Find x: 32 ^ x * 16 ^ (- 2x) = 4 * 2 ^ (- 5x)

The values that are a solution to the inequality are x<-1/4.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The inequality are

7x +6/2 < 3x +2

According to given question we have

The expression is :

7x +6/2 < 3x +2

compare like terms we get

7x +6/2 < 3x +2

7x-3x<2-3

4x<-1

Divide both sides by 4 we get,

x<-1/4

Hence, the values that are a solution to the inequality are x<-1/4.

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Answer:

The bench costs $388.

Step-by-step explanation:

Let the cost of the bench be x

The cost of the garden table = x + 87

x + (x + 87) = 863

2x + 87 = 863

2x = 776

x = 388

The bench costs $388 and the garden table costs 388 + 87 = $475

475 + 388 = 863

Answer

I disagree

she said that the square root of 100 and of 121 is 4 and 5

the square root of 100 is 10 and the square root of 121 is 11.

Answer:

628/1300

Step-by-step explanation:

The required solution of the given expression is F(3)=16.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The given in the function

F(x)=x²+7

According to given question we have

The function

F(x)=x²+7

At x=3 we get

F(3)=3²+7

F(3)=9+7

F(3)=16

Therefore, the required solution of the given expression is F(3)=16.

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Based on the fact that Sean made a dozen brownies with 3/4 cups of sugar, the amount of sugar in each brownie is 1 / 16 cups of sugar

A dozen brownies were made with 3/4 cups of sugar. This means that 12 brownies were made by using 3/4 cups of sugar.

To find the amount of sugar used per brownie, the formula is:
= Number of cups of sugar / Number of brownies made

Solving for the cups of sugar per brownie gives:
= 3/4 ÷ 12

= 0.75 / 12

= 0.0625

= 1 / 16 cups of sugar

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The probability that no one in a family of five will be hospitalized in a year 0.2373 .

Let P(E) denote the probability of being hospitalized during a year and P'(E) the probability of not being hospitalized during a year

Then , using equation (1) , we get

          [tex]0.25+P'(E)=1\\P'(E)=1-0.25\\P'(E)=0.75[/tex]

The probability that no one in a family of five will be hospitalized in a year is equal to [tex](P'(E))^n[/tex] where n is the number of member .

   [tex](P'(E))^n=(0.75)^5\\(P'(E))^n=0.2373[/tex]

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Answer:(x−3)2+ (y−5)2=5 8

Step-by-step explanation:

The volume of the fiberglass shell is nearly = 508.2 in³

Volume is just a three-dimensional quantity used to determine a solid shape's capacity. It indicates that the volume of a closed figure decides how much of three-dimensional space it can occupy.

The capa.city of an object is measured by its volume. A cup's volume is 100 ml if it can carry 100 ml of water higher than or equal to the brim. A 3-dimensional object's volume can alternatively be described as the amount much space it takes up.

Cube side are 11 inches.

cube is covered with a coat of fiber glass 0.1 inch

need to find the volume of fiberglass.

area of cube = 6(11)²

                     = 6(121)

                     = 726 inch².

thickness of fiberglass = 0.7 inch.

dv ≅ ads

= 726(0.7)

= 508.2 in³

The volume of the fiberglass shell is nearly = 508.2 in³.

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The distance that the plane flies between the two cities is 2475 miles.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

Time taken = distance covered / velocity

In the first case ;

Time taken = 5 hour.

Velocity = V(Let's say)

Distance covered = x

So,

5 = x/V

x = 5V

Now,

In the second case ;

Velocity = V - 99 (99 slower to first)

Time taken =  6 hours and 15 minutes = 6.25 hour

Distance covered = x

So,

6.25 = x/(V - 99)

x = 6.25V - 618.75

By equating

6.25V - 618.75 = 5V

1.25V = 618.75

V = 495 miles / hour

Now,

x = 5(495) = 2475 miles.

Hence "The distance that the plane flies between the two cities is 2475 miles".

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The answer is - 17

here, we have to apply BODMAS rule

given ,- 22 + (10) = 15

            = - 22 - 10 + 15

           = -32 + 15

           = - 17

BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.

B=Brackets

O=Off

D=Division

M=Multiplication

A=Addition

S=Subtraction

The four basic Mathematical rules are addition, subtraction, multiplication, and division.

Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.

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Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

A function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable = domain

The dependent variable = Range

We are given a graph where the x-axis contains the radius value and the y-axis contains the circumference value.

We can write the function as:

f(x) where x can be 4, 8, 12, 16, 20, 24, 28, 32, 36

f(0) = 0

f(4) = 22.5

f(8) = 52.5

f(12) = 75

f(16) = 105

f(20) = 127.5

f(24) = 150

The domain is between 0 to 150 and the range is between 0 and 28.

Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

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Part A: Yes, there is a correlation between the number of hours students spent studying and the score on the music test because  As we increase the hours of studying by 0.5 hours, then the music score increases by 2.

Part B: A function that best fits the data is; y = 60 + 4x

Part C: The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.

We have given the table below showing the data:

Number of hours spent studying (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score on music test (y) 60 62 64 66 68 70 72 74 76

A) As we increase the hours of studying by 0.5 hours, then the music score increases by 2.

B) The function which best fits the data for the correlation from the above is; y = 60 + 4x

C) The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.

The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.

The y-intercept gives the music score when the number of hours spent on studying is zero.

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Answer:

unlimited is the weight

Step-by-step explanation:

Weight : 58283624946946784640469267619046404.4691649469464846404694956596894

The maximum value of f(4) will be 23.

What is Mean value theorem?

Mean value theorem states that if a function f is continuous on the closed interval [a ,b] and differentiable on the open interval (a ,b), then there exists a point c in the interval (a, b) such that f'(c) is equal to the function's average rate of change over [a, b].

That is;   [tex]f'(c) = \frac{f((b) - f(a)}{b - a}[/tex]

Given that;

⇒ f(0) = -1 and f′(x) ≤ 6 for all values of x.

Now, According to Mean value theorem;

[tex]f'(x) = \frac{f(4) - f(0)}{4 - 0}[/tex]

Since, f′(x) ≤ 6

Hence,

[tex]f'(x) \leq 6\\\\ \frac{f(4) - f(0)}{4 - 0}\leq 6\\\\ f(4) -(-1) \leq 24\\\\f(4) \leq 23[/tex]

So, The maximum value of f(4) will be 23.

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Type of rotation of Anticlockwise and clockwise .

A point in coordinate geometry can be rotated through 180 degrees around the origin by drawing an arc with a radius equal to the distance between the provided point's coordinates and the origin, and then extending an angle of 180 degrees at the origin.

The point must be rotated around the origin with regard to its location in the cartesian plane. It is nicely explained in the next part of the 180-degree rotation formula.

The formula for 180-degree rotation of a given value is as follows: if R(x, y) is a point that has to be rotated around the origin, then coordinates of R(x, y) .

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Answer:

C: 88

Step-by-step explanation:

There is a triangle that contains y, 53°, and 39°. So by this, you know that y + 53 + 39 = 180 (sum of triangle angles).

y = 180 - 53 - 39

y = 88°

Hope this helps! :)

Answer:

57 Months

Step-by-step explanation:

Should take 57 months. Simple division, just divide 12,825 and 225 and you end up with 57 months.  4 years and 9 months simplified. Hope this helps.

Answer:

3/2

Step-by-step explanation:

29-8=21

9-(-5)=14

21/14 =3/2

Answer:

x = −10

Step-by-step explanation:

8x−2(x+1)=7x+8

Step 1: Simplify both sides of the equation.

8x−2(x+1)=7x+8

8x+(−2)(x)+(−2)(1)=7x+8(Distribute)

8x+−2x+−2=7x+8

(8x+−2x)+(−2)=7x+8(Combine Like Terms)

6x+−2=7x+8

6x−2=7x+8

Step 2: Subtract 7x from both sides.

6x−2−7x=7x+8−7x

−x−2=8

Step 3: Add 2 to both sides.

−x−2+2=8+2

−x=10

Step 4: Divide both sides by -1.

−x/−1 = 10/−1

x=−10

The equation of a line that passes through the given point (4, 3) and is perpendicular to y = 2x + 2 is given by: y = -x/2 + 5.

The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

y = mx + c ≡  y = 2x + 2

m₂ = 2

For perpendicularity, we have:

m₁ × m₂ = -1

m₁ × 2 = -1

m₁ = -1/2.

Next, we would use the point-slope form to write the equation of this line at point (4, 3):

y - y₁ = m(x - x₁)

y - 3 = -1/2(x - 4)

y - 3 = -x/2 + 2

y = -x/2 + 2 + 3

y = -x/2 + 5.

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Complete Question:

Write an equation for a line perpendicular to y = 2x + 2 and passing through the point (4, 3).

The length of the first, second, third pieces of sidings are 8 ft, 24ft and 32 ft respectively.

The 64 ft piece of siding is cut into three pieces so that the second piece is  three times as long as the first piece and the third piece is four times as long as the first piece.

The length of the three pieces of siding can be found as follows:

x = length of the first piece

Therefore,

Second piece = 3x

Third piece = 4x

Hence,

x + 3x + 4x = 64

8x = 64

divide both sides by 8

x = 64 / 8

x = 8

Therefore, the length of all the pieces are as follows;

First piece = 8 ft

Second piece = 3(8) = 24 ft

Third piece = 4(8) = 32 ft

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Answer:

11/10 and 3/4

Step-by-step explanation:

To find the better cost, you need to determine which options has a lower cost per bagel.

The value of the mean is a 33.75 in the normal distribution.

According to the statement

We have to find that the students' favorite color was red.

So, For this purpose, we know that the

A mean is simply defined as the average of the given set of numbers.

From the given information:

On a test that has a normal distribution, a score of 45 falls two standard deviations above the mean, and a score of 30 falls three standard deviations below the mean.

Then

The interval for score = 45- 30= 15

If we divide it by the 4 standard deviations; the interval result into

= 15/4

= 3.75

Then, the standard deviation is 3.75, and

The mean = 30+ 3.75

The mean = 33.75

So, The value of the mean is a 33.75 in the normal distribution.

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From the set given, the variables we look is as follows

Cricket only

let the number of children for cricket be c = 15

cricket only = 15 - (8 - 5) - (6 - 5) - 5

= 15 - 3 - 1 - 5

= 6

neither cricket tennis nor swimming

tennis only = 18 - (8 - 5) - (9 - 5) - 5

= 18 - 3 - 4 - 5

= 6

swimming only = 17 - (6 - 5) - (9 - 5) - 5

= 17 - 1 - 4 - 5

= 7

tennis and swimming only = 9 - 5 = 4

tennis and cricket only = 8 - 5 = 3

swimming and cricket only = 6 - 5 = 1

tennis cricket and swimming = 5

cricket only = 6

neither cricket tennis nor swimming = all the children - sum of the variables found

= 32 - (6 + 6 + 7 + 4 + 3 + 1 + 5)

= 32 - (32)

= 0

tennis and cricket but not swimming

= tennis and cricket only + cricket only + tennis only

= 3 + 6 + 6

= 15

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Step-by-step explanation:

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner. The missing numbers in the given number sentence are 4000 and 20.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.

The given number is

24321

This we can express in standard form as,

20000+4000+300+20+1.

The given expression is 20 000 +x+300+y+1.

If we compare the above expression with standard form of 24321 we get the values of x and y. so x is 4000 and y is 20.

The missing numbers in number sentence are 4000 and 20.

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In a picture we have a triangle with 3 sides. Sides are a,8 and 2. The side a=2[tex]\sqrt{15}[/tex].

Given that,

In a picture we have a triangle with 3 sides.

sides are a,8 and 2.

by using Pythagorean theorem

The Pythagorean Theorem, generally referred to as Pythagoras' Theorem, is a basic relationship between a right triangle's three sides. The Pythagorean theorem states that, given a right triangle, which is a triangle in which one of the angles is 90 degrees, the hypotenuse, the right triangle's longest side, forms a square whose area is equal to the sum of the areas of its other two sides.

In other words, given that the triangle's longest side, c, is also its hypotenuse and that sides a and b are its other two sides:

a² + b² = c²

a²+(2)²=8²

a²+4=64

a²=64-4

a²=60

Take root on both sides

[tex]\sqrt{a^{2} } =\sqrt{60}[/tex]

a=2[tex]\sqrt{15}[/tex]

Therefore, the side a=2[tex]\sqrt{15}[/tex].

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