tom has 6 quarters and 12 dimes in his pocket how many coins does he need to take out his pocket to make sure he has 4 quarters

The options of the question are

A.)BFC B.)CFG C.)GFD D.)EFA

we know that

A linear pair forms a straight angle which contains [tex] 180 [/tex]º, so you have [tex] 2 [/tex] angles whose measures add to [tex] 180 [/tex] degrees, which means they are supplementary.

Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines).Vertical angles are congruent

in this problem

Part a) Linear Pair

1) m∠EFA+m∠EFD=[tex] 180 [/tex]°

angles ∠EFA and ∠EFD are a linear pair

2) m∠BFD+m∠EFD=[tex] 180 [/tex]°

angles ∠BFD and ∠EFD are a linear pair

3) m∠BFD+m∠BFA=[tex] 180 [/tex]°

angles ∠BFD and ∠BFA are a linear pair

4) m∠BFA+m∠AFD=[tex] 180 [/tex]°

angles ∠BFA and ∠AFD are a linear pair

Part b) Vertical angles

1) m∠EFA=m∠BFD

angles ∠EFA and ∠BFD are a vertical angles

2) m∠AFB=m∠EFD

angles ∠AFB and ∠EFD are a vertical angles

therefore

the answer is the option

D.) EFA

Answer:

Option C: 60%

Step-by-step explanation:

The number of blue candies with nuts = 20

The number of blue candies without nuts = 30

The total number of blue candies = 20 + 30 = 50

As the chosen candy is blue, the probability that is does not contain any nuts will be = (The number of blue candies without nuts)/(Total number of blue candies)

So, the probability = 30/50 = 0.6 *100% = 60%

Answer: 20%

Step-by-step explanation:

The answer is:  B. 1 - Only one of the five people is telling the truth.

In this scenario, we are given that five people are sitting around a circle. Some always tell the truth, while others always lie. Each person claims to be sitting between two liars.

Let's analyze the possibilities:

If all five people were telling the truth, each person's claim of sitting between two liars would be true. However, this would mean that all five people are telling the truth, which contradicts the given information.

If none of the five people were telling the truth, each person's claim of sitting between two liars would be false. However, this also contradicts the given information.

Given these two possibilities, we can conclude that there must be a combination of truth-tellers and liars among the five people.

Considering the options given:

A. 0: This suggests that none of the people are telling the truth. However, this contradicts the given information that some people always tell the truth.

B. 1: This suggests that only one person is telling the truth. In this case, this person's claim of sitting between two liars would be true, while the claims of the other four people would be false. This option aligns with the given information and is a valid possibility.

C. 2, D. 3, E. 4: These options suggest that multiple people are telling the truth. However, if more than one person tells the truth, their claims of sitting between two liars cannot all be true.

Based on the analysis, the answer is:

B. 1 - Only one of the five people is telling the truth.

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Answer:

[tex]n=\frac{P_{out}}{P_{in}}[/tex]

Step-by-step explanation:

We know that,

[tex]\text{Energy efficiency}=\frac{\text{Energy out put}}{\text{Energy in put}}[/tex]

If [tex]P_{in}[/tex] represents the energy input,

[tex]P_{out}[/tex] represents the energy output,

And, n represents energy efficiency,

Hence, the required formula would be,

[tex]n=\frac{P_{out}}{P_{in}}[/tex]

i.e. OPTION B is correct.

To find the smallest positive value for x where y = sin^2x reaches its maximum, we can set sin^2x = 1 and solve for x. The smallest positive value of x where y = sin^2x reaches its maximum is pi/2.

To find the smallest positive value for x where y = sin^2x reaches its maximum, we need to consider the properties of the sine function. The sine function oscillates between -1 and +1, with the maximum value of sin^2x being 1. Since the maximum value of sin^2x is 1, we can set sin^2x = 1 and solve for x.

Applying the property of sin^2x = 1, we have:

sin^2x = 1
Taking the square root of both sides, sinx = ±1
Since we are looking for the smallest positive value of x, we take sinx = 1
This means that x = π/2 + 2πn, where n is an integer.

Therefore, the smallest positive value for x where y = sin^2x reaches its maximum is π/2.

The annual interest rate paid for the pawned guitar is calculated to be 640%, which is obtained by dividing the interest paid by the original loan amount to find the monthly rate and then multiplying by 12.

To calculate the annual interest rate paid for pawning the guitar, we need to first determine the total interest paid, then the monthly interest rate, and finally convert that to an annual rate. The interest paid is the difference between the amount received from pawning the guitar and the amount paid to redeem it, which is $1,472 - $960 = $512.

As the loan was for one month, we can determine the monthly interest rate by dividing the interest paid by the principal amount. This gives us $512 / $960 = 0.5333 or 53.33%. To find the annual interest rate, we multiply the monthly rate by 12 (the number of months in a year). Thus, the annual interest rate is 53.33% * 12 = 640%.

It's important to note that this is an extremely high rate of interest, which is not uncommon for pawnshop loans or other short-term high-risk loans.

If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then the degree measure of angle EOC is 108°.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

Therefore, the measure of each interior angle is given by;

Interior angle of a pentagon = 540°/5

Interior angle of a pentagon = 108°

From triangle EAO, we have:

2m∠EOA = 180° - (54 + 54)°

m∠EOA = 72°/2

m∠EOA = 34°

Now, we can determine the measure of angle EOC;

m∠EOC = 180° - (34 + 34)°

m∠EOC = 108°

Answer:

His gross pay would be reduced $174.66.

Step-by-step explanation:

Gross pay of Marquis = $816

His withholding are :

Federal tax = $92.00

Social security tax = 6.2% of $816

                               = 0.062 × 816

                               = $50.592

Medicare tax      = 1.45% × 816

                           = 0.0145 × 816

                           = $11.832

State tax            = 22% × 92

                          = 0.22 × 92

                         = $20.24

Total withholding = 92 + 50.59 + 11.83 + 20.24

                             = $174.66

His net pay = $816 - $174.66 = $641.34

His gross pay would be reduced $174.66

Answer:

(5,5)

Step-by-step explanation:

Step 1) Find the perpendicular bisector of BP Step 2) Find the perpendicular bisector of BH Step 3) The intersection point of the perpendicular bisector is where the showers would be built. This is the circumcenter of the circumscribed circle. After doing all of this, you should get that answer.. (5,5)

He should work 20 hours every week to optimize his profits. The maximum profit will be $164.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

He should tutor as many hours as possible because he is paid more for it. He may only work for a maximum of 20 hours every day. He must tutor for at least 3 hours but no more than 8 hours to optimum profit, he must tutor for 8 hours leaving 12 hours as a teacher's helper.

To optimize his profits, he should work 20 hours every week.

⇒ 8(10) + 12(7)

⇒ 80 + 84

⇒ 164

Therefore, he should work 20 hours every week to optimize his profit and the maximum profit will be $164.

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Answer:

B ) ellipse.Domain: { -4 ≤ x ≤ 4 }Range: { -3 ≤ y ≤ 3 }

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The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. Its domain is \([-4, 4]\) and its range is \([-3, 3]\).

The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. To identify its domain and range, we need to understand its shape and orientation.

Step 1: Standard Form of an Ellipse

The standard form of an ellipse with its center at the origin is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where \( a \) and \( b \) are the semi-major and semi-minor axes lengths, respectively.

Step 2: Compare Equations

Comparing the given equation [tex]\( 9x^2 + 16y^2 = 144 \)[/tex] with the standard form, we see that [tex]\( a^2 = \frac{144}{9} = 16 \)[/tex] and [tex]\( b^2 = \frac{144}{16} = 9 \).[/tex]

Step 3: Determine Axis Lengths

This means the semi-major axis length \( a \) is [tex]\( \sqrt{16} = 4 \)[/tex]and the semi-minor axis length \( b \) is [tex]\( \sqrt{9} = 3 \).[/tex]Step 4: Shape of the Ellipse

Since \( a > b \), the ellipse is stretched more horizontally than vertically, meaning it's wider than it is tall.

Step 5: Domain and Range

The domain of the ellipse is determined by the values of \( x \) and the range by the values of \( y \). For this ellipse, the \( x \)-values vary from \( -4 \) to \( 4 \) (domain), and the \( y \)-values vary from \( -3 \) to \( 3 \) (range).

Therefore, the domain is \([-4, 4]\) and the range is \([-3, 3]\).

Final answer:

To find the number n in the inequality '8 less than a number n is less than 11', we can set up and solve the inequality n - 8 < 11. The answer is that the number n is less than 19.

Explanation:

The question states that 8 less than a number n is less than 11. To solve this, we can set up the inequality:

n - 8 < 11

To isolate n, we can add 8 to both sides:

n < 11 + 8

n < 19

So, the answer is that the number n is less than 19.

Answer:

Option C is the answer.

Step-by-step explanation:

A florist sale is for it's first month is represented by the equation y = 168x + 8

Here y represents the sales in dollars and x represents number of days.

Now we have to calculate the number of days it took to reach $3200 in sales.

For this we will substitute $3200 in place of y and find the value of x by solving the equation.

3200 = 168x + 8

168x = 3200 - 8 = 3192

[tex]x=\frac{3192}{168}=19[/tex]

Therefore Option C. is the correct option.

The 40th term of the arithmetic sequence 21,18,15,12,9.. is -96

using Arithmetic progression formula,

a = first term = 21

common difference =  d = 18 - 21 = - 3

Therefore,

aₙ = a + (n - 1)d

a₄₀ = 21 + (40 - 1)-3

a₄₀ = 21 +(39)(-3)

a₄₀ = 21 - 117

a₄₀ = -96

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The lines r and s are parallel

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Given data ,

From the figure m4 = m5

And , m4 and m5 are alternate angles

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size

So , m1 = m5 are corresponding angles

Or angle 1 = angle 5

Corresponding angles are the pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are equal in size.

Similarly , m2 = m6 or angle 2 = angle 6

Hence , the lines r and s are parallel by the properties of angles in parallel lines.

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∆ABC~∆PQR

AB~PQ , c~r

c:r

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that triangles ABC and PQR are similar triangles.

The sides of the triangle ABC are AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR=p and PR=q.

If two triangles are similar, then their corresponding sides proportional.

Since ABC and PQR are similar triangles, therefore

[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]

[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]

It can be written as

[tex]\frac{c}{r}=\frac{b}{q}[/tex]

[tex]\frac{a}{p}=\frac{b}{q}[/tex]

Therefore b:q is equal to c:r or a:p. Option 2 is correct.

The value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .

To add two matrices, we have to add the element present in the same position in the respective matrices.

(A+B)ij= Aij + Bij

where i is the no. of row and j is the no. of column.

In order to multiply a scalar by the matrix, we have to multiply that scalar with every element of the matrix.

nA= nAij

Here given matrix is

A= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]

and the other matrix is

B= [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]

The sum of the matrix is A+B=  [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]+  [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]

⇒ A+B =[tex]\left(\begin{array}{ccc}2+1&-3+0\\0+10&5+(-1/2)\\7+3&-2+1\end{array}\right)[/tex]

⇒ A+B= [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex]

the value of 3A= 3 [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]=  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex]

Therefore the value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is  [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .

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