find the real cube root of the perfect cube

The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The distributive property is given as:

a(b + c) = ab + ac

3(20 + 16) = 3(20) + 3(16) = 60 + 48 = 108

Also:

4(13 + 14) = 4(13) + 4(14) = 52 + 56 = 108

The distributive property expressions 3(20 + 16) and 4(13 + 14) are equal to 108

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The width of the patio, given the area of the pool and the patio, can be found to be 19. 59 ft

The area of the pool is said to be equal to the area of the patio which means that to find the width of the patio, you need to find the area of the pool which is :

= 16 ft x 24 ft

= 384 ft ²

The patio is such that the width is the same on every side which makes it a square shaped patio. The width of the patio is therefore:

Width = √ Area of square patio

= √ 384

= 19. 59 ft

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The Pearson correlation coefficient r for the given points is: 0.191.

We can use the formula for Pearson correlation coefficient r:

r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)²][nΣ(y²) - (Σy)²])

where n is the number of data points, Σ represents the sum, x and y are the variables, and xy, x², and y² represent the products and squares of the variables.

We can first calculate the sums and products:

n = 7

Σx = 28

Σy = 36

Σ(x²) = 140

Σ(y²) = 248

Σ(xy) = 152

Using these values, we can plug them into the formula for r:

r = [nΣ(xy) - ΣxΣy] / sqrt([nΣ(x²) - (Σx)² ][nΣ(y²) - (Σy)²])

= [7(152) - (28)(36)] / sqrt([7(140) - (28)^2][7(248) - (36)²])

=  56 / 293

= 0.191

Therefore, the Pearson correlation coefficient r is 0.191.

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Answer:

50, 75, 90, 105, 110

Step-by-step explanation:

All angles of a pentagon add up to 540 degrees

So;

Finding all the inner angles first;

x = 180 - 50 = 130

y = 180 - 75 = 105

So, 130 + 105 + 90 + (2x + 10) + (2x + 5) = 540

or, 4x = 200

Therefore, x = 50

2x + 5 = 105

2x + 10 = 110

Hence, the angles in ascending order are:

50, 75, 90, 105, 110

]Therefore , the solution of the given problem of deviation comes out to be  the confidence interval contains both positive and negative values.

Statistics uses variance as a gauge of difference. The image of that figure is used to compute the average variance between the collection and the mean. It includes those data points itself into the calculations, unlike many other real measures of variability, by comparing also every figure to the mean.

Here,

Since the population standard deviation is unknown and the sample number is less than 30, we can use a t-distribution to build the confidence interval. The confidence interval's calculation is:

=>CI =  x t /2 × (s/n).

Since we need a 99% confidence range, = 0.01 and /2 = 0.005, and (n-1) = (49-1) = 48 is the number of degrees of freedom.

We discover that t/2 = 2.678 using the t-distribution table with 48 degrees of freedom and 0.005 significance level.

When we enter the numbers, we obtain:

=> CI = 3.1 ± 2.678 * (16.5/√49) = 3.1 ± 7.34

The estimated mean net change in LDL cholesterol following treatment, according to the 99% confidence range, is (4.24, 10.44) mg/dL.

We cannot say with 99% certainty that garlic is effective at lowering cholesterol because the confidence interval contains both positive and negative values.

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[tex]\dfrac{x^{2} + 10x + 21}{x + 7} = \dfrac{(x+3)(x+7)}{x + 7} = \bf x + 3[/tex]

___

[tex]x^{2} + 10x + 21 = x^{2} + 3x + 7x + 21 = x(x+3)+7(x+3) = (x+3)(x+7)\\[/tex]

The answer of the given question based on the triangle which is  sequences of transformations of △ABC exhibit the congruence between the two triangles the answer is given below,

Congruent triangles are two or more triangles that have  same shape and size. In other words, they have same angles and  same side lengths.

The congruence between the two triangles can be exhibited by the following two sequences of transformations:

a) a rotation of 180° about the origin and a translation of 1 unit left

c) a rotation of 180° about the origin and a translation of 1 unit right

Option b) and option e) involve a translation and a reflection that do not preserve orientation, so they do not result in a congruent triangle.

Option d) involves two reflections, which do not commute, so the order matters. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit right, followed by a reflection across the line x = -1, which does not result in a congruent triangle.

Option f) is similar to option d) in that it involves two reflections that do not commute. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit left, followed by a reflection across the line x = 1, which also does not result in a congruent triangle.

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We get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.

In trigonometry, the sine function is one of the primary trigonometric functions that relates the ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. The sine function is defined as:

sine (θ) = opposite / hypotenuse

where θ is the measure of the acute angle in radians or degrees.

The sine function is a periodic function, meaning it repeats itself after every 2π radians or 360 degrees. The graph of the sine function is a wave that oscillates between -1 and 1, with the midline at y = 0. The amplitude of the wave is 1, which represents the maximum height of the wave above and below the midline.

The sine function is used in many real-world applications, such as in engineering, physics, and astronomy to model waves, oscillations, and periodic phenomena. It is also used in geometry to calculate the sides and angles of triangles, as well as in calculus to solve differential equations and to describe the motion and behavior of complex systems.

Using a calculator, we get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.

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The value of x/y is 3/25, Hence the correct option is b.

An equatiοn is a mathematical statement that shοws that twο expressiοns are equal. It cοntains an equal sign (=) that separates the twο expressiοns. An equatiοn can have variables, cοnstants, cοefficients, and arithmetic οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, and expοnentiatiοn.

Starting with the given equation:

(5x+y)/y = 8/5

5x+y = 8

y = 5

When y = 5

Then,

5x + (5) = 8

5x + (5) = 8

5x = 3

x = 3/5

Therefore x/y = (3/5)/5 = 3/25

Thus, The value of x/y is 3/25, Hence the correct option is b.

So the correct option is not listed in the answer choices.

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Answer:

Step-by-step explanation:

[tex]i=80[/tex]° (opposite angles in a cyclic quadrilateral are supplementary)

[tex]e=84[/tex]° (An exterior angle of a cyclic quadrilateral is equal to the interior

             angle at the opposite vertex.)      

Answer:

1/4

Explanation:

The denominator is four because it represents the four possibilities about what gender the babies will be. The numerator is 1 because there is one chance out of four that (insert gender ratio) will be picked.

Examples:

There is one chance out of four chances that all four of the children will be girls.

There is one chance out of four chances that at least one child will be a girl.

There is one chance out of four chances that all four will be of the same sex.

There is one chance out of four chances that not all four will be of the same sex.

Based on the above, the Perimeter of the triangle DEF is 43.3 units

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, reduction, multiplication, division, exponents, and so forth.

Given the triangle DEF. Using trigonometric ratio:

sin(38) = EF / 18EF = 11.1

Also: cos(38) = DF / 18DF = 14.2

The perimeter of triangle

DEF = DE + EF + DF

= 18 + 11.1 + 14.2 = 43.3 units

Hence, the Perimeter is 43.3 units

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Answer:

w = 7.27 x 10-5 rad/s

v = 467.99 m/s

Explanation:

First, we will find the angular velocity of the person:

Angular Velocity =w= Angular Distance

Time

Angular distance covered 1 rotation = 2π

radians

Time = (24 h)(3600 s/1h) = 86400 s

Therefore,

2π rad 86400 s 3

w = 7.27 x 10-5 rad/s

Now, for the linear velocity:

v = rw

where,

v = linear velocity = ?

r = radius of earth = (4000 miles)(1609.34 m/1 mile) = 6437360 m

Therefore,

v = (6437360 m) (7.27 x 10-5 rad/s)

v = 467.99 m/s

Answer:

The Social Security tax rate is 6.2% and the Medicare tax rate is 1.45%. To calculate the amount deducted from the nurse's aide's earnings this month for Social Security and Medicare:

Social Security:

Multiply the earnings for the month by the Social Security tax rate:

$1,970 x 0.062 = $121.94

Therefore, $121.94 is deducted from the nurse's aide's earnings this month for Social Security.

Medicare:

Multiply the earnings for the month by the Medicare tax rate:

$1,970 x 0.0145 = $28.54

Therefore, $28.54 is deducted from the nurse's aide's earnings this month for Medicare.

Note that the graphing form and vertex of each quadratic function are given as follows:


a) for f(x)=x² +6x+15, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b) for y= x²-4x+9 the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c) for  f(x)= x² +8x, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d) for . y=x² - 4x+9, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

a. To complete the square for the quadratic function f(x)=x² +6x+15, we add and subtract the square of half of the coefficient of x, which is (6/2)² = 9:

f(x) = x² + 6x + 15

= (x² + 6x + 9) + 6

= (x + 3)² + 6

Therefore, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).

b. To complete the square for the quadratic function y= x^2-4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x^2 - 4x + 9

= (x^2 - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

c. To complete the square for the quadratic function f(x)= x² +8x, we add and subtract the square of half of the coefficient of x, which is (8/2)² = 16:

f(x) = x² + 8x

= (x² + 8x + 16) - 16

= (x + 4)² - 16

Therefore, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).

d. To complete the square for the quadratic function y=x² - 4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:

y = x² - 4x + 9

= (x² - 4x + 4) + 5

= (x - 2)² + 5

Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).

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Therefore, the likelihood of a vehicle accident just on road is 3/25. The ultimate solution is 3/25 because there is no other way to simplify this fraction.

The probability is typically defined as the proportion of favourable findings to all results inside the poll area. The formula for probability of an event is P(E) = (Number of positive occurrences) (Sample space).

If the odds against a car crash on the road are stated as "22:3", it means that for every 22 unfavorable outcomes (no car crash), there are 3 favorable outcomes (car crash).

The total number of outcomes is 22 + 3 = 25.

Therefore, the probability of a car crash on the road is:

3 favorable outcomes / 25 total outcomes = 3/25

So, the probability of a car crash on the road is 3/25. This fraction cannot be reduced further, so the final answer is 3/25.

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The sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.

The length οf the rοad is 5/9 οf a mile.

Tο find the length οf the sectiοn that needs tο be repaved, we can multiply

the length οf the rοad by the fractiοn that represents the fractiοn οf the rοad that needs tο be repaved:

length οf sectiοn tο be repaved = (2/3) * (5/9) mile

Multiplying the numeratοrs and denοminatοrs separately, we get:

length οf sectiοn tο be repaved = (2 * 5) / (3 * 9) mile

Simplifying the fractiοn, we get:

length οf sectiοn tο be repaved = 10/27 mile

Therefοre, the sectiοn οf the rοad that needs tο be repaved is 10/27 οf a mile lοng.

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Answer:

It is not clear what is meant by "a log can Kate use to fill remaining 1/3 meters." However, if we assume that Kate has a gap of 1/3 meters that she needs to fill, she could use a log that is 1/3 meters long to fill the gap. Alternatively, she could use any other object that is 1/3 meters long to fill the gap.

Answer: i think the answer is A

Step-by-step explanation:i think bc i is a quadratic function

Answer: D

Step-by-step explanation:

A and B don't make sense, since the maximum value > 0, and the function is more negative than positive. C and D are our remaining answers. C would be incorrect, since if X reaches \infinity , the function isn't infinite. The only way to make C correct, is a sudden spike in the function to infinity. So, the only correct answer is D.

Hope this helps (please respond if I'm wrong)

Answer:

In question 3 a triangle can be formed however in question 4 it can't be formed

Step-by-step explanation:

there is a theorem that states that two sides of a triangle when added up should be greater than the third one which isn't true in question 4 as

12+9=21 so its equal to the third side but not greater hence a triangle can't be formed

By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.

The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.

We have the inequality:

-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49

We can rewrite this inequality as:

-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1

Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.

As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:

-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1

0 ≤ lim f(x) ≤ 1

Therefοre, by the squeeze theοrem, we have:

lim f(x) = 0 as x apprοaches -5.

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According to the solving Triangle The Value of X in the given figure is 20°

Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.

The three angles are given as ∠1=84°, ∠2=41°, ∠3=2x+15°.

Adding three angles

84° + 41° + 2x + 15° = 180° (sum of interior angle is 180°)

140° + 2x = 180°

2x = 180°-140°

2x = 40°

x = 20°

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Answer:

Step-by-step explanation:

x= 20 (12) =240, Interest%= 6.4, Pv + 0, PMT= 275,temporarily skip FV,P/Y and C/Y= 12,

After 20 years, the value is $133,970.26

The simple interest value of the investment after 20 years is approximately $30,637.45

Future value (FV) is the value of an investment at a future date, based on a series of regular payments (or a lump sum) and assuming a certain interest rate over a period of time. In other words, it's the amount of money an investment will be worth after earning a certain rate of interest over a certain period of time.

Simple interest is a method of calculating interest on a loan or investment, where interest is only charged on the original principal amount. In other words, the interest is not compounded over time.

In the given question:

We can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where: FV = future value

PMT = monthly payment

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values, we have:

FV = 275 x [(1 + 0.064/12)^(12*20) - 1] / (0.064/12)

FV = 275 x (1.00533²⁴⁰ - 1) / 0.00533

FV = 275 x 111.034

FV = 30,637.45

Therefore, the value of the investment after 20 years is approximately $30,637.45.

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In Vincent's garden, about 34/48 of the flowers are neither daisies nor snapdragons.

We need to find the fraction of flowers in Vincent's garden that are neither daisies nor snapdragons. To do this, we need to subtract the fractions of daisies and snapdragons from 1.

The fraction of flowers that are daisies is 1/6, and the fraction that are snapdragons is 1/8. To find the common denominator, we can multiply 6 and 8 to get 48.

So, the fraction of flowers that are neither daisies nor snapdragons is:

1 - 1/6 - 1/8

= 48/48 - 8/48 - 6/48

= (48 - 8 - 6)/48

= 34/48

Therefore, 34/48 of the flowers in Vincent's garden are neither daisies nor snapdragons.

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Answer:

New price of exercise machine = $680.40

Step-by-step explanation:

19% of 840 = 159.6

840 x 19 = 15960

15960 / 100 = 159.60

840 - 159.60 = 680.40

The value of the expression -x³ + 3x² - x + 20 when x = -1 is 23.

Given the expression in the question;

-x³ + 3x² - x + 20

To determine the value of the expression,

First, we substitute -1 for x in the expression:

-( -1 )³ + 3( -1 )² − ( -1 )) + 20

Next, we simplify each term using the order of operations (also known as PEMDAS):

-( -1 )³ = -( -1 ) = 1

(recall that the exponent is evaluated first, then the negative sign is applied)

3( -1 )² = 3(1) = 3

(recall that the exponent is evaluated first)

-( -1 ) = 1

(recall that subtracting a negative is the same as adding a positive)

Now, putting these simplified terms back into the original expression, we get:

1 + 3 + 1 + 20

Finally, we add these terms together to get the final answer:

23

Therefore, the value of the expression is 23.

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The area of the floor covered by the larger speaker is 2(two) times greater than the area of the floor covered by the smaller speaker.

The shape of the big speaker is similar to the shape of the smaller speaker but with different dimensions.

The shape of the larger speaker has the following dimensions:

base = 2b

height = 2h

The shape of the smaller speaker has the following dimensions :

base = b

height = h

Scale factor = 2b/b = 2

Therefore, the larger speaker is 2(two) times greater than the area of the floor covered by the smaller speaker.

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Answer:

James needs 5 gallons of water.

Step-by-step explanation:

1 gallon = 8 pints

40 ÷ 8 = 5

5 gallons

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Full question "Making Connections: Selecting a Career. Apply Your Knowledge" Top Career Choice, Job Description, Personal Attributes, Education, Experience, Certification, Employment, Job Outlook, Earnings, Work Environment, Related Occupations

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