Simplify.
6y + 5y



Please help me!!!!!!!

Katelyn needs to mow 3 lawns to have enough money to buy the skateboard.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' be the no. of lawns she has to mow.

Given, Katelyn wants to buy a $75.00 skateboard and she has $25.00 saved and she mows lawns to make extra money and earns $20.00 for each lawn he mows.

Therefore the inequality that represents this context is,

20x + 25 ≥ 75.

20x ≥ 75 - 20.

20x ≥ 55.

x ≥ 55/20.

x ≥ 2.75, But she has to mow a lawn completely to get paid so she must mow 3 lawns.

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Answer:

3 lawns

Step-by-step explanation:

25 is what she haves now

3x20(how much she gets paid)=60

25+60=85

85-75=10 (she has 10 dollars left after she buys the skateboard

Answer: 15 inches

Step-by-step explanation:

The pythagorean theorem is a^2 + b^2 = c^2

a is one side of the triangle

b is the other side of the triangle

c is the hypotenuse

In our case, a = 36 inches, b is unknown, and c is 39 inches.

If we use the Pythagorean theorem above (a^2 + b^2 = c^2) we get

36^2 + b^2 = 39^2

b^2 = 39^2 - 36^2

b^2 = 225

b = sqrt(225) = 15 inches

Answer:

a) p = 28/100    p  =  0,28      or     p  =  28%

b) SE = 0,0448

c) CI 95 %  =  ( 0.1921 ; 0.368 )

We can support with 95 % of confidence that the proportion of people with a College degree would be found within these limits

Step-by-step explanation:

a) Sample proportion:  Is the number of positive success divide by sample size

That is from 100 ( individuals) ( sample size ) it was found that 28 had College degree  ( positive success)

Then p = 28/100    p  =  0,28      or     p  =  28%

b) The standard error is

SE =  (√p*q)/n

p = 0,28   then  q =  1  -  0,28     q  =  0,72

SE =   √ (0.28)*(0.72)/100

SE =  √0.002016

SE = 0,0448

c) CI =  95 %     then  significance level is  α =  5 %    α = 0.05  

α/2 =  0.025

From z- table we find z(c)  = 1.96

Then  CI 95 %  =  p₀  ±  z(c) * SE

CI 95 %  =  0.28  ±  1.96*0.0448

CI 95 %  =  ( 0.28 ±  0.088 )

CI 95 %  =  ( 0.1921 ; 0.368 )

d) We can support with 95 % of confidence that the proportion of people with college degree would be found within these limits

This doesn’t make since

The integral of the product of x and the derivative of a function f over the interval [0, 2] is equal to 3, given the values of f(0), f(2), and the definite integral of f(x) over the same interval.

We can solve this problem using the Fundamental Theorem of Calculus and the properties of integrals.

According to the Fundamental Theorem of Calculus, if F(x) is an antiderivative of f(x), then ∫[a,b] f(x)ⅆx = F(b) - F(a).

Given that ∫[0,2] f(x)ⅆx = 7, we can infer that F(2) - F(0) = 7.

Now, let's find the expression for ∫[0,2] x⋅f'(x)ⅆx.

By applying integration by parts, we have:

∫[0,2] x⋅f'(x)ⅆx = x⋅f(x)∣[0,2] - ∫[0,2] f(x)ⅆx.

Applying the limits of integration:

= 2⋅f(2) - 0⋅f(0) - ∫[0,2] f(x)ⅆx.

Since f(0) = 1 and f(2) = 5, the expression simplifies to:

= 2⋅5 - 0⋅1 - 7

= 10 - 7

= 3.

Therefore, ∫[0,2] x⋅f'(x)ⅆx is equal to 3.

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Some key definitions:

Reflexive property: angles, line segments, shapes are congruent to themselves. Its easier to think of a shape: if you have a circle, then this circle is equal to itself.

Symmetric property: you can interchange the equal signs of an equation. So think of a=b is the same as b=a, its just the same thing written in a different order.

Transitive property:  If a=b, and b=c, then a=c. Basically think of it as a=b=c, all of these variables are the same as each other.

So for the first clue, you have the reflexive property.

The second clue is the symmetric property.

The third clue is the transitive property.

The dimensions of a norman window of maximum area if the total perimeter is 14 feet are 2 ft and 4 ft respectively.

Given:

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window

we are asked to  find the dimensions of a norman window of maximum area if the total perimeter is 14 feet.

the area of the semicircle is given by:

A = πr²/2

The area of the rectangle is just the product of its length and width.

Letting A be the area of the window and adding the two ares, we have:

A = xy + π(y/2)²/2

= xy + π(y²/4)/2

= xy+πy²/8

we know the circumference = πd

the circumference of a semicircle is half of that. The perimeter of a rectangle is the sum of twice the length and twice the width. However, one of the sides is replaced by the semicircle, so we remove it from the equation.

Hence, we have the following equation for the perimeter.

14 = 2x+y+πy/2

let us isolate x from this equation

14 = 2x+y+πy/2

14-y-π/2 = 2x

x = 7-y/2-πy/4

substituting x to the equation for the area, w have:

A = xy + πy²/8

= (7 - y/2 - πy/4)y + πy²/8

= 7y - y²/2 - πy²/4 + πy²/8

= 7y - y²/2 - 2πy²/8 + πy²/8

= 7y - y²/2 - πy²/8

differentiating A with respect to x.

A = 7y - y²/2 - πy²/8

A' = 7 - y - πy/4

⇒ 7 - y - πy/4 = 0

⇒ 28 - 4y - πy=0

⇒ 28 = 4y+πy

⇒ 28=(4+π)y

⇒ y = 28/4+π ≈ 4 ft

perimeter:

14 = 2x+y+πy/2

14 = 2x + 28/4+π + π(28/4+π)/2

14(8+2π)=2x(8+2π)+28(2)+28π

112+28π = 16x+4πx+56+28π

112-56=16x+4πx

56=(16+4π)x

x=56/16+4π

= 14/4+π

x=14/4+π≈ 2 ft.

Hence the dimension are 2 ft and 4 ft.

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The partial derivatives ∂T/∂U and ∂U/∂T are approximately -7.548 and -6.416 respectively.

To calculate the partial derivatives ∂T/∂U and ∂U/∂T using implicit differentiation of the equation (TU−V)² ln(W−UV) = ln(13), we'll differentiate both sides of the equation with respect to T and U separately.

First, let's find ∂T/∂U:

Differentiating both sides of the equation with respect to U:

(2(TU - V)ln(W - UV)) * (T * dU/dU) + (TU - V)² * (1/(W - UV)) * (-U) = 0

Since dU/dU equals 1, we can simplify:

2(TU - V)ln(W - UV) + (TU - V)² * (-U) / (W - UV) = 0

Now, substituting the values T = 3, U = 4, V = 13, and W = 65 into the equation:

2(3 * 4 - 13)ln(65 - 3 * 4) + (3 * 4 - 13)² * (-4) / (65 - 3 * 4) = 0

Simplifying further:

2(-1)ln(53) + (-5)² * (-4) / 53 = 0

-2ln(53) + 20 / 53 = 0

To express this fraction in symbolic notation, we can write:

∂T/∂U = (20 - 106ln(53)) / 53

Substituting ln(53) = 3.9703 into the equation, we get:

∂T/∂U = (20 - 106 * 3.9703) / 53

= (20 - 420.228) / 53

= -400.228 / 53

≈ -7.548

Now, let's find ∂U/∂T:

Differentiating both sides of the equation with respect to T:

(2(TU - V)ln(W - UV)) * (dT/dT) + (TU - V)² * (1/(W - UV)) * U = 0

Again, since dT/dT equals 1, we can simplify:

2(TU - V)ln(W - UV) + (TU - V)² * U / (W - UV) = 0

Substituting the values T = 3, U = 4, V = 13, and W = 65:

2(3 * 4 - 13)ln(65 - 3 * 4) + (3 * 4 - 13)² * 4 / (65 - 3 * 4) = 0

Simplifying further:

2(-1)ln(53) + (-5)² * 4 / 53 = 0

-2ln(53) + 80 / 53 = 0

To express this fraction in symbolic notation:

∂U/∂T = (80 - 106ln(53)) / 53

Substituting ln(53) = 3.9703 into the equation, we get:

∂U/∂T = (80 - 106 * 3.9703) / 53

= (80 - 420.228) / 53

= -340.228 / 53

≈ -6.416

Therefore, the partial derivatives are:

∂T/∂U = -7.548

∂U/∂T = -6.416

Therefore, the values of ∂T/∂U and ∂U/∂T are approximately -7.548 and -6.416, respectively.

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Calculate The Partial Derivatives ∂T/∂U And ∂U/∂T Using Implicit Differentiation Of (TU−V)² ln(W−UV) = Ln(13) at (T,U,V,W)=(3,4,13,65).

(Use symbolic notation and fractions where needed.) ∂/∂T= ∂T/∂=

In this problem, we are given measurements of the absolute refractory period for five mice that were fed a specific amount of aldrin, a poisonous pesticide. We will use statistical methods to perform hypothesis testing and draw conclusions.

Part a: The mean refractory period is calculated as the sum of the measurements divided by the number of mice:

Mean refractory period = (2.3 + 2.3 + 2.4 + 2.5 + 2.6) / 5 = 2.42 milliseconds

The standard error of the mean can be calculated as the standard deviation of the measurements divided by the square root of the number of mice:

Standard error of the mean = standard deviation / sqrt(n)

Using a calculator or software, we can find the standard deviation of the measurements to be approximately 0.129 milliseconds. Therefore, the standard error of the mean is:

Standard error of the mean = 0.129 / sqrt(5) = 0.058 milliseconds

Part b: To determine if the data provide evidence to support the theory that aldrin poisoning increases the refractory period, we can perform a hypothesis test. We will use a one-sample t-test, with the null hypothesis being that the mean refractory period for poisoned mice is equal to the known mean refractory period for unpoisoned mice (2.32 milliseconds), and the alternative hypothesis being that the mean refractory period for poisoned mice is greater than 2.32 milliseconds.

Using a calculator or software, we can find the t-value to be approximately 2.148, and the p-value to be approximately 0.06. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that aldrin poisoning increases the refractory period.

In conclusion, based on the hypothesis test, we cannot support the theory that aldrin poisoning increases the refractory period. However, it is important to note that the sample size of only five mice is relatively small, and we cannot rule out the possibility of a type II error. Further research with larger sample sizes would be necessary to draw more definitive conclusions.

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The required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,

Maximum and minimum points of the function y = 2 sin 2(x + π) + 3. can be determined by drawing the graph of the function, from the graph maximum of point of the function is (-3π/4, 5) and the minimum point is (-π/4, 1).

Thus, the required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

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Answer:

let me see hold up

Step-by-step explanation:

The zeros of the function y = (x − 4)(x2 − 12x 36) as calculated from the given data is  4 and 6.

As the quadratic term is a perfect square.

On factorizing the equation we get,

y = (x -4)(x -6) (x -6)

y = (x -4)(x -6)²

x = 4 and 6

The values of x that result in these factors being zero are 4 and 6.

Factorisation is the process of expressing an algebraic equation as a product of its components. These variables, numbers, or algebraic expressions can be used as factors.

Factorization  or factoring in mathematics is the process of representing a number or any mathematical object as a product of numerous factors, usually smaller or simpler things of the same kind.

3 and 5 is a factorization of the integer 15, for example, while (x - 2)(x + 2) is a factorization of the polynomial x2 - 4.

A meaningful factorization for a rational number or rational function, on the other hand, can be derived by putting it in lowest terms and factoring its numerator and denominator separately.

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Answer:  d) 6   e) 10     g) 900

Step-by-step explanation:

d) \(\sqrt{9610} = 98.0306\)

98² = 9604

9610 - 9604 = 6

e) \(\sqrt{2906}=53.9073\)

54² = 2916

2916 - 2906 = 10

g)              10            12          15

                 ∧             ∧            ∧

               2·5         2·2·3       3·5

The Perfect square is: 2² · 5² · 3² = 30²

30² = 900

Given statement solution is:-Aiza and Glaiza's scores are in the 60th percentile. This means that 60% of the scores fall below their score, and 40% of the scores fall above their score.

1. There are 15 students with scores less than 12.

2. There are 10 students with scores greater than 12.

To determine the number of students with scores less than 12 and the number of students with scores greater than 12, we need to analyze the information given.

Let's break it down step by step:

We know that Aiza and Glaiza both scored 12. This means that their scores are not unique.

The scores of all 25 students are unique except for Aiza and Glaiza. This implies that the remaining 23 students must have distinct scores.

Aiza and Glaiza's scores are in the 60th percentile. This means that 60% of the scores fall below their score, and 40% of the scores fall above their score.

Since Aiza and Glaiza's scores are in the 60th percentile, we know that 60% of the scores fall below 12. Out of the 25 students, 60% corresponds to (60/100) * 25 = 15 students.

Therefore, there are 15 students with scores less than 12.

As mentioned earlier, Aiza and Glaiza's scores are in the 60th percentile, which means 40% of the scores fall above 12. Out of the 25 students, 40% corresponds to (40/100) * 25 = 10 students.

Therefore, there are 10 students with scores greater than 12.

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Answer:

2y+10/y

Step-by-step explanation:

Plato

Answer:

2(y+5)/y

Step-by-step explanation:

edmentum

Answer:

$ - 2

Step-by-step explanation:

$19 - $13 + 2 - $14  + 4 = - $2

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find which expression represents the description "twice the quantity m plus n".

\(\triangle~\fbox{\bf{KEY:}}\)

First, add m and n:

\(\star~\large\pmb{m+n}\)

Now, multiply two times this sum:

\(\star~\large\pmb{2(m+n)}\)

See, the parentheses around the sum show that we multiply two times both m and n.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

2(m + n)

Step-by-step explanation:

The words describe a quantity. "Twice" means two-times the previous amount. m and n are the unknown numbers that are being added, so you must put them in parentheses to indicate that they should be added first.

The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

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Using proportions, it is found that the final payment if the loan is paid off with the fifth payment is of $488.152.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, balance of $435.85 with interest rate of 12%, hence the final payment is given by:

P = 435.85 x 1.12 = $488.152.

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Therefore, a 2 by 4 by 1.5-inch juice box holds approximately 34 square inches of cardboard.

An inch is a unit of measurement commonly used to express length or distance in the United States, Canada, and the United Kingdom. It is defined as exactly 2.54 centimeters, or 1/12th of a foot. The symbol for inch is "in" or double prime ("). The inch is often used to measure small distance.

To determine the amount of cardboard used by a juice box, we need to calculate the surface area of the box.

A 2 x 4 x 1.5 inch juice box has six sides, each with a different surface area. The formula for calculating the surface area of a rectangular box is:

\(Surface Area = 2lw + 2lh + 2wh\)

where l, w, and h are the length, width, and height of the box.

For the juice box in question, we have:

\(l = 4 inches\\w = 2 inches\)

\(h = 1.5 inches\)

So, the surface area of the juice box is:

\(Surface Area = 2(4 x 2) + 2(4 x 1.5) + 2(2 x 1.5)\)

\(= 16 + 12 + 6\)

\(= 34 square inches\)

Therefore, a 2 by 4 by 1.5-inch juice box holds approximately 34 square inches of cardboard.

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Answer:

Hope this helps you.

Step-by-step explanation:

I plugged in x for t, but it is the same graph.

Answer:

x = 6 (C)

Step-by-step explanation:

x is 6,

it came from formula :

\( \large \boxed{ \sf y - y_1 = m(x - x_1)}\)

we just need to fill the x1 with point (6, 1),

so the answer is :

\( \sf y - 1 = - \frac{1}{3} (x -6)\)

━━━━━━━━━━━━━━━━━

Hope it helps!

Answer:

length=50m

width=25m

Step-by-step explanation:

perimeter is the distance all round,hence

2(l+w)=2(2x+x)=

4x+2x=6x=150

6x=150x

x=25

l=50m

w=25m

okay so since the area is 22cm^2 , you will need to simplify it.

Which you will get 22*22 and the total would be 484. Which u will divide by 4 ( Square) to get each of the side your looking for.

So your answer is... 121

The desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

What is the sample proportion of respondents who prefer to live somewhere other than where they currently live?

The sample proportion of respondents who prefer to live somewhere else can be calculated by dividing the number of respondents who indicated a preference for a different location by the total number of respondents.

To make confidence intervals and perform hypothesis testing in this scenario, the researcher can use formulas based on proportions. Since the question asks respondents about their preference (either yes or no), it involves a binomial distribution.

1.Confidence Interval Formula (Proportions): To construct a confidence interval for the proportion of people who prefer to live somewhere other than their current location, the researcher can use the following formula:

Confidence Interval=p​±Z×\(\sqrt{\frac{p(1-p)}{n} }\)

where:

2.Hypothesis Testing Formula (Proportions): To perform a hypothesis test to determine if the proportion of people who prefer to live elsewhere is significantly different from a particular value (null hypothesis), the researcher can use the following formula:

\(Z=\frac{p-p_{0} }{\sqrt{\frac{p_{0}(p_{0} -1)}{n} } }\)

​​where:

By comparing the calculated Z-value with the critical value(s) for the desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

Answer:

The magnitude of the resultant vector is 11.53 km/h

Step-by-step explanation:

Please find the attached image for explanation;

Answer:

the square root of 121 is 11

A quadratic function in standard form that represents each area as a function of the width is; A = -x² + 20

We are told that she is enclosing a new garden and has 40 ft of fencing.

Now, let the two sides be labelled x and y.

We know that area of a rectangle is;

A = length * width

Thus;

A = xy

Now, since she has 40 ft of fencing, then it means that;

y = 0.5(40) - x

y = 20 - x

Thus, the area expressed in quadratic function formula is;

A = x(20 - x)

A = 20x - x²

A = -x² + 20

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Complete question is;

Write a quadratic function in standard form that represents each area as a function of the width.

Remember to defi ne your variables