HELP ASAP PLEASE NO LINKS
Matthew invested $200 at an interest
rate of 5%, compounded monthly.
How much is his investment worth
after 6 years?

The number of bags that the truck can move is given as follows:

31 bags.

(plus one extra package of 175 lbs).

The number of bags that the truck can move is obtained applying the proportions in the context of the problem.

The total weight that the truck can carry is given as follows:

4675 lbs.

Each bag has 150 lbs, hence the number of bags needed is given as follows:

4675/150 = 31 bags (rounded down).

The remaining weight will go into the extra package of 175 lbs.

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The unit rate for miles per gallon is 24.4 miles/gallon.

Given,

Distance travelled, d = 30 1/2 miles.

Grace used 1 1/4 gallons of gasoline.

We need to find the unit rate for miles per gallon. It can be calculated by dividing no of miles by gallons of gasoline. So,

R = 30 1/2 / 1 1/4

R = 61/2/5/4 miles per gallon

R = 61/2 × 4/5

R = 24.4 miles per galllon.

Hence we get the answer as 24.4 ,miles per gallon.

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The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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The two positive numbers are x = 10 and y = 10.

Product of two numbers = 100

Let the first numbers be = x

Let the second number be = y

Any integer higher than zero is considered a positive number. Even natural numbers are included in its concept of numbers.

Therefore, according to the question -

xy = 100

y = 100/x

Thus, as two numbers are given,

f(x, y) = x + y

f(x) = x + 100/x

Now, minimum of f(x) is obtained at the point where f’(x) = 0

Therefore,

f’(x) = 1 - 100/x² = 0

x = ±10.

x = 10

Similarly,

y = 10

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Answer:

Two different possibilities for the angle measures of an isosceles triangle are-:

Step-by-step explanation:

AN ISOSCELES TRIANGLE -: The term isosceles, with the focus on the "sos," is pronounced "eye-sos-ell-ease." It is any triangle of the same length that has two sides. The unequal side of a triangle of isosceles is generally referred to as the triangle's 'base'. An isosceles triangle's base angles are always equal.

Multiply this result by two (it's a 2-story house); then, multiply it by the cost per square foot and add the land cost.

Then, the value of the listing is $262558

The value of the integral ∫√x/(x - 4) dx from 9 to 16 is 3.022

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

∫√x/(x - 4) dx from 9 to 16

The above expression can be integrated using integration by parts method

When integrated, we have

∫√x/(x - 4) dx = 2(√x - ln(√x + 2) + ln(|√x - 2|))

Recall that the x values are from 9 to 16

This means that

∫√x/(x - 4) dx = 2(√16 - ln(√16 + 2) + ln(|√16 - 2|)) - 2(√9 - ln(√9 + 2) + ln(|√9 - 2|))

So, we have

∫√x/(x - 4) dx = 2(4 - ln(4 + 2) + ln(|4 - 2|)) - 2(3 - ln(3 + 2) + ln(|3 - 2|))

Solving further, we get

∫√x/(x - 4) dx = 2(4 - ln(6) + ln(2)) - 2(3 - ln(5) + ln(1))

Evaluate

∫√x/(x - 4) dx = 3.022

Hence, the value of the integral is 3.022

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Answer:

Probability of getting an even number = 0.5

Probability of getting a number less than 3 = 0.5

To calculate sin(135°) and cos(135°) exactly, we can use the fact that the point P corresponding to 135° on the unit circle lies on the line y = -x. As a result, Thus, sin(135°) = √2/2 and cos(135°) = -√2/2. Value of cosine is  -√2/2

Let's consider a right triangle formed by the point P, the x-axis, and the y-axis. The hypotenuse of the triangle is the radius of the unit circle, which is 1. The legs of the triangle are the x and y coordinates of the point P.

Since the point P lies on the line y = -x, we know that the x and y coordinates are equal in magnitude but opposite in sign. Let's assume the x and y coordinates to be -a and a, respectively.

Using the Pythagorean theorem, we have: (-a)^2 + a^2 = 1^2 2a^2 = 1 a^2 = 1/2 a = ±√(1/2) = ±√2/2 Since the y-coordinate is positive, we choose a = √2/2. Therefore, the coordinates of point P are (-√2/2, √2/2).

Now, let's calculate sin(135°) and cos(135°) using the coordinates of point P: sin(135°) = y-coordinate = √2/2 cos(135°) = x-coordinate = -√2/2 Thus, sin(135°) = √2/2 and cos(135°) = -√2/2.

These exact values of sine and cosine at 135° can be used in various calculations and equations without any approximation.

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Answer:

96

Step-by-step explanation:

180 - 31 - 53 = 96

Answer:

96 should be the right answer.

Step-by-step explanation:

straight line means 180 degrees. so:

53 + 31 + x = 180

84 + x = 180

make x the subject:

x = 180 - 84

= 96

Answer:

D. (-1,-2)

Step-by-step explanation:

Every number in the third quadrant of the coordinate plane has negative x and y-coordinates.

Answer:

15

Step-by-step explanation:

18 - 9 ÷ 3 = 18 - 3       {First division should be done}

               = 15

Answer:

15

Step-by-step explanation:

9 ÷ 3 = 3

18 - 3 = 15

so 15 is your answer

The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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Answer:

$0.29 is the price difference

Step-by-step explanation:

Ten years ago, you could buy a loaf of bread for $1.21. Twenty years ago, you could buy a loaf of bread for $0.92.

Answer:

x = 1,  x = 2,  x = 3

Step-by-step explanation:

Hello, please consider the following.

\((x^2-4x)^2+7x^2-28x+12=0 \\\\(x(x-4))^2+7x(x-4)+12=0\\\\\text{Let's note }X = x(x-4)\text{ the equation becomes}\\\\X^2+7X+12=0\\\\\text{The sum of the zeroes is -7=-3+(-4) and the product is 12=(-4)*(-3).}\\\\\text{Wo we can factorise.}\\\\X^2+7X+12=X^2+4X+3X+12=X(X+4)+3(X+4)=(X+4)(X+3)=0\\\\X=-4 \ \ or \ \ X=-3\)

So we need to solve:

\(x(x-4)=-4 \ \ or \ \ x(x-4)=-3\\\\<=> x^2-4x-4=(x-2)^2=0 \ \ or \ \ x^2-4x+3=(x-1)(x-3)=0\)

So, the solutions are x = 2, x = 1, x = 3

Thank you

In Method 1, the expression to answer the questions are: b is a/b times as large as a. b is (a/b) * 100% of a. If x varies from x = a to x = b, it changes by ((b - a)/a) * 100%.

Method 1 considers the relationship between a and b in terms of ratios and percentages. In part (i), b is a/b times as large as a because the ratio of b to a is b/a. In part (ii), b is expressed as a percentage of a by multiplying the ratio b/a by 100%. In part (iii), the percent change in x is calculated by finding the ratio of the change in x (b - a) to the initial value a, and then multiplying it by 100% to express it as a percentage.

Method 2 focuses on the change in x (∆x) from a to b. In part (i), ∆x is calculated as the difference between b and a. In part (ii), the amount x changed by (∆x) is expressed as a ratio to the initial value a, which is (∆x/a). Finally, in part (iii), the percent change in x is obtained by multiplying the ratio (∆x/a) by 100%.

It's worth noting that the answers to part (iii) in both methods are algebraically equivalent, meaning they can be rearranged to match each other.

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Answer:

D. 2 (1/3) hours

Step-by-step explanation:

'Of' means multiplication, so we are going to multiply

3 (1/2) x (2/3) = 2 (1/3)

or

3.5 x 0.66 = 2.333

I hope this helps!

The probability that a bridge hand will have exactly 2 queens is 0.45%.

To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:

P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the total number of trials

k is the number of successes in the trials

p is the probability of success in a single trial

In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).

Plugging these values into the formula, we get:

P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹

= (78) * (1/169) * (4/13)¹¹

= (4/169) * (4/13)¹¹

This simplifies to:

P(exactly 2 queens) = (4/169) * (4/13)¹¹

= (4/169) * (4/169)¹¹

= (4/169)¹²

The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.

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The system of equations has two solutions: (0,2) and (-4/5, -6/5).

The substitution method is a way to solve a system of two linear equations with two variables. The method involves solving one of the equations for one of the variables, and then substituting that expression into the other equation in place of the same variable. This process reduces the system of two equations and two variables to a single equation and a single variable, which can then be solved.

We have the system of equations:

4x² + y² = 4 ........(1)

y = x + 2 ........(2)

We can solve this system of equations by substitution.

Substitute (2) into (1) to eliminate y:

4x² + (x + 2)² = 4

Simplify and solve for x:

4x² + x² + 4x + 4 = 4

5x²+ 4x = 0

x(5x + 4) = 0

x = 0 or x = -4/5

If x = 0, then from equation (2), y = 2. So one solution is (x,y) = (0,2).

If x = -4/5, then from equation (2), y = -6/5. So the other solution is (x,y) = (-4/5, -6/5).

Therefore, the system of equations has two solutions: (0,2) and (-4/5, -6/5).

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The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.

Percentage is used to denote a fraction of a hundred.

Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:

w1 = 60% q = 0.6 q

Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:

w1 = 80% x 70 = 56 lb

The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:

weight of rye grass = w1 + w2

                                = 0.6 q + 56

Total weight of the final mixture = (q + 70) lb

74% = 0.74 = (0.6 q + 56) / (q + 70)

0.6 q + 56 = 0.74 (q + 70)

0.74 q - 0.6 q = 56 - 0.74 x 70

0.14 q = 4.2

q = 4.2/0.14 = 30

Hence, the weight of 60% mixture is 30 lb.

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Answer:

28>x

Step-by-step explanation:

7>x/4

remove the denominator by multiplying both sides by 4

4×7>x/4×4

28>x

Answer:

12:40

Step-by-step explanation:

The formula for standard deviation is: Standard deviation = √(Σ(X - μ)2 / N).

The researcher designs a questionnaire to measure sexism so that she can test the participants' level of sexism before and after the intervention. She tests one version of the questionnaire with 45 statements and a shorter version with 12 statements. In both questionnaires, the participants respond to each statement with a rating on a 5-point Likert scale, with O equaling "strongly disagree" and 4 equaling "strongly agree."The overall score for each participant is the mean of his or her ratings for the different statements on the questionnaire. This method of computing scores uses a 5-point Likert scale with a range from 0 to 4. To visualize the variability, we need to calculate the range, variance, and standard deviation.The formula for the range is: Range = Maximum score – Minimum score. The formula for variance is: Variance = ((Σ(X - μ)2) / N), where Σ is the sum of, X is the data value, μ is the mean, and N is the number of observations.

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The research question involves the usage of a questionnaire with a Likert scale to gather data on sexism levels. The mean of the participants' ratings represents their average sexism level. The mathematical subject applicable here is statistics, where the mean and variability of these scores are studied.

The researcher's work appears to involve both aspects of sociology and psychology, but the maths behind her questionnaire design firmly falls within the field of statistics. The questionnaire is an instrument for data collection. In this case, the researcher is using it to gather numerical data corresponding to participants' level of sexism. The Likert scale is a commonly used tool in survey research that measures the extent of agreement or disagreement with a particular statement. Each statement on the questionnaire is scored from 0 to 4, indicating the degree to which the participant agrees with it.

The mean of these scores provides an average rating of sexism for each respondent, allowing the researcher to easily compare responses before and after the intervention. Variability in these scores could come from a range of factors, such as differing interpretations of the statements or variations in individual attitudes and beliefs about sexism. Statistics is the tool used to analyze these data, as it provides methods to summarize and interpret data, like calculating the mean, observing data variability, etc.

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The car wash made $600 since "there will be 8 teams" meaning 8 * $75.

The length of the car wash will be five and a half hours, with two 15-minute breaks for each team.

Thus, each team works for five hours.

Two automobiles will be washed per hour by each team.

Ten vehicles per squad, then.

[5*2]

Given that "there will be 8 teams," 80 vehicles will be washed (assumed to be in a continuous line of vehicles) [10*8].

The charge must be $600/80=$7.50 each car in order to make $600.

Check (extremely important): "each crew will wash two cars per hour," meaning that each team will earn $15 per hour; "the car wash will run five and a half hours," and "each team will take two 15-minute breaks." As a result, five times $15 equals $75 earned each team.

The car wash made $600 since "there will be 8 teams" meaning 8 * $75.

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The function is called an if/else statement function lets you test if something is true or false and then do different things depending on which result you get.

An if/else statement is a type of control flow statement that allows a program to execute different instructions depending on the result of a logical expression. The statement begins with an if condition, followed by a set of instructions to be performed if the condition is true. If the condition is false, the program executes the instructions after the optional else statement. The syntax for an if/else statement looks like this: if (condition) { // Instructions to execute if condition is true } else { // Instructions to execute if condition is false } By using an if/else statement, a program can make decisions and perform different actions based on the results of a logical expression.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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The probability that Audrey picked the winning horse is 0.2, or 20%

Hi! In this scenario, there are five horses in the race and Audrey picks two of them at random to bet on. To find the probability that Audrey picked the winner, we need to determine the number of favorable outcomes (picking the winning horse) divided by the total number of possible outcomes (all combinations of picking two horses).

There are a total of C(5,2) combinations of picking two horses out of five, where C(n, k) is the number of combinations of choosing k items from a set of n items. C(5,2) = 5! / (2!(5-2)!) = 10 combinations.

Since Audrey picked two horses, one of them must be the winner. So, there are two favorable outcomes (either her first pick or her second pick is the winner).

The probability that Audrey picked the winner is the number of favorable outcomes divided by the total number of possible outcomes:

P(Audrey picked the winner) = Favorable outcomes / Total outcomes = 2/10 = 1/5 = 0.2

So, the probability that Audrey picked the winning horse is 0.2, or 20%.

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