The perimeter of a rectangle is 30 inches. The width of the rectangle is two-thirds of its
length, as shown.



What are the length and the width of the rectangle? Check your solution.

The simplified value is [tex]\frac{7a^{8}+12 }{21a^{5}}[/tex].

What is a mathematical expression?

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is [tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}[/tex].

This can be simplified by cross-multiplying and adding.

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{5}*a^{3}+4*3}{3*7a^{5}} \\=\frac{7a^{8}+12}{21a^{5}}[/tex].

Therefore the simplified value of the given expression is :

[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{8}+12 }{21a^{5}}[/tex]

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(1) The hypothesis is stated that completing a 2-week mindfulness training course

(2) The type of study design this is randomized controlled trial.

(3) The choice of the study type is randomized controlled trial is justified. (4) The list of the two variables with their operational definitions is 2-week mindfulness training course and GRE scores.

(5) Yes, this study demonstrate that the relationship between the two variables is causal

In a study conducted by Mrazek et al. (2013), it was found that students who completed a 2-week mindfulness training course scored higher on the GRE than those who did not participate in the training.

The hypothesis of this study is that completing a 2-week mindfulness training course will result in higher scores on the GRE compared to those who do not complete the training.

This study design is a randomized controlled trial. In this type of study, participants are randomly assigned to either a treatment or control group, and the effects of the treatment are compared to the effects of no treatment (or a placebo). In this case, the treatment group received the 2-week mindfulness training course, while the control group did not.

The choice of study type as a randomized controlled trial is justified because it allows for the comparison of two groups while minimizing the effects of confounding variables. Random assignment to groups helps to ensure that any differences in outcomes between the groups are due to the treatment and not some other factor.

The two variables in this study are the completion of the 2-week mindfulness training course and GRE scores. The operational definition of completion of the training course is that participants in the treatment group attended all sessions of the 2-week course. The operational definition of GRE scores is the score that participants received on the exam.

This study does suggest a causal relationship between completion of the mindfulness training course and higher GRE scores. The randomized controlled trial design helps to reduce the effects of confounding variables, making it more likely that any observed differences in outcomes between the treatment and control groups are due to the treatment.

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Answer:

Step-by-step explanation:

a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be

a) 3<x<∞

Or

b) -∞<x<3

b) the graph is attached below.

c) The equation of the inverse of f(x) can be found by switching x and y:

X = (y-3)²

√x = y - 3

y = √x + 3

However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.

Thus y = +√x + 3

The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.

In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.

To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.

G = Total Distance Traveled / MPG

To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.

T = G x C

Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:

=> T = G x C

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Complete Question:

Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.

Write an algebraic expression for the total cost of the gasoline.

Answer:

Midpoint M (2,5)

S (3,2)

R (x,y) {we will find values for x and y}

(x + 3) / 2 = 2 and (y + 2) /2 = 5

x + 3 = 4 and y + 2 = 10

x = 4-3 and y = 10-2

x = 1 and y = 8

Therefore, coordinates of R (1,8)

The crane's shadow is 45 meters long when the crane is 24 meters tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"

Let the shadow cast by the crane be x.

The triangle formed by the tower and by the crane are similar.

Using the rule of similar triangles we have:

16/24 = 30/x

16x = (30)(24)

x = 45

Hence, the crane's shadow is 45 meters long.

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By simplifying the ratio and adding the fractions, we found that 1/7 of the beads are purple pyramids.

Ratios are used to compare two quantities or values. They are often expressed in the form of a fraction or as a percentage.

The given ratio of purple pyramids to yellow spheres is 1:6. This means that for every 1 purple pyramid, there are 6 yellow spheres. We can express this ratio as a fraction:

Purple pyramids : Yellow spheres = 1 : 6

This can be simplified by dividing both sides by 6:

1/6 Purple pyramids : 1 Yellow sphere = 1/6 : 1

Now, we can add the two fractions to get the total fraction of pyramids in the necklace:

1/6 + 1 = 7/6

This means that out of every 7 beads, 1 is a purple pyramid. We can express this as a fraction:

1/7 of the beads are purple pyramids.

So, the fraction of the beads that are pyramids is 1/7.

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Complete Question:

A necklace is made from purple pyramids and yellow spheres in a 1:6 ratio . What fraction of the beads are pyramids?

The percent table is:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

The initial price of the Loungy chair was $400.

So, the initial price(P₀) = $400

The price of the chair has gone up by 20%

So, increase in price(r) = 20%

The final price will be calculated by using the formula:

                          P = P₀(1 + r/100) (where P is the final price)

                          P = 400(1 + 20/100)

                          P = 400(1 + 0.2)

                          P = 400 × 1.2

                          P = $480

Hence, the final price of the Loungy chair is $480

Percent table:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

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The equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:

Form of point slope, Form of a slope-intercept, Two-point form for intercepting.

The point slope form is given as:

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

The point is (18, 16) and the slope is 11/8.

Substituting the values we have:

y - 16 = 11/8 (x - 18)

8(y - 16) = 11(x - 18)

8y - 128 = 11x - 198

8y = 11x - 70

Hence, the equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.

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It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true

The set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.

Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.

Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.

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The exponential equation after solving gives -26.

Exponential equations are equations where the independent variable, x is in the exponent.

The given equation is,

[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]

We know that 125 = 5³

[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]

The base in the both sides of the equation is 5.

So,

7x + 5 = 3(2x - 7)

7x + 5 = 6x - 21

7x - 6x = -21 - 5

x = -26

Hence the value of x is -26.

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The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.

The sampling distribution of p hat follows a normal distribution thus,

Mu Subscript p hat = p

Here, the value of p = 0.12

Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

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Answer:

A. Mu Subscript p hat = p = 0.12

Step-by-step explanation:

The solutions of the system of equations are (-1, 2) and (3, -5)

Here we have a graph of a system of equations. The solutions are all the points where the graphs of the two equations intersect.

Here we can see two intersection points, thus, we have two solutions. We can see that the first intersection is at (-1, 2) and the second intersection is at (3, -5)

So these two are the solutions of the system of equations.

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Answer:

SOLVE IT!

Step-by-step explanation:

A. 45.50+0.11= answer

B. 65.50+0.17= answer

Minus A plus B to get answer!

Answer:

Step-by-step explanation:

ghjhkvfgfgnfdgn

The missing side length is x = 30

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tan of an angle is equal to the opposite side/adjacent side

from the given figure,

tan 37° = x/40

0.75 = x/40

x = 30

Therefore, The missing side is 30.

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If the difference between the water temperature and the room temperature is halved every 5 minutes, then the water temperature in degrees fahrenheit, after 15 minutes 86 f        

If a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes .

Temperature can be measured in degree celsius, degree fahrenheit and kelvin. so here the temperature measured in degree fahrenheit

Initially the difference between water and room temperature is,

212 - 68 = 144f                

For every 5 minutes the difference of water and room temperature is halved,

After 5 minutes the difference is, 144/2 = 72 f

After 10 minutes the difference is, 72/2 = 36 f

After 15 minutes the difference is, 36/2 = 18 f

So the water temperature in degrees fahrenheit, after 15 minutes will be the sum of room temperature and difference between the temperatures of water and room after 15 minutes and it is given as, 18 f + 68 f = 86 f

Therefore, the water temperature in degrees fahrenheit, after 15 minutes is 86 f.

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Answers: Each twin is 11 years old. Barb is 33 years old

Work Shown:

x = age of each twin

3x = Barb's age

x+x+3x = 5x = total of their ages = 55

5x = 55

x = 55/5

x = 11

Each twin is 11 years old. Barb is 3x = 3*11 = 33 years old.

Check: twin1+twin2+barb = 11+11+33 = 55

The answers are confirmed.

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.

To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).

After reflecting the function over the x-axis, we get the new function g(x) = -f(x).

To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).

Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).

Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.

Hence,

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function

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Answer:

[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]

[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]

Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.

Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.

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In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.

To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:

Future value = Present value * (1 + inflation rate)^n

where:

Present value = $897.20/month

Inflation rate = 4% per year

n = number of years

When we substitute the specified values, we get:

Future value = $897.20 * [tex](1 + 0.04)^9[/tex]

= $897.20 * 1.3981

= $1254.77 (to two decimal places in rounding)

Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

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Answer: The simple interest will be 20%.

Step-by-step explanation:

we know the simple interest of borrowed amount is:

S.I.= (P x R x T)/100 ..... (i)

where P⇒ Principal amount

R⇒ rate of interest

T⇒ time

and

total Pays Back amount = Principal amount + S.I.

Hence S.I. = Pays Back amount - Principal amount

Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means

if Principal amount = P

then Pays Back amount = 2P ⇒ S.I.= P

Rate of Interest = R

and Time = 5 years

P= (P x R x 5)/100

R= 100/5

R = 20%

Therefore, the simple interest is 20% annually.

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Answer: pay attention

Step-by-step explanation:

Answer:

10) m∠2 = 139°

11) m∠3 = 139°

12) m∠4 = 41°

Step-by-step explanation:

Question 10

∠2 and the adjacent angle of 41° are supplementary angles since they lie on opposite sides of the same line; they must add up to 180°

m∠2 + 41° = 180°

m∠2 = 180-41 =139°

Question 11

∠2 and ∠3 are formed by the intersection of two rays. They are vertically opposite angles and therefore they must be equal

m∠3 = m∠2 = 139°

Question 12

Angles  ∠3 and ∠4 are supplementary angles (same reasoning as q 10)

Therefore m∠4 = 180°  - m∠3

= 180° - 139° = 41°

Note that there are many ways to arrive at the answers for m∠4

Step-by-step explanation:

A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.

For example:

[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]

Since root 1, is a perfect square, we will have rational roots.

B.

[tex] {b}^{2} - 4ac < 0[/tex]

[tex]49 - 16c < 0[/tex]

[tex] - 16c < - 49[/tex]

[tex]c > \frac{49}{16} [/tex]

If c is greater than 49/16, we will have no x intercepts.

Answer:

here you go

Step-by-step explanation:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.

Answer:

y=5

divide 40 by 8

times 5 by 8 to check your solution

Answer:

see explanation

Step-by-step explanation:

40 = 8y ( isolate y by dividing both sides by 8 )

5 = y

As a check

substitute y into the right side of the equation and if both sides are equal then it is the solution.

right side = 8y = 8 × 5 = 40 = left side

since both sides are equal then y = 5 is the solution to the equation

Answer: Distributive property and Commutative property (of multiplication)

Step-by-step explanation:

From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.

From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.

HOPE THIS HELPS _- MM