at a picnic each person shakes hands with every other person once. if there are 10 handshakes in total how many people are at the picnic​

Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.

Step-by-step explanation:

To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:

overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)

         = 932.77 - 2082.05

         = -1149.28

Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.

Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.

The lowest angle of elevation at which a shell should be fired to hit the target is 27⁰.

The maximum horizontal distance covered by the projectile is called the range of the projectile.

Mathematically, the range of a projectile is given as;

R = u² sin(2θ) / g

where;

Substitute the given parameters and solve for the angle of projection of the gun as shown below.

sin(2θ) = Rg/u²

sin(2θ) = (3,600 x 9.8) / (210²)

sin(2θ) = 0.8

2θ = arc sin(0.8)

2θ = 53.13

θ = 53.13/2

θ = 26.6⁰ ≈ 27⁰

Thus, the lowest angle of elevation at which a shell should be fired to hit the target is 27⁰.

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The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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Answer:

-48

Step-by-step explanation:

Answer:

x=-48

Step-by-step explanation:

x/6-5=-13     Get x by itself

    +5   +5

x/6=-8    You can multiply 6 times -8 to find x

x=-48

The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

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

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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68% of states have an infant mortality rate between 5.36 and 8.60 percent.

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

In this problem, we have that:

Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births)?

\(\sf 5.36 = 6.98 - 1\times1.62\)

So, 5.36 is one standard deviation below the mean.

\(\sf 8.60 = 6.98 + 1\times1.62\)

So 8.60 is one standard deviation above the mean.

Therefore, by the Empirical Rule, 68% of states have an infant mortality rate between 5.36 and 8.60 percent.

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Answer:

RM = 12 cm

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\)

Assuming 20 is the hypotenuse cus there is no picture:

\(a^{2} + 16^{2} = 20^{2}\)

\(a^{2} +256 = 400\)

\(a^{2} = 144\)

\(a=144\)

If It's not the hypotenuse:

\(16^{2}+ 20^{2} =c^{2}\)

\(256+400 =c^{2}\)

\(656=c^{2}\)

\(c = 25.61249695\)

But I find it unlikely that 20 wasn't the hypotenuse so ignore that unless it applies.

Hope this helped. :0)

The slope of the line represents the speed in miles per hour

The y intercept represents the initial distance

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

The graph

Where, we have

x = time in hours

y = distance in miles

The slope is

slope = change in y/x

So, we can conclude that the slope is the speed

By definition, the y intercept is the initial value of the graph

In this case;

y intercept = initial distance

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Answer:

the answer is option D because it cant be division or multiplication and minus does not work

Answer:

log 1/9 * log k

Step-by-step explanation:

\(\frac{1}{9} /k\) = 1/9 * k/1 = 1/9 * k

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

To solve for the second number given the GCF and LCM of two numbers and one of the numbers, we can follow the steps below:

\(\sf{Let\:the\:two\:numbers\:be\: represented\:by}\)\:\(\sf{a\:and\:b,\:where\: a\: is \:given\: as\:45.\)

\text{We know that the GCF of } a \text{ and } b \text{ is 3, which means that 3 is a factor of both } a \text{ and } b.} \

\text{We also know that the LCM of } a \text{ and } b \text{ is 180, which means that } a \text{ and } b \

\text{have no common factors other than 3, and their product divided by 3 equals 180:} \

a \times b &= 3 \times \text{LCM}(a, b) \

&= 3 \times 180 \

&= 540 \

\text{Since we know that } a = 45, \text{ we can substitute this into the equation above to solve for } b: \

45 \times b &= 540 \

\text{Dividing both sides by 45, we get:} \

b &= 12 \

\end{align*}

Therefore, the second number is 12.

Answer: b=12

The equation of the curve that intersects at right angles to every curve of the family y=(1/x)+k is y=lnx

y=-x+k is the equation of a curve that meets at right angles every curve in the family y=(1/x)+k (where k can take any real value). This is known as the 'orthogonal curve' of the y=(1/x)+k family. It is calculated by obtaining the reciprocal of the original equation and then removing k from the y-axis.

A straight line with a negative slope is given by the equation y=-x+k. Every point on the line has an x-value that is the inverse of its y-value. At the point where x=1/k and y=k, the equation will always meet the curve of the family y=(1/x)+k at a right angle. This point is the same for all values of k and is known as the 'origin' of the function.

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Answer:

Hope this will help you.

Answer:

w=3 1\4

Step-by-step explanation:

A=LxW

a=14 1\12

l=4 1\3

w=?

14 1\12=4 1\3 x w

14 1\12 divided by 4 1\3=13\4=3 1\4

w=3 1\4

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

Step-by-step explanation:

Area of parallelogram = base * height

                                      = 6 * 8

                                      = 48 square units

Answer:

Area = Base × Height

Area = 6 × 8

Area = 48 units²

\( \\ \)

Answer:

x=25

y= 64.5

Step-by-step explanation:

When lines are parallel, 2x=2(the number)

But, 2 isn't an angle.  However, 50degrees is congruent to 2 since they are verticle angles.

2x=50

x=25

When lines are parallel, 2y+1=1(the number)

But, 1 doesn't have a verticle angle.  However, 180-50 would be equal to 1

180-50=2y+1

130=2y+1

129=2y

y= 64.5

The decimal that represents the amount of pine and spruce trees in Hidden Forest is

If 50% of the trees in Hidden Forest are spruce,

10% are maple, and

25% are oak, then

the remaining percentage must be pine trees.

To find the percentage of pine trees, we solve as below

100% - 50% - 10% - 25% = 15%

Therefore, 15% of the trees in Hidden Forest are pine trees.

To write a decimal that represents the amount of pine and spruce trees, we can add the percentage of spruce trees and pine trees together and convert it to a decimal:

50% + 15% = 65%

Converting 65% to a decimal, we get:

0.65

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The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

top bar on 3. 120 dollars for strawberry milk per month

bottom bar on 3. 100 dollars chocolate milk per month

#4. bars help an individual know information visually and may help an individual understand better.

Answer:

I am definitely not one...Lol

Step-by-step explanation:

Answer:

BE = 49 cm

Step-by-step explanation:

Use Pythagorean theorem

(hypotenuse)² = (base)² + (leg)²

ΔDEF,

DE² + EF² = FD²

DE² + 63² = 65²

DE² + 3969 = 4225

              DE² = 4225 - 3969

              DE² = 256

             DE = √256 = √(16*16)

DE = 16 cm

ΔCBD,

BC² + BD² = CD²

56² +BD² = 65²

3136 + BD² = 4225

           BD² = 4225 - 3136

           BD² = 1089

          BD = √1089 = √(33*33)

BD = 33 cm

BE = BD + DE

    = 33 + 16

BE = 49 cm

Answer:

  -5

Step-by-step explanation:

You want the numerical coefficient of -5x.

A coefficient is one of the factors in a product. In simple terms consisting of the product of a constant and one or more variables, an unqualified reference to the coefficient is a reference to the constant.

The coefficient can also be that part of the product that multiplies a designated factor.

For example, the coefficient of x in the term "3abxy" is "3aby".

The numerical coefficient in the term -5x is -5.

Explanation

For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.

then, Let

Now, replace

so, the answer is

I hope this helps you