1. Marina and Brian have a joint checking account. They have a balance of $3,839.25 in the
check register. The balance on the bank statement is $3,450.10. Not reported on the
statement are deposits of $2,000, $135.67, $254.77, and $188.76 and four checks for
$567.89, $23.83, $598.33, and $1,000. Fill in the blanks to determine if the account is
reconciled.
Checking Account Summary
Current Account Balance
Outstanding Deposits
Outstanding Checks
Revised Statement Balance
Check Register Balance

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

D

Step-by-step explanation:

5(x-5)=353 + x

the first 5 is all his tests, in the parenthesis x is the average score, and -5 is the 5 points lower mentioned in the problem.

Answer:

B

Step-by-step explanation:

We are given that Markus scored 85, 92, 82, and 94 on his first four tests and x on his fifth.

We know that his score on the fifth test is five points lower than the average of all five tests.

To find the average, we add up all the values and divide by the number of values there are. Therefore, the average of all five tests is:

\(\displaystyle \frac{85+92+82+94+x}{5}\)

Simplify:

\(\displaystyle =\frac{353+x}{5}\)

His test score x is five points lower than the average. Hence:

\(\displaystyle x=\left(\frac{353+x}{5}\right)-5\)

Rewrite. We can add five to both sides:

\(\displaystyle x+5=\frac{353+x}{5}\)

And multiply both sides by five. Hence:

\(\displaystyle 5(x+5)=353+x\)

Thus, our answer is B.

Notes:

By solving the equation, we see that x = 82. So, Markus scored 82 points on his fifth test.

If that is true, then his average score of all fives tests will be:

\(\displaystyle \frac{85+92+82+94+82}{5}=87\)

82 is indeed five points fewer than 87, so our answer is correct and matches the given information.

Answer:

here is your aneswer

the answer. will be 40

The internal values of all triangles are worth 180°, so knowing this, just form a 1st degree equation to respond, remembering that the value 180°, will stay after the equal sign of the equation.

Answer:

165

Step-by-step explanation:

tn = t1 + (n - 1)(d)

t31 = 405 + (31 - 1)(-8)

t31 = 405 + (30)(-8)

= 405 - 240

= 165

The pilot is approximately 1145.47 miles from her starting position.

For the first part of the flight, the pilot covers a distance

Distance = Speed x Time

Distance = 620 miles/hour x 1.5 hours

Distance = 930 miles

Now, let's consider the second part of the flight. The pilot changes direction by 10 degrees to the right. This means that she will not be flying directly away from her starting position, but at an angle to it. To calculate the distance she travels during this part of the flight, we need to use some trigonometry.

We can use the following formula to calculate the distance the pilot travels at an angle

Distance = (sin(angle) x Hypotenuse)

In this case, the angle is 10 degrees, and the hypotenuse is the distance the pilot travels in the second part of the flight. To find the hypotenuse, we can use the formula

Hypotenuse = Speed x Time

Hypotenuse = 620 miles/hour x 2 hours

Hypotenuse = 1240 miles

Now we can use the formula to find the distance the pilot travels at an angle

Distance = (sin(10) x 1240)

Distance = 215.47 miles (rounded to two decimal places)

Therefore, the total distance the pilot is from her starting position is the sum of the distance she traveled in the first part of the flight and the distance she traveled at an angle in the second part of the flight

Total distance = 930 + 215.47

Total distance = 1145.47 miles

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Answer:

the answer of this question is number D. 2

HOPE IT HELPED YOU !!!

Answer:

D. x = 2

Step-by-step explanation:

Rearrange so that the variable is on one side and the rest are on the other

0.6x = 2.4 - 1.2

0.6x = 1.2

To make x on its own, you divide 0.6 from both sides

x = 2

The most appropriate method of data collection for a study to determine the chance of getting three girls in a family of three children is Simulation.

What is Simulation?

Simulation is the act of imitating the behavior of a real-world system or process over time. It allows the study of systems that are complex or difficult to understand or predict, such as a nuclear reactor or an economy, without endangering the system or wasting resources.

While conducting the simulation, it is essential to consider how variables change over time and what factors influence those changes. The data obtained through simulations can be used to make predictions and improve performance in a variety of fields, including engineering, finance, and healthcare.

Therefore, the most appropriate method of data collection for a study to determine the chance of getting three girls in a family of three children is Simulation.

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Simulation would be the most appropriate method of data collection in this case since it allows for the investigation of a wide range of possible outcomes and does not require the manipulation of variables or the use of a biased sample.

To determine the chance of getting three girls in a family of three children, the most appropriate method of data collection is simulation. This is because simulation is a technique that involves creating a model that mimics the real-world situation or process under investigation. The simulation model is used to run multiple trials, each with slightly different inputs, to generate a range of possible outcomes.A simulation study would be conducted using a computer program that would simulate many families and their possible outcomes. In each simulated family, the gender of each child would be randomly assigned as male or female. By running the simulation many times, it would be possible to estimate the probability of getting three girls in a family of three children.In an observational study, researchers would simply observe families and record whether or not they have three girls. This method would not be appropriate in this case since it would be difficult to find enough families with three children, let alone three girls.The experiment would involve randomly assigning families to either a treatment group or a control group and observing the outcomes. This method would also not be appropriate since it would be unethical to manipulate the gender of children in families.A survey would involve collecting data from families with three children about the gender of their children. This method would also not be appropriate since the sample would be biased towards families with three children and may not accurately represent the population as a whole.

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Answer:

For the first one:

A' (-8,6)

B' (-9,10)

C' (-3,9)

D' (-2,5)

Step-by-step explanation:

The distance from the bird to the top of the tree is 61.95 feet.

We have,

Angle of elevation to the top of the tree: 38 degrees.

Angle of elevation to the bird: 60 degrees.

Distance from the base of the tree to your position: 84 feet.

Let the distance from the bird to the top of the tree as 'x'.

Using Trigonometry

tan(38) = height of the tree / 84

height of the tree = tan(38) x 84

and, tan(60) = height of the tree / x

x = height of the tree / tan(60)

Substituting the value of the height of the tree we obtained earlier:

x = (tan(38) x 84) / tan(60)

x ≈ 61.95 feet

Therefore, the distance from the bird to the top of the tree is 61.95 feet.

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Answer:

3

Step-by-step explanation:

Parallel lines have the same slope

So if line Q has a slope of 3

Line R which is parallel to Q must have a slope of 3

Answer:

These are two secant lines meaning we can use theorem 6-17 to find the value of x: 6x + 8x times 8x = 16 times 7

14x times 8x = 112

112x^2 = 112

x^2 = 1

x = 1

Answer:

x=1

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(9+7) *7 = (6x+8x)*8x

16*7 = 14x*8x

112 =112 x^2

Divide by 112

112/112 = 112x^2/112

1 = x^2

Take the square root

1 =x

Answer:

apple being picked: 8 times

given:

probability:

(apples/total fruits)*times picked

(4/10)*20

8 times

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

$0.13

Step-by-step explanation:

7.98/60 = 0.133

round down to 0.13

Answer:

I believe the answer is $0.13

Step-by-step explanation:

You need to divide the price of the air heads ($7.98) by how many bars there were in the box (60).  7.98/60= 0.133

Then you round the answer to the nearest hundredth: 0.133= $0.13

Answer:

28 units

Step-by-step explanation:

Firstly, we can see that the vertical sides are 9 units each.

To get the diagonal sides, we can turn the ends into right triangles, which we can then use with the Pythagorean Theorum.

To make the top side into a triangle, we would draw a horizontal line connecting points (-1, 3) and (3, 3). This creates a right angle which is essential when using the Pythagorean Theorum.

A^2 + B^2 = C^2

We can plug in values for the Pythagorean Theorum because we can see that going across horizontally from point (-1, 3) to (3, 3), there are 4 units in between the two points. This will be our A value. We will do the same but vertically from points (3, 6) to (3, 3). The 3 units between the two points will be our B value. Now, we can plug in our values into the Pythagorean Theorum to find side C, the hypotenuse.

4^2 + 3^2 = C^2

16 + 9 = C^2

25 = C^2

√25 = C

C = 5

Now that we know the diagonal value of the side, we also know the same diagonal value of the bottom side. When you add all four sides together,

9 + 5 + 9 + 5 = 28

you get 28, which is the perimeter of the parallelogram.

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

what

Step-by-step explanation:

The probability that hour 10 is the first sample at which x exceeds 1 is 0.0086.

Let X denotes the number of parts in the sample of 20 that require rework. We can model the number X of parts in a random sample of 20 that require rework with a binomial distribution \($X\sim B(20,0.01)$\). We want to find the probability that the first sample at which X exceeds 1 occurs at hour 10. To do this, we need to compute two probabilities:

- The probability that in the first 9 samples, no sample has more than 1 part needing rework.

- The probability that in the 10th sample, there are at least 2 parts needing rework.

To compute the first probability, we use the binomial distribution with n=20 and p=0.01, and note that each of the first 9 samples is independent. Thus, the probability that no sample in the first 9 has more than 1 part needing rework is

\($$P(X\le 1)^9 = \left(\binom{20}{0}(0.01)^0(0.99)^{20} + \binom{20}{1}(0.01)^1(0.99)^{19}\right)^9 \approx 0.435$$\)

To compute the second probability, we just use the binomial probability mass function with n=20 and p=0.01:

\($$P(X\ge 2) = 1 - P(X=0) - P(X=1) \approx 0.0198$$\)

Finally, we can multiply these probabilities to get the desired probability:

\($P(\text{first sample with } X > 1 \text{ is at hour } 10) = 0.435\times 0.0198 \approx \boxed{0.0086}.$\)

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The number of days would be 10 and the maximum percent of the population infected would be 25.752%.

What are exponential functions?

The exponential function, denoted by \(e^x\), is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

\(p(t) = 7te^{-\frac{t}{10}}\)

percentage of infected people a maximum when p '(t) = 0

                    \(p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10\)

Hence percentage of infected people reaches a maximum after 10 days

maximum percent of the population infected = p(10)

    \(p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%\)

Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.

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Answer:

y=-6/5x-3

Step-by-step explanation:

Formula: y-y1=m(x-x1)

y-3=-6/5(x-(-5))

y-3=-6/5(x+5)

y-3=-6/5x-6

y=-6/5x-3

Answer:

y=-6/5x-3

Step-by-step explanation:

:)

Answer:

4

Step-by-step explanation:

Answer:

i think its the first one i hope this helps

Step-by-step explanation:

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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Answer:

<C = 54 degrees

b = 123.6

a = 72.6

Step-by-step explanation:

<C = 180 - 90 - 36 = 54 degrees

b = 100/sin54 = 123.6

a = sqrt (123.6^2 - 100^2) = 72.6

Answer:

\(a_n=a_{n-1}+2^{n-1}\ \ n>1\)

Step-by-step explanation:

Recursive Sequence

We are given the following sequence:

-1, 1, 5, 13...

It's required to find the recursive term for the sequence.

A recursive formula calculates each term as a function of one or more previous terms.

To find the recursive formula, we must find a pattern and transform it into a math expression.

Let's write the sequence, and below it, the difference of consecutive terms:

-1,   1,   5,   13...

+2,  +4,  +8

Note the difference between consecutive terms is always a power of 2, starting from 2^1, 2^2, 2^3.

The exponent is one less than the number of the term, thus:

\(a_n-a_{n-1}=2^{n-1}\)

Thus:

\(\mathbf{a_n=a_{n-1}+2^{n-1}\ \ n>1}\)

Testing:

n=1

\(a_1=-1\) (given).

n=2

\(a_2=a_{1}+2^{2-1}=-1+2^{1}=1\)

n=3

\(a_3=a_{2}+2^{3-1}=1+2^{2}=5\)

n=4

\(a_4=a_{3}+2^{4-1}=5+2^{3}=13\)

Answer:

70

Step-by-step explanation:

triangle xbc is an isosceles triangle.

there are 180 degrees in a triangle.

angle xbc=55.

so that means angle xcb is also 55.

55+55=110

180-110=70

hope this helps

There are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.

To count the number of arrangements of 12 people with Dr. Tucker and Dr. Stanley positioned 3 apart, we can treat Dr. Tucker and Dr. Stanley as a single block of two people, and then arrange the resulting 11 blocks in a row.

Since Dr. Tucker and Dr. Stanley can occupy any of the 10 possible positions (the first two positions, the second and third, and so on up to the last two positions), there are 10 ways to form this block.

After the block is formed, we are left with 10 remaining people to arrange in the remaining 10 positions. There are 10! ways to arrange these people, so the total number of arrangements is:

10 x 10! = 3,628,800

Therefore, there are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.

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