Estimate the values to the nearest hundredth to complete the table.

angleadjacent leg ++ hypotenuse
A= 0.31
C= (blank)

opposite leg ++ hypotenuse
A= 0.95
C= (blank)

opposite leg ++ adjacent leg
A= 3.06
C= (blank)

Answer: 26r^2 + 36r

Step-by-step explanation:

−2r(−16r + 3r − 18)

32r^2 - 6r^2 + 36r

26r^2 + 36r

Answer:

26[tex]r^2[/tex] + 36r

Step-by-step explanation:

Combine like terms:

-2r(-13r - 18)

Use the distributive property:

-2r(-13r) + (-2r)(- 18)

26[tex]r^2[/tex] + 36r

The statement "a paired samples test for the difference between two means can be used for segmentation purposes " is true

The given statement is

"A paired samples test for the difference between two means can be used for segmentation purposes"

The segmentation is the process of dividing the similar characteristics objects and group them together.

Here the a paired sample test for the difference between two mean is used for the segmentation process. It can be used for the segmentation purpose because A paired samples test for the difference between two means are  samples in which natural or matched couplings occur

Therefore, the give statement is true

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Answer:

x < -3

Step-by-step explanation:

15 < -5x

15/-5 > -5x/-5

-3 > x

Move the variable to the left and flip the inequality

x < -3

The attached figure represents the complete flowchart.

What does the Congruent Supplements Theorem say?

The Congruent Supplements Theorem shows that when two angles are considered to be supplements of a certain angle, then those two angles must be congruent.

The given statement is:

∠1 ≅ ∠2

To prove:

∠3 ≅ ∠4

By vertical angle theorem, we have:

∠2 ≅ ∠4

By the transitive property of congruence, we have:

∠2 ≅ ∠3

By the transitive property of congruence, we have:

∠1 ≅ ∠3

By vertical angle theorem, we have:

∠3 ≅ ∠4

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The expression is written as a number in scientific notation as 2.16 × 10^1. Option B

Scientific notation can be described as a form of expressing or representing  large numbers or very small numbers in a more simpler form.

It is also called index form or standard form.

From the information given, we have;

Now, let's substitute the values

3. 6 × 10^5 ×  1. 5 × 10^8/2. 5 × 10^4

Multiply the decimals and add the powers

5. 4 × 10^5/2. 5 × 10^4

Divide the values and subtract the powers, we get

2. 16 × 10^5-4

2. 16 × 10^1

Hence, the value is 2. 16 × 10^1

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Answer:

The expression is written as a number in scientific notation as 2.16 × 10^1. Option B

Step-by-step explanation:

Answer:

The value of SU is 36

Step-by-step explanation:

So,

ST/SE = SU/SF

Here,

Let us take SU as x

Now,

ST/SE = SU/SF

39/13 = x/12

3 = x/12

Multiply 12 from both sides we get,

3 × 12 = x/12 × 12

36 = x

x = SU = 36

Thus, The value of SU is 36

ST/SE = SU/SF

39/13 = 36/12 = 3

Hello,

I hope you and your family are doing well!

Since AB || DC and AD = BC, trapezoid ABCD is a parallelogram, which means that its opposite sides are parallel and congruent. Therefore, angle A is congruent to angle C and angle B is congruent to angle D.

Since mA = 4x+20 and m/C= 3x - 15, we know that mA + mC = 4x+20 + 3x - 15 = 7x + 5.

Since angles A and C are congruent, we can set their measures equal to each other:

mA = mC

4x+20 = 3x - 15

Solving this equation for x gives us x = 5. Substituting this value back into the equation mA + mC = 7x + 5 gives us:

mA + mC = 7 * 5 + 5 = 35

The answer is 35 (Option 2)

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Happy Holidays & New Year!

The solution is, the value of m is is 35 (Option 2).

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

hee, we have,

Since AB || DC and AD = BC, trapezoid ABCD is a parallelogram, which means that its opposite sides are parallel and congruent. Therefore, angle A is congruent to angle C and angle B is congruent to angle D.

Since mA = 4x+20 and m/C= 3x - 15, we know that mA + mC = 4x+20 + 3x - 15 = 7x + 5.

Since angles A and C are congruent, we can set their measures equal to each other:

mA = mC

4x+20 = 3x - 15

Solving this equation for x gives us x = 5.

Substituting this value back into the equation mA + mC = 7x + 5 gives us:

mA + mC = 7 * 5 + 5 = 35

The answer is 35 (Option 2)

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Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.

A percentage is a relative figure that has the ability to represent 1/100th of any quantity.

Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.

By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.

So, Luce is single and makes $763 twice weekly.

She does not request any compensation from federal withholding.

The value of this amount ranges from $760 to $780.

If we look at the table in the issue, the federal tax for this slab is $86.

Federal taxes now make up 19% of all state taxes.

Hence, the $86 in federal tax at a rate of 19% is:

Tax = 86 * 19/100

Tax = 16.34

Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.

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Correct question:

Use the tax table to help answer the following question.

A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.

Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?

a. $12.92

b. $15.13

c. $15.77

d. $16.34

Answer:

25.80$

Step-by-step explanation:

Original Price for Football:$24

Rate of Tax:7.5%

[tex]Formula for Tax[/tex]

[tex]\frac{Taxpercent}{100} x 24[/tex]

[tex]\frac{7.5}{100} x24\\=1.80[/tex]

[tex]Tax \\Applied:[/tex]24+1.80=25.80$

The maximum and minimum values of the given function will be equal to -1.47 and -6.52.

The 2nd equation in x is known as a quadratic function. ax² + bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.

As per the equation given in the question,

f(x) = x² + 8x + 9.6

D = b² - 4ac

= 8² - 4(1)(9.6)

D = 25.6

Now, find the roots,

-(b ± √D)/2a

-(8 ± 5.05)/2

So, the roots are,

-(8 + 5.05)/2 = -1.47,  (x + 1.47)

-(8 - 5.05)/2 = -6.52,  (x + 6.52)

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The equation of the line y = - (13 / 5) · x - 56 / 5 passes through the points (x₁, y₁) = (- 7, 7) and (x₂, y₂) = (- 2, - 6).

In this question we must derive the equation for a line that passes through two points on Cartesian plane. This can be done by means of the following two formulas:

Secant line formula

m = Δy / Δx

Equation of the line in slope-intercept form

y = m · x + b

Where:

First, write the given points:

(x₁, y₁) = (- 7, 7), (x₂, y₂) = (- 2, - 6)

Second, determine the slope of the line:

m = (- 6 - 7) / [- 2 - (- 7)]

m = - 13 / 5

Third, calculate the intercept of the equation of the line:

b = y - m · x

b = - 6 - (- 13 / 5) · (- 2)

b = - 6 - 26 / 5

b = - 30 / 5 - 26 / 5

b = - 56 / 5

Fourth, write the resulting equation of the line:

y = - (13 / 5) · x - 56 / 5

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Answer: x = − [tex]\frac{y}{2}[/tex] - 1

Steps for solving linear equation.

y = − 2x − 2

Swap sides so that all variable terms are on the left-hand side.

−2x − 2 = y

Add 2 to both sides.

−2x = y + 2

Divide both sides by −2.

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{y + 2}{-2}[/tex]

Dividing by −2 undoes the multiplication by −2.

x = [tex]\frac{y+2}{-2}[/tex]

Divide y + 2 by −2.

x = -[tex]\frac{y}{2}[/tex] - 1

Graph:

This situation would be known as a positive-sum game for team members.

In game theory, a scenario is said to as a positive-sum game if the sum of the profits and losses is more than zero. When resources are somehow expanded and a strategy is developed that satisfies the wants and requirements of everyone involved, a positive sum results. One instance would be when two parties engage in a competition and, regardless of the outcome, both sides stand to profit financially. In situations of distributive bargaining, where various interests are discussed in order to satisfy everyone's wants, positive-sum outcomes take place.

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Answer:  This is a valid probability distribution.

The P(x) values add to 1; each P(x) is between 0 and 1 inclusive.

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

Further Explanation:

A valid probability distribution is when,

The given data table is:

[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{P(x)}\\\cline{1-2}1 & 0.49\\\cline{1-2}2 & 0.05\\\cline{1-2}3 & 0.32\\\cline{1-2}4 & 0.07\\\cline{1-2}5 & 0.07\\\cline{1-2}\end{array}[/tex]

It's fairly clear that rule 2 has been satisfied. Something like [tex]0 \le 0.49 \le 1[/tex] is indeed a true statement. It's like saying 49% is between 0% and 100%. The other P(x) values are similar in nature.

---------

Let's see what the P(x) probability values add to:

0.49+0.05+0.32+0.07+0.07 = 1

We see that rule 1 has been met as well.

Since both rules have been satisfied, this means we have a valid probability distribution.

The Area of the Shaded Region is 184.61 sq. mm

What is Area?

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Solution:

Area of the Shaded Region = Area of Rectangle - 2 * Area of Circles

Area of Recatangle = Length * Breadth = 21 * 13 = 273 sq. mm

2 * Area of Circle = 2* πr² = 2 * 22/7 * 7.5/2 * 7.5/2

= 88.39 sq. mm  

Area of the Shaded Region = 273 - 88.39 = 184.61 sq. mm

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Answer:

Step-by-step explanation:

You want to know the measure of angle 1 given that angle 2 is 14° more and their total is 80°.

The angle sum theorem tells you the whole is equal to the sum of the parts.

  ∠1 +∠2 = ∠ABD

Using the given values, we have ...

  ∠1 +(∠1 +14°) = 80°

  2×∠1 = 66° . . . . . . . . . subtract 14°

  ∠1 = 33° . . . . . . . . divide by 2

  ∠2 = 33° +14°

  ∠2 = 47°

Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.

What is the binomial probability distribution formula?

The formula is:

P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ

Cₙ,ₓ = n!/x!(n-x)!

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

About 30% of frozen chickens are contaminated, hence p=0.3.

Chickens are delivered to grocery stores in crates of 24, hence n=24

The probability that a certain crate has more than 4 contaminated chickens is:

P(X>4)=1-P(X≤4)

In which:

P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

Then

P(X=x) =  Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ

P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002

P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020

P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097

P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305

P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687

Hence

P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

= 0.0002+0.0020+0.0097+0.0305+0.0687

= 0.1111

0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

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The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The probability that of the next 20 marbles selected it is expect to be yellow marbles,

=9/20

The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.

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Answer:

the answer is 10

Step-by-step explanation:

ixl says its ten

The waterwheel takes 40 seconds to make one turn.

To find the period of the function, we need to find the time it takes for the function to repeat itself. In this case, we want to find the time it takes for the waterwheel to complete one turn.

The function h = 15 cos (π/20) t models the height of the cloth in relation to sea level as a function of time.

The cosine function has a period of 2π, so the period of the function h = 15 cos (π/20) t will be 2π divided by (π/20) which simplifies to 40 seconds.

Therefore, it takes 40 seconds for the waterwheel to complete one turn.

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Answer

55

Step-by-step explanation:

5w+25= c

5(6)+25=55

Answer: B.

Step-by-step explanation:

x+2y≤4

3x-y≥2

Answer: grace has the most money

Step-by-step explanation:

Because

Grace has 2 quarters = 50 cents

Jen has 4 dimes and 1 nickel = 45 cents

Keesha has 3 dimes and 3 nickels = 33 cents

Terry has 1 quarter and 1 dime = 26 cents

so as you can see grace has the most money

Answer:

2

Step-by-step explanation:

-2 and -4 are less than 0

2 is greater than

If you write down in descending order ===> 2, -2 , -4

The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.  

Given:

range: 68,71,74,77,80

Domain:1,2,3,4,5

Here, the situation is not given.

So, the reasonable domain is { 1,2,3,4,5 }

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The probability that your cards are all face cards are,

We know that Total number of cars is 52 .

26 red and 26 is black.

13 are hearts ,

13 are diamonds,

13 are clubs,

13 are spades.

(​a) The first club you get is the third card dealt,

Probability P (first club get is the third card dealt) = P(Non-club x Non club x club)

So,

P = [tex]\frac{39}{52} * \frac{38}{51} * \frac{13}{50}[/tex]

P = 0.145

(b) Your cards are all black,

[tex]P_{all are black}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]

[tex]P_{all are black}[/tex] = 0.116

(c) You get no hearts,

[tex]P_{no heart}[/tex] = [tex]\frac{39}{52} *\frac{38}{51} *\frac{37}{50}[/tex]

[tex]P_{no heart}[/tex] = 0.413

(d) You have at least one red card,

[tex]P_{at least one red}[/tex] = 1 - [tex]P_{no red}[/tex]

[tex]P_{no red}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]

[tex]P_{no red}[/tex] = 0.116

[tex]P_{at least one red}[/tex] = 1 - 0.116

[tex]P_{at least one red}[/tex] = 0.884

Therefore,

The probability that your cards are all face cards are,

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Answer: x < −4

Step-by-step explanation:

4 - 2x > 12

4 - 2x/2x > 12/2x (switch it around)

x < −4

By using the substitution property, the value of f(-2) is -4.

What is the substitution property of equality?

In an expression or equation, one value can be substituted for another and the result will still be the same. This is known as the substitution property of equality. If the values of x and y are the same, then x and y can be substituted for one another.

Given, f(x) = x² + 3x - 2

To find the value of f(-2), apply substitution property

f(-2) = (-2)² + 3(-2) - 2 = 4 - 6 - 2 = -2-2 = -4

Hence, the value of f(-2) is -4.

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The inverse function is given by f⁻¹(x) = 1.06x.  2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars

Given that: the two different currencies is modeled by a linear function f(x) = x/1.06

where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros

To find the inverse function f⁻¹(x). Let y = f(x):

y = x/1.06

x = 1.06y

Since x = f⁻¹(y) = 1.06y

Thus, f⁻¹(x) = 1.06x

Note: f⁻¹(x) will help you convert from euros to dollar

2 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(2) = 1.06(2) = 2.12

Thus, 2 euros is equivalent to 2.12 U.S. dollars

4 euros to dollars will be:

f⁻¹(x) = 1.06x

f⁻¹(4) = 1.06(4) = 4.24

Thus, 4 euros is equivalent to 4.24U.S. dollars

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