i need help with 1 and 2

Answer:

12

Step-by-step explanation:

To convert an annual interest rate to a daily interest rate based on simple interest, divide the annual interest rate by 365, the number of days in a year.

This way,

The daily interest rate is 0.05%

To get the simple interest in a 30 day period, we use the formula for simple interest and get:

The interest for a 30 day period is $23.15

Answer:

Mari's mom paid more than Mari's dad.

Step-by-step explanation:

Mari's mom paid $27.39. This is a bit more than $27.

Mari's dad paid $23.79. This is a bit more than $23.

Since $27 > $23, then $27.39 > $23.79.

Mari's mom paid more than Mari's dad.

Answer:

Mari's dad paid less than Mari's mom.

Step-by-step explanation:

23.79 is less than 27.39

Hope it helped!

All of the following are measures of central tendency except the range.

The range is a measure of dispersion, representing the difference between the largest and smallest values in a dataset. It provides information about the spread or variability of the data but does not provide information about the central tendency.

On the other hand, measures of central tendency are statistical measures that aim to summarize the center or typical value of a dataset. They include the mode, median, and mean.

The mode represents the most frequently occurring value(s) in the dataset.

The median is the middle value when the data is arranged in ascending or descending order. It divides the dataset into two equal halves.

The mean is the arithmetic average of all the values in the dataset. It is calculated by summing all the values and dividing by the total number of values.

Therefore, option C, range, is not a measure of central tendency as it focuses on the spread or dispersion of the data rather than summarizing the central or typical value.

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Answer:

x = 0

Step-by-step explanation:

add 23 on both side and x equals zero

substitute x for 0, and the equation is still correct

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)

Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.

Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.

The former describes condition which cannot both (or all) obtain. and so exclude one another.

i.e., "not - (both A and not - A)"

The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"

I presume you intend to refer to the latter.

Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.

It is thus certain, not merely probable, that one or the other will obtain.

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The relationship between the number of bags (x) and the price of each bag (y) in this situation is that as the number of bags increases, the price per bag decreases.

Walter has three options to purchase bags of dog food. He can buy 2 bags for $12 each, 3 bags for $8 each, or 4 bags for $6 each. If he buys 2 bags for $12 each, his total cost will be $24. If he buys 3 bags for $8 each, his total cost will be $24 as well. However, if he buys 4 bags for $6 each, his total cost will only be $24, which means that he gets a better deal per bag.

To determine the relationship between the number of bags and the price per bag, we can create a table:

| Number of Bags (x) | Price per Bag (y) | Total Cost |
| ----------------- | ----------------- | ---------- |
| 2                 | $12               | $24        |
| 3                 | $8                | $24        |
| 4                 | $6                | $24        |

From the table, we can see that as the number of bags increases, the price per bag decreases. This is because Walter is able to take advantage of bulk pricing discounts. Therefore, the statement that is true about the relationship between the number of bags (x) and the price of each bag (y) in this situation is that as the number of bags increases, the price per bag decreases.

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The expected gain or loss of an experiment over the long run is called the expected value.

The expected value is the weighted average of all possible outcomes, where the weights are the probabilities of those outcomes occurring. It is calculated by multiplying each possible outcome by its probability of occurring and then adding up these products. The expected value can be used to make decisions and assess risk in various fields, including finance, economics, and gambling. If the expected value is positive, it means that, on average, the experiment will result in a gain, while a negative expected value indicates a loss.

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Answer:

Perpendicular Bisectors

Step-by-step explanation:

Recall that a perpendicular bisector intersects a line segment at its midpoint and is perpendicular.

The gestation period is a critical stage in the development of a fetus. It is during this time that the baby's body systems and organs develop to function optimally after birth. As a result, proper prenatal care and monitoring are crucial to ensure a safe and healthy delivery of a full-term baby.

One critical aspect of the gestation period is the weight of the baby at birth, which is directly linked to the baby's development and overall health outcomes. The probability of a baby weighing between 6 and 9 pounds varies based on the gestation period.The weight of the baby at birth increases with gestational age. For a full-term baby, a gestational period of 37 to 40 weeks, there is an 80% chance of the baby weighing between 6 and 9 pounds.

Babies born between 34 and 36 weeks have a 60% chance of weighing between 6 and 9 pounds, while those born before 34 weeks have a lesser chance of weighing between 6 and 9 pounds. Proper prenatal care, including regular monitoring of the baby's weight and development, can help identify any risk factors or issues that may impact the baby's birth weight and health outcomes.

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Answer:

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=1,\:y=-3\)

As the system of equations has only one solution, thus the solution consistent.

Step-by-step explanation:

Given the system of equations

4x - 5y = 19

y = x - 4

Solving the system of equations by using the substitution method.

\(\begin{bmatrix}4x-5y=19\\ y=x-4\end{bmatrix}\)

\(\mathrm{Subsititute\:}y=x-4\)

\(\begin{bmatrix}4x-5\left(x-4\right)=19\end{bmatrix}\)

\(4x-5\left(x-4\right)=19\)

\(-x+20=19\)

isolate x for \(-x+20=19\)

\(-x+20=19\)

\(-x=-1\)

Divide both sides by -1

\(\frac{-x}{-1}=\frac{-1}{-1}\)

\(x=1\)

\(\mathrm{For\:}y=x-4\)

\(\mathrm{Subsititute\:}x=1\)

\(y=1-4\)

\(y=-3\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=1,\:y=-3\)

As the system of equations has only one solution, thus the solution consistent.

Please remember that if the system of equations has only one solution, then it is an independent system of equations.

The roots of the given function is \(\rm F(x)= x^{3}-9x^{2} +26x-24\) are 2,3&4

Given: x=2 is a root of the function. So, (x-2) will be a factor of this function

Remainder theorem is a theorem if any function is divided by (x-a), then the remainder is equal to f(a). If f(a) is equal to 0 then c is the root of the function.

Here we will use the synthetic division method to divide the function f(x) by (x-2).

\(\rm f(x)=(x-2)(x^{2} -7x+12)\\f(x)=(x-2)(x^{2}-4x-3x+12)\\f(x)=(x-2)(x(x-4)-3(x-4))\\f(x)=(x-2)(x-3)(x-4)\)

In order to find the roots of the given equation the function we equate the function equal to 0

Therefore, the roots of the given function are 2,3 and 4.

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Answer:  A: x = 2, x = 3, or x = 4

Step-by-step explanation: EDG 2022

Equation which represents a line that has a slope of 1/3 and passes through the point (-2,1) is:

\(y=\frac{1}{3} x+\frac{5}{3}\)

What is the Equation of a Line?

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

Let the equation of line be y=mx+c

Where m is the slope and c is the y-intercept

⇒ m=1/3

and The line passes through (-2,1)

Putting it in the equation

\(\begin{aligned}&1=\frac{1}{3} \times-2+c \\&c=1+\frac{2}{3} \\&c=\frac{5}{3}\end{aligned}\)

Hence,

An equation that represents a line that has a slope of 1/3 and passes through the point (-2,1) is: \(y=\frac{1}{3} x+\frac{5}{3}\)

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Answer: 38

Solution: An isosceles triangle has two equal sides: 3x - 5 and 19-x.; 3x - 5 = 19 - x; 4x = 24; x = 6

Let's check it out: 3(6) - 5 = 13; 19 - (6) = 13; 2(6) = 12

Two equal sides are 13 and base 12

Perimeter is 13 + 13 + 12 = 38 units

Answer is: 38

The perimeter of the given isosceles triangle is 38 cm.

The perimeter of an isosceles triangle refers to the addition of all the three sides of the triangle. Since the base angles of an isosceles triangle have two angles and two sides equal;

We can say that the perimeter of an isosceles triangle is:

P = 2a + b

where;

3x - 5 =  19 - x

3x + x = 19 + 5

4x = 24

x = 24/4

x = 6

The perimeter of the isosceles triangle is:

= 3x - 5 + 19 - x + 2x

= 3(6) - 5 + 19 - 6 + 2(6)

= 18 + 8 + 12

= 38 cm

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

log₃(-2x - 3) = 2

Step-by-step explanation:

logₓ(36) = 2:

To solve this equation, we need to find the value of x for which logₓ(36) equals 2. Rewriting this equation in exponential form, we have x² = 36. Taking the square root of both sides gives us x = 6.

log₃(2x - 9) = 3:

3^(log₃(2x - 9)) = 3³

By applying the property of logarithms that states logₓ(x^a) = a, we can simplify the equation further:

2x - 9 = 27

Now, let's solve for x:

2x = 27 + 9

2x = 36

x = 36/2

x = 18

log₃(216) = x:

log₃(6³) = x

3log₃(6) = x

3 + 3log₃(2) = x

log₃(-2x - 3) = 2:

- 2x - 3 = 3²

- 2x - 3 = 9

- 2x + 3 = 9 + 3

- 2x = 9 + 3

- 2x = 12

- 2x / -2 = 12/-2

x = -6

In summary, the equation that has x = -6 as the solution is the last equation: log₃(-2x - 3) = 2

The dimensions of the rectangular metal tank that requires the least material to build are approximately 7.58 feet by 7.58 feet by 7.58 feet.

Let the length, width, and height of the tank be L, W, and H, respectively. Since the tank has an open top, its volume is given by V = LWH. We are given that V = 364.5 cubic feet. We want to minimize the surface area of the tank, which is given by A = 2LW + 2LH + 2WH.

To minimize A, we can use the volume constraint to eliminate one of the variables. Solving for one of the variables, say H, we get H = V/LW. Substituting this into the equation for A, we get A(L,W) = 2LW + 2V/L + 2V/W. To minimize A, we take partial derivatives with respect to L and W and set them equal to zero. This gives us the system of equations:

2 + 2V/L^2 = 0

2 + 2V/W^2 = 0

Solving for L and W, we get L = W = sqrt(V/2) = 7.58 (rounded to two decimal places). Substituting these values into the equation for H, we get H = V/LW = 7.58. Therefore, the dimensions of the tank that require the least amount of material to build are approximately 7.58 feet by 7.58 feet by 7.58 feet.

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The tank that requires the least amount of material to build has Length = 1 ft. Width = 1 ft. Height = 364.5 ft

To find the dimensions of the tank that require the least amount of material to build, we need to minimize the surface area of the tank while keeping its volume constant.

Let's denote the length, width, and height of the tank as L, W, and H, respectively.

The volume of a rectangular tank is given by:

Volume = Length × Width × Height

In this case, the volume is given as 364.5 cubic feet:

364.5 = L × W × H

The surface area of a rectangular tank can be calculated by considering the four sides and the bottom:

Surface Area = 2(LW + LH + WH)

We need to minimize the surface area while keeping the volume constant. To achieve this, we can express one of the dimensions in terms of the other two using the volume equation and substitute it into the surface area equation.

From the volume equation, we can express H in terms of L and W:

H = 364.5 / (LW)

Substituting this value of H into the surface area equation, we have:

Surface Area = 2(LW + L(364.5 / (LW)) + W(364.5 / (LW)))

Simplifying further:

Surface Area = 2(LW + 2 * 364.5 / W + 2 * 364.5 / L)

To find the dimensions that minimize the surface area, we need to differentiate the surface area equation with respect to L and W and set the derivatives equal to zero.

Differentiating with respect to L:

d(Surface Area) / dL = 2W - (2 * 364.5 / L^2) = 0

Differentiating with respect to W:

d(Surface Area) / dW = 2L - (2 * 364.5 / W^2) = 0

Solving these equations will give us the values of L and W that minimize the surface area.

2W - (2 * 364.5 / L^2) = 0

2L - (2 * 364.5 / W^2) = 0

Simplifying:

W = 364.5 / L^2

L = 364.5 / W^2

Substituting these expressions into the volume equation:

364.5 = (364.5 / L^2) * L * W

364.5 = 364.5 / L * W

Simplifying:

L * W = 1

This implies that the product of the length and width is equal to 1.

Since we want to minimize the amount of material used, we can set one of the dimensions to 1 and solve for the other dimension.

Let's set W = 1:

L * 1 = 1

L = 1

Therefore, the dimensions that require the least amount of material to build the tank are:

Length = 1 ft

Width = 1 ft

Height = 364.5 ft

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\(x < \frac{17}{5}+\frac{7}{20}\)

\(x < \frac{15}{4}\)

According to "SEC-rules", fingerprinting is required for all of "broker-dealer" employees EXCEPT (d) A receptionist at "broker-dealer" which regularly answers calls from customers.

The Fingerprinting is a regulatory requirement imposed by the Securities and Exchange Commission (SEC) for certain broker-dealer employees to undergo background checks. It helps ensure the integrity and security of the financial industry.

The fingerprinting is not required for a receptionist at a broker-dealer who primarily handles customer calls. Receptionists do not have access to sensitive customer funds or engage in activities that would warrant fingerprinting under SEC rules.

The correct option is (d).

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The given question is incomplete, the complete question is

According to SEC rules, fingerprinting is required for all of the following broker-dealer employees EXCEPT

(a) A sales representative that sells only government bonds,

(b) An officer of a national securities exchange,

(c) A manager of a transfer agent that oversees custody of customer funds,

(d) A receptionist at a broker-dealer that regularly answers calls from customers.

Answer:

A

Step-by-step explanation:

I am not 100% sure how to show it but i graphed it and it's A

If the mean weight of 4 backfield members on the football team is 211lb and the mean weight of the 7 other players is 203lb, the mean weight of the 11-person team is 206lb.

The mean refers to the average of the data value.

The mean can be computed as the quotient of the total value divided by the number of items in the data set.

The mean weight of 4 backfield members on the football team = 211lb

The total weight of the 4 backfield members = 844lb (211 x 4)

mean weight of the 7 other players on the football team = 203lb

The total weight of the 7 other players = 1,421lb (203 x 7)

The total weight of the 11 football team members = 2,265lb (844 + 1,421)

The average or mean weight of the 11 members = 205.9lb (2,265 ÷ 11)

= 206lb

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Answer:

x = 11.14717238

Step-by-step explanation:

Answer:

165 g

Step-by-step explanation:

Median means the middle number so here the middle number is 165g.

Given data:

The given figure is shown.

The expression for sin(θ) is,

Thus, the line of sight distance from the television to the base of a stadium​ is 1,653.426 m.

I believe the answer is football.

Answer:

210

Step-by-step explanation:

easy bro just Times ten

The probability that an employee is sick more than two days in a three-month period is 0.1991.

Poisson distribution: Poisson distribution is a probability distribution which is used to measure the probability of a certain number of events occurring in a given time period if the events are rare and random.

The formula for calculating the Poisson distribution is: P(X=k) = (e^-λ * λ^k) / k!

Where, X = Random variable

k = Number of occurrences of the event

λ = Expected value of the event

e = Euler’s constant = 2.71828….

k! = Factorial of k

Mean of Poisson distribution: Given, Mean of the Poisson distribution is 1. Let X be the random variable which represents the number of days an employee is sick in a month.

∴ P(X=k) = (e^-λ * λ^k) / k!

The probability that an employee is sick more than two days in a three-month period is P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + .....

To calculate the probability, we need to find the value of λ for three months.

λ for three months = Mean for a month * Number of months∴ λ = 1 * 3 = 3

Now, we have λ = 3P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + .....= (e^-3 * 3^3) / 3! + (e^-3 * 3^4) / 4! + (e^-3 * 3^5) / 5! + .....= 0.1991

Hence, the probability that an employee is sick more than two days in a three-month period is 0.1991.

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