A taxpayer’s annual Social Security tax is $6,107 and the social security tax is 6.2%. What is the taxpayer’s gross annual salary? Tax rate = tax amount / gross income.

The sum of decimals 4.2 and 466.99​ evaluates to 471.19

Decimals are numbers that consist of two parts namely, a whole number part and a fractional part separated by a decimal point e.g 2.35

Given:  4.2 and 466.99​

To evaluate the sum of 4.2 and 466.99​, you simply need to add the two numbers. Arrange the numbers as shown below and add as you would add other numbers.

    4.2

466.99

.................

  471.19

................

Therefore, the sum 4.2 and 466.99​ is  471.19

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Answer:

2

Step-by-step explanation:

The y-intercept is the point at which the graph crosses the y-axis.

(I have marked it in blue on the attached graph).

From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.

The tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

We have,

First car price is  =  $13,500

and tax of the first car is = $910

Second car price is  =  $16,500

and tax of the second car is = ?

so,

 $13,500 -----    100,

  $910      -----    x

x = 910 * 100 / 13500

x =  6.7

therefore, the rate of tax is 6.7%

so, we will calculate the tax for the second car,

$16,500 -----    100,

    y        -----    6.7

y = 6.7 * 16,500 / 100

y = $1105.5

difference of tax price between two cars = $1105.5 - $910 = $195.5

Hence, the tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

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Answer:

the answer is no

Step-by-step explanation:

Answer: True

Step-by-step explanation:

-The f-distribution curve is positively skewed towards the right with a range of 0 and ∞

The value of F is always positive or zero. It never has negative values.

The vertices of the triangle after reflection over the y - axis are  P'(2,-4) , Q'(-2 , -5) and R'(1 , -8)  .

In the question ,

it is given that ,

the vertices of the triangle PQR are P(-2, -4), Q(2, -5) and R(-1, -8),

we have to write the coordinates after reflection over y axis .

we know that the coordinate (x,y) after reflection over y axis become (-x,y).

So , the coordinate P(-2 , -4) after reflection is P'(2,-4) .

the point Q(2,-5) becomes Q'(-2 , -5) .

the vertex R(-1 , -8) becomes R'(1 , -8) .

Therefore , the vertices of the reflected triangle are P'(2,-4) , Q'(-2 , -5) and R'(1 , -8) .

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a) Producing and selling 2200 units will give us a profit of $60,000

b) The number of units that must be produced to avoid a loss is; 200 units

c) The graph of P(x) = 30x - 6000 is as shown in the attached file

We are given the profit function as;

P(x) = 30x - 6000

where x is the number of hats produced and sold.

a) To get a profit of $60000, we will solve for x as;

30x - 6000 = 60000

30x = 66000

x = 66000/30

x = 2200

b) The number of units that must be produced to avoid a loss is;

P(x) = 0

30x - 6000 = 0

30x = 6000

x = 6000/30

x = 200 units

c) The graph of the profit function is as attached.

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suppression

prevention - keeping a pest from becoming a problem. suppression - reducing pest numbers or damage to an acceptable level, and . eradication - destroying an entire pest population.

How can we manage the population pest?

In the field, there are three main approaches to biological control: Natural enemy conservation, the introduction of new natural enemies, and the establishment of a stable population are referred to as "classical biological control." Bulk raising and periodic release, whether on a seasonal or inundative basis, are the other two methods.

What are the elements that influence the expansion of the pest population?

In general, heat, humidity levels, light quality or quantity, wind, or any combination of these elements affect all important life stages of insect pests, diseases, and weeds (survival, reproduction, and dissemination).

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reducing pest populations to a level where their effects are tolerable or acceptable is termed suppression.

Prevention is the process of preventing a pest from becoming a problem. Suppression is the process of reducing pest numbers or damage to an acceptable level, and Eradication is the destruction of an entire pest population.

There are three main approaches to biological control in the field: "Classical biological control" refers to the conservation of natural enemies, the introduction of new natural enemies, and the establishment of a stable population. The other two methods are bulk raising and periodic release, whether seasonal or inundative.

What factors influence the expansion of the pest population?

In general, heat, humidity, light quality or quantity, wind, or any combination of these elements affect all important life stages of insect pests, diseases, and weeds (survival, reproduction, and dissemination).

reducing pest populations to a level where their effects are tolerable or acceptable is termed suppression.

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Answer:

30

Step-by-step explanation:

Solve for f by simplifying both sides of the equation, then isolating the variable. It is pretty much like what we do with the normal equation.

Answer:

remainder = 30

Step-by-step explanation:

given f(x) divided by (x - h) then the remainder is f(h)

f(x) is divided by (x - 3) then remainder is f(3)

f(3) = 4(3)² - 3 - 3 = 4(9) - 6 = 36 - 6 = 30

The value of the test statistic is -1.72.

It is given that, a publisher reports that 76% of their readers own a particular make of car.

At the null hypothesis we test, if the proportion is of 76%

⇒ H₀ : p = 0.76

At the alternate hypothesis, we test if the proportion is different from 76%

⇒ H₁ : p ≠ 0.76.

We know the test statistic is,

z = x - μ / (σ/[tex]\sqrt{n}[/tex])

where x is the sample mean,

μ is the value tested at the null hypothesis,

σ is the standard deviation

and n is the size of the sample.

Therefore 76% tested at the null hypothesis

⇒μ = 0.76 and σ = [tex]\sqrt{0.76 * 0.24}[/tex]

Now a random sample of 200 found that 71% of the readers owned a particular make of car.

⇒ n = 200 and x = 0.71

then the value of test statistic implies that,

z = (0.71 - 0.76) /([tex]\sqrt{0.76 * 0.24}[/tex] / [tex]\sqrt{200}[/tex])

  = - 0.05 /(0.42/14.14)

  = - 0.05 / 0.029

z = - 1.72

So z = -1.72 has a p value 0.4272.

implies that 0.01 * 0.4272 =0.04272

So 0.042 > 0.01

which means that there is not sufficient evidence at the 0.01 level to support the executive's claim.

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T|=|S|⟹ there is bijection F:S→T.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

According to our question-

The function f:ST |S||T| has an injective and not a surjective nature.

Assume an injective function exists: g:TS|T||S|. |T|=|S|

(this follow from the Cantor-Bernstein theorem).

|T|=|S|⟹ F:S:T has a bijection.

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The two true statements about these are,

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.

So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.

The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

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The ratio for the number of egg in three boxes to the total number of egg is 1 : 10

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

According to the question,

Total boxes of  eggs a farmer have = 30 boxes of egg

Number of eggs in each box = 6

Total number of eggs in 3 boxes = 6 × 3

=> 18 eggs

Total number of eggs in 30 boxes = 30 × 6

=> 180 eggs

Ratio of number of egg in three boxes to the total number of egg = 18 : 180

=> 1 : 10 is the ratio

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Eighty-seven and Seven hundred twenty-eight thousandths in decimal form is 87.728.

How to change in decimal form?

Eighty-seven and Seven hundred twenty-eight thousandths in decimal form:

= 87 + 728/1000

= 87 + 0.728

= 87.728

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Check the picture below.

Answer:

360

Step-by-step explanation:

You have degrees, so just plug stuff in and cross multiply. This gives you 20π=180*(x radians). (x is what we're solving for.) Solving gives x= π/9 radians.

Now we know θ in terms of radians. We can just plug our numbers in and solve!

40=r(π/9)

Divide by π/9 to get r=360/π cm!

The total number of people at the stadium was 6800 people .

A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .

For Example : 2% is = 2/100   .

In the question ,

it is given that ,

percent of teenagers fans in the stadium is = 5%

number of teenagers present at the football stadium is = 340

which means 5% represents 340 people ,

So , 1% will be 340/5 = 68 people .

the total percent of people present in the stadium is = 100% ,

multiplying both sides by 100 ,

we get ,

So , 100%  = 68 × 100 = 6800 people

Therefore , The total attendance at the football stadium was 6800 people .

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Answer:39.3 percent

Step-by-step explanation:

3700 out of 6100 is  39.34 percent

The required margin of error construct a 98% confidence interval for p1 - P2 is 0.0403.

Margin of errors, in statistics, is the level of blunder in results got from irregular examining overviews. A higher wiggle room in measurements shows less probability of depending on the consequences of a review or survey, for example the certainty on the outcomes will be lower to address a populace.

given data

 n1 =1 000   x1 = 250

pˆ1 = x1n1 = 2501000 = 0.250

n2 = 1200    x2 = 195

pˆ2 = x2n2 = 1951200 = 0.1625

We have given confidence interval ,

98% ci for p1−p2.

Then,

α = 1 - 0.98 = 0.02

[tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.01}[/tex] = 2.326

Again,

E = [tex]Z\sqrt{\frac{p1(1-p1)}{n1}+ \frac{p2(1-p2)}{n2} }[/tex]

E = [tex]2.326\sqrt{\frac{0.250(1-0.250)}{1000}+ \frac{0.1625(1-0.1625)}{1200} }[/tex]

E = 0.0403

Thus, required margin of error is 0.0403.

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Answer:

Step-by-step explanation:

4,505 tickets were sold 219 times.

4,505 x 219

The answer is 986,595

[tex]\begin{array}{ccll} hours&days\\ \cline{1-2} 6 & 2\\ x& 14 \end{array} \implies \cfrac{6}{x}~~=~~\cfrac{2}{14} \implies \cfrac{6}{x}=\cfrac{1}{7}\implies 42=x[/tex]

Answer:  42 hours

add 6 every 2 days

The Trigonometric ratios are:

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

H/P = Cosecθ

H/B = Secθ

B/P = Cotθ

Where,

'P' represents the perpendicular

'B' represents the base

'H' = represents the hypotenuse

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

A. As the values of p, b or h are not given.

Pythagoras Theorem states that:

h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]

Altitude of a triangle is usually given by the perpendicular,

So,

h² = p² + b²

h² - b² = p²

p² = h² - b²

p  = [tex]\sqrt{h^2 - b^2}[/tex]

B. The trigonometric ratios for θ = 60°

Sin 60 = √3/2

Cos 60 = 1/2

Tan 60 = √3

C. The trigonometric ratios for θ = 30°

Sin 30 = 1/2

Cos 30 = √3/2

Tan 30 = 1/√3

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Answer:

200*1-0.95-0.95+0.9025

200*1-1.9+0.9025

200*0.0025

0.5

The point F lies on 4.5 in the number line.

What is the number line?

The number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on

= (my+nx)/(m+n) in the number line.

Here in the given problem that,

Point D lies on -6 in the number lin

Point E lies on 8 in the number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence, the point F lies on 4.5 in the number line.

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4300 workers are there in all.

What is algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Here, we have

In a company, 90% of the workers are women.

430 people work for the company who aren’t women.

% of male = 10%

Now,

10% of x = 430

10÷100 × x = 430

x = 4300

Hence, 4300 workers are there in all.

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Saul's claim about the new function is incorrect

The function that models the decrease of an initial population of 200 organisms at a decay rate of 10% each hour is given as

f(x) = 200(0.90)ˣ

When the initial value is increased by 100, the initial value becomes

Initial value =200 + 100 = 300

A population function with 10% decrement is represented as

g(x) = Initial value * (0.90)ˣ

So, we have

g(x) = 300(0.90)ˣ

See that f(x) = 300(0.90)ˣ does not equal g(x) = 200(0.90) x + 100

Hence, Saul is incorrect

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The production level that a maximum profit is   186000 and the maximum profit will at the points of (200, -4000) , under the concept of absolute maximum value.

The  P(x, y) = 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000, the first partial differentiate  of the  given equation with respect to x and  y,

Px= ( 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000) = 8-0.001(2x-y) ....2

Py= 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000)  = 10-0.001(x-2y) ... 3

Considering the above  equation to  be equal to  zero  :

=>8-0.001(2x-y) =0 =>0.001(2x-y) =8 .....4

=>10-0.001(x-2y) =0 =>0.001(x-2y) =  10 ...5

Solving the equations 4 and 5 we get the lues of x and  y  we get are :

x= 2000, and y = -4000 , Now the partial differentiate for the equations 2  ad 3  are with respect to x and y :

pxx(x,y)=-0.002

pyy(x,y)=  0.002

pxy(x,y) =-1

The discriminant of the function wil  be  at (2000,-4000):

D = 0.002*-0.002 -(-1)^2 =-1.0004 ,here D <0,  so the  critical values (200, -4000) reaches the maximum value .So the  production level will be :

P(2000, -4000) = 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000 = 186000

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Answer:

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

RHS and HL refer to same thing.

A right angled triangle has one hypotenuse and two sides.

If the hypotenuse and one side of one triangle is congruent to hypotenuse and one side of another triangle, then the two triangles are congruent.

We know sides of a right triangle are also called the hypotenuse and legs. RHS is also called HL because they both refer to hypotenuse and one side or leg.

Answer:

x = 9

Step-by-step explanation:

(7x + 7) + 60 = 13x + 13 (exterior angle)

7x + 67 = 13x + 13

6x = 54

x = 9