Multiply the numerator and the denominator of the given fraction by the following factor to find an equivalent fraction
Fraction: 8/15
Factor: 4x

The solutions to the equation x⁴ + 2x² + 2 = 0 are

To solve the equation x⁴ + 2x² + 2 = 0, we can use a substitution to simplify the equation. Let's substitute y = x²:

Now, the equation becomes y² + 2y + 2 = 0.

We can solve this quadratic equation for y using the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 2, and c = 2. Plugging these values into the quadratic formula, we get:

y = (-2 ± √(2² - 4 * 1 * 2)) / (2 * 1)

= (-2 ± √(4 - 8)) / 2

= (-2 ± √(-4)) / 2

Since we have a square root of a negative number, the equation has complex solutions. Simplifying further:

y = (-2 ± 2i) / 2

= -1 ± i

Now, we substitute y back into the equation y = x²:

x² = -1 ± i

To solve for x, we take the square root of both sides:

x = ±√(-1 ± i)

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Answer:

a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

70% of adult women visit their doctors for a physical examination at least once in two years.

This means that \(p = 0.7\)

20 adult women

This means that \(n = 20\)

(a) Fewer than 14 of them have had a physical examination in the past two years.

This is:

\(P(X < 14) = 1 - P(X \geq 14)\)

In which

\(P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916\)

\(P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789\)

\(P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304\)

\(P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716\)

\(P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278\)

\(P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068\)

\(P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008\)

So

\(P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079\)

\(P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921\)

0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

(b) At least 17 of them have had a physical examination in the past two years

\(P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)\)

From the values found in item (a).

\(P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107\)

0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Answer:

Step-by-step explanation:

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Answer:

The answer would be 24$

Step-by-step explanation:

If the relationship is proportional then it would be equal so if were adding 12 plus a number (which is 6) adds up which is 12 plus 6 = 18 plus 6 is our answer 24 then plus 6 is 30 as you can see we were adding by six proportionally and so the answer was 24

Answer:

D

Step-by-step explanation:

A has √16 which is 4

B has -(√64) which is -(8)

C has -(√16) which is -(4)

D doesn't have any roots that are integers.

P.S Memorizing the times table would help a lot in algebra*

To prove congruence using SAS Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

All triangles are contained in a single plane if all geometry is on the Euclidean plane, but in higher-dimensional Euclidean spaces, this is no longer the case.

The definition of the terminology used to classify triangles can be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.

Hence, To prove congruence using S Theorem, you must understand that pairs of two angles are congruent as well as the pair of sides that are next to one of the specified angles.

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Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

\(\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces\)

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer:

7

Step-by-step explanation:

=[(5)×2]+[(30)-5]÷5

=(10)+(25)÷5

=35÷5

=7

Answer:

a. K

b. KL and JK

c. ∠JKL, ∠LKJ, and ∠K

d. obtuse

hope this helps!

Answer:

x=7/2+1/2√29 or x=7/2+−1/2 √29

Step-by-step explanation:

hope that helps

Answer:

431.2

Step-by-step explanation:

Area of a regular polygon = # of sides * side length of 1 side * apothem

We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters

So # of sides = 7

apothem = 8

side length = 7.7

so the area would equal 7 * 8 * 7.7 = 431.2

It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth

Answer:

That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2

15.6

Step-by-step explanation:

A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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The measure of angle Z1 is equal to 3 times the value of x, and the measure of Angle Z2 is equal to x plus 72.

The measure of angle Z1 is equal to 3 times some value x, and the measure of angle Z2 is equal to the sum of that value x and 72.

To clarify, it seems that we are dealing with two angles, Z1 and Z2, and their measures are expressed in terms of a variable x.

the given information:

- mZ1 = 3x

- mZ2 = x + 72

These equations indicate that the measure of angle Z1 is equal to 3 times the value of x, and the measure of angle Z2 is equal to x plus 72.

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Answer:

122 degrees

Step-by-step explanation:

The two intersecting lines are parallel for this problem, which means that the angle next to angle3 is the same degree measure as the one that is 58 degrees.

Also, remember that two angles next to each other on a straight line are supplementary, meaning that they add to 180 degrees.

When keeping these two things in mind, you can solve like this:

180 = angle3 + 58

180 - 58 = angle3

angle3 = 122

122 degrees

The value of the expression is between 7/9 and 8, since 7/9 < 56/9 < 8. So the correct option is D.

Algebraic expressions can represent real-world situations, formulas, and equations. They are commonly used in algebra, which is a branch of mathematics that deals with symbols and the rules for manipulating these symbols.

Algebraic expressions are important tools in solving equations and real-world problems that involve variables and unknowns. They are also used in calculus, physics, engineering, and other fields that require mathematical modeling and analysis.

The value of the expression 8×7/9 can be simplified using the order of operations (PEMDAS) as follows:

8×7/9 = (8×7)/9 = 56/9

Therefore, the value of the expression is between 7/9 and 8, since:

7/9 < 56/9 < 8

So the correct statement is: D) between 7/9 and 8.

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2 3/4m for textbooks + 1 1/2m for Notebooks

2 3/4 + 11/2

11/4 + 3/2

11/4 + 6/4

17/4

4 1/4

5 1/2 - 4 1/4

11/2 - 17/4

22/4 - 17/4

5/4

1 1/4

1 1/4 meters of plastic cover will be left

HOPE THIS HELPS. GOODLUCK:)

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14   let's call this equation 1.

x-2y=-12   let's call this equation 2.

-x+Зу-2z =13  let's call this equation 3.

USING EQUATION 1 AND EQUATION 3.

2х+5y-3z-=14   (EQUATION 1)

-x+Зу-2z =13  (EQUATION 3)

LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.

2х+5y-3z-=14   (EQUATION 1) * 2

-x+Зу-2z =13  (EQUATION 3) * 3

4х+10y-6z-=28   let's call this equation 4.

-3x+9у-6z =39  let's call this equation 5.

TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).

4х+10y-6z-=28   (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11  let's call this equation 6.

USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.

x-2y=-12  (EQUATION 2)

x + y = -11  (EQUATION 6)

x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.

We will subtract equation 6 from equation 2. Take note of the signs.

x-2y=-12  (EQUATION 2)

- (x + y = -11)  (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

Divide both sides by -3.

-3y/-3 = -1/-3

y = 1/3

LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.

x-2y=-12  (EQUATION 2)

x-2(1/3)=-12  

x -2/3 = -12

Add 2/3 to both sides.

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.

2х+5y-3z-=14   (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14  

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

Add 21 to both sides.

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

Divide both sides by -3.

-3z/-3 = 35/-3

z = -35/3 or  

Therefore, x = -34/3, y = 1/3, and z = -35/3

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Answer:

y = 19

Step-by-step explanation:

y = 7x - 2

=> y = 7(3) - 2

=> y = 21 - 2

=> y = 19

Therefore, y = 19

Hoped this helped.

Answer:

C. 7°F

Step-by-step explanation:

Answer:

(x+5,y) = Yes

(5x,5y) = No

(.5x,.5y) = No

(x,-y) Yes

(-x,-y) Yes

Step-by-step explanation:

Answer:

the last answer... i hope this helps

Step-by-step explanation:

Answer:

Twice as many students had 3 brothers or sisters as students who had 1 brother or sister

Step-by-step explanation:

Im certain. Pls mark brainliest

Answer:

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b) $34.50

(c) 356

Step-by-step explanation:

Let x = number of minutes.

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b)

Here, x = 350, so x > 200.

f(x) = 0.03(x - 200) + 30

f(350) = 0.03(350 - 200) + 30

f(350) = 0.03(150) + 30

f(350) = 4.5 + 30

f(350) = 34.5

$34.50

(c)

f(x) = 0.03(x - 200) + 30

0.03(x - 200) + 30 = 34.68

0.03(x - 200) = 4.68

x - 200 = 156

x = 356

Answer:

Note that both relations and functions have domains and ranges. The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.