please help me out with my math

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 equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:

2y - 4x = -10.

A system of equations is called inconsistent when the number of equations of the system is of zero.

The system in this problem is composed by linear equations, which have the following format:

y = mx + b.

In which:

For inconsistent system, we have that the equations:

The function in this problem is given as follows:

y = 2x + 5.

Hence the inconsistent system is formed with:

2y - 4x = -10.

Which is simplified by 2 as follows:

y - 2x = -5.

y = 2x - 5.

Having the same slope of 2, but a different intercept.

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Answer: 2y – 4x = –10

Step-by-step explanation: trust.

The statement that is correct based on the data is that the table shows a proportional relationship

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

Mango Used Smoothie Size

Kim 1 8 oz

Bri 3 24 oz

Angela 4 32 oz

Express  properly

So, we have

        Mango Used Smoothie Size

Kim         1                       8 oz

Bri           3                       24 oz

Angela    4                        32 oz

Start by checking if the table has a constant rate

This is represented as

Constant rate = Smoothie Size/Mango Used

So, we have

Constant rate = 8/1 = 8

Constant rate = 24/3 = 8

Constant rate = 32/4 = 8

See that the constant rate is the same for all values

Hence, the table shows a proportional relationship

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Answer:

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

Step-by-step explanation:

:]

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 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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Answer:

The answer is 2990.8

Step-by-step explanation:

Answer:

volume = 980π = 3078.790801  

Step-by-step explanation:

14 ÷ 2 = 7 = radius

π x [tex]r^{2}[/tex]=  = 49π = area

area x 20 = volume

volume = 980π = 3078.790801  

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

A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).

Generally,  In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.

In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.

The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.

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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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A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C

Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.

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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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Explanation:

All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.

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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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:

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:

Step-by-step explanation:

For the given congruent triangles, the values of x = -1 and y = 3.

Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.

The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.

3y + x = y + 5 ...........(1)

y - x = x + 5 ..............(2)

Equation

1:3y + x = y + 5

3y - y = 5 - x

2y = 5 - x

x = 5 - 2y ..............(3)

Substitute this value of x in equation (2)

y - x = x + 5 y = x + x + 5y

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

= 10 - 4y + 54y + y = 15

5y = 15 y = 15/ 5

y = 3

Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1

Therefore, x = -1 and y = 3

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

Step-by-step explanation:

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 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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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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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.

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]

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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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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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