measure of ∠CAE = 80°

∠BDE = 60°

Amy says that m∠CEA = 20°

Brent says that it is 30°

Carlos says that it is 40°

Debra says it is 50°

Now, by inspection, it is clear that ΔCAE is congruent to ΔBDE by SAS Congruency postulate and as such we can say that;

∠A = ∠B and ∠C = ∠D

Thus;

∠B = 80° and ∠C = 60°

Sum of angles in a triangle is 180 degrees and so;

∠CEA = 180 - (80 + 60)

∠CEA = 180 - 140

∠CEA = 40°

Which means that Carlos is correct.

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The inequality to describe the possible side length for the third side is  5 < x ≤ 23.

What is the inequality of a triangle?

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.

The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

We have given,

Two sides of a triangle have lengths 9 and 14.

The third side is represented by x.

So by triangle inequality, we have the following inequality:

x ≤ 9 + 14

x ≤ 23

Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

14 - 9 < x

5 < x

Hence, the inequality to describe the possible side length for the third side is 5 < x ≤ 23.

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The number of commercials and movies on which the songs were played are 5 and 2.respectively

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

The number of commercials is x, and the number of movies is y

The above parameters when represented as an equation is as follows

40x + 120y = 440

x = y + 3

Substitute x = y + 3 in 40x + 120y = 440

40(y + 3) + 120y = 440

Expand

40y + 120 + 120y = 440

Evaluate the like terms

160y = 320

Divide by 160

y = 2

Recall that

x = y + 3

So, we have

x = 2 + 3

x = 5

Hence, the number of commercials is 5 times

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Answer:

d.) 100

Step-by-step explanation:

To solve, first find the value of g(-2):

[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]

Next, use this value to find f(-10):

[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]

Answer:

Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle

Step-by-step explanation:

:]

The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V /  π r².

An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.

Given:

V = π r² h

Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.

Take the remaining term of the right side to the left as shown below,

V /  π r²  = h

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At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.

After getting excellent news, people often behave more generously. After receiving negative news, do they become less giving? Adult Americans tip 20% of the whole bill on average. Give 20 diners a notice on their bill informing them that the weather is going to be poor tomorrow, and then keep track of the tip % they left. The tips are shown in Table 1 as a percentage of the total bill.

Table :  18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2 14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4

Suppose that tip percentage is Normal with ? = 2 and assume that the patrons in this study are a random sample of all patrons of this restaurant. Is there good evidence that the mean tip percentage for all patrons of this restaurant is less than 20 when they receive a message warning them of tomorrow’s bad weather? State [tex]H_{o}[/tex] and [tex]H_{a}[/tex] and carry out a significance test. Use significance level 0.05.

The given data is :

18.0, 19.1, 19.2, 18.8, 18.4, 19.0, 18.5, 16.1, 16.8, 18.2, 14.0, 17.0, 13.6, 17.5, 20.0, 20.2, 18.8, 18.0, 23.2, 19.4

Therefore, sample mean,

X = ∑x / n

X = [tex]\frac{18+19.1+19.2+19.3+....19.5}{20}[/tex]

X = 18.19

Now test : μ  < 20 with normal distance

Hypothesis test:

[tex]H_{o}[/tex] = μ ≥ 20

[tex]H_{a}[/tex] = μ ≤ 20

This is the lower tailed test.

X = 18.19

σ = 2

n = 20

Significant level, α = 0.05

Test statistics,

z = ( X-μ ) / (σ / [tex]\sqrt{n}[/tex] )

z = [tex]\frac{18.19-20}{2\sqrt{20} }[/tex]

z = -4.05

P value is in direction of alternative hypothesis or [tex]H_{a}[/tex]

Since,  [tex]H_{a}[/tex] ≤ 20 P value = P(Z<-4.05)

P value is the area to the left of the test statistics = -4.05 (from the figure)

P value = P(Z< -4.05) = 0.000 (from z table)

P value = 00000

Rejection rule : Reject  [tex]H_{o}[/tex]  if P value < α

Using excel functional normdist (   [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] , 0 , 1 , TRUE ) or TI's function normaldf ( 1E-99 ,   [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] )  answer is 0.0000259078

Decision : Since 0.0000 < 0.05, we reject the null hypothesis

Therefore,

At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.

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The equation of the line is y = x/4 + 13/2 .

A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

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

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

And here we have the slope,

m = 1/4

And (x₁ ,y₁)  =  (-2,6)

then the equation of line is

y - y₁ = m (x - x₁)

y - 6 = (1/4) (x +2)

y = x/4 + 13/2

Therefore, the equation is y = x/4 + 13/2.

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If the company has made 6732.16 in³ wax , Total number of candles made is 67

According to the question,

It is given that a wax candle is in cylindrical shape

Diameter of candle = 4 in

Radius will be = 4 / 2

=> 2 in

Height of each candles = 8 in

Company has used 6732.16 in³ of wax

We have to calculate number of candles company has made

Volume of cylinder = πr²h

Where r is radius and h is height

Substituting all the values,

Volume of candle = π (2)² (8)

=> V = 3.14 × 4 × 8   (putting π = 3.14)

=> V = 100.48

Therefore , Number of candles made = Total volume /volume of one candles

=> 6732.16 / 100.48

=> 67 candles are made by company

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The area of the given figure is 52.26 ft².

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given question,

The radius of semicircle r = 3 ft.

Height of the triangle = 4 ft.

Lateral side of triangle = 5 ft.

And the base of triangle = 2 x 3 = 6 feet

To find the area of the given figure, individually find area of semicircle and triangle.

Area of semicircle = π x r² = 3.14 x 3 × 3 = 28.26 square feet.

Area of triangle having height 4 feet and base 6 feet.

Area of triangle = base x height = 4 x 6 = 24 square feet.

The Area of the whole figure = Area of semicircle + area of triangle

                                  = 28.26 +24

                                  = 52.26 ft²

The required area of figure is 52.26 ft².

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Answer:

a. four and thirty four thirty fifths