in the first week of July, a record 1,020 people went to the local swimming pool. In the second week, 100 fewer
people went to the pool than in the first week. In the third week, 135 more people went to the pool than in the second week.
In the fourth week, 137 fewer people went to the pool than in the third week. What is the percent decrease in the number of
people who went to the pool over these four weeks?

Answer:

12 weeks

Step-by-step explanation:

if 280=420

then 8=×

cross multiply

280×=420×8

280×=3360

divide both sides with the co efficient of x

280×/280=3360/280

leaving the answer to be 12

35 encyclopedias can be fit on the bookrack.

What is an encyclopedia?

An encyclopedia (American English) or encyclopaedia (British English) is a reference source or compendium that provides summaries of general or specific information to a certain topic or discipline. Encyclopedias are organized into articles or entries that are either alphabetically sorted by article name or by subject categories, or are hyperlinked and searchable by random access. The entries in encyclopedias are longer and more thorough than those in most dictionaries. In general, encyclopedia articles focus on factual information about the subject specified in the title, as opposed to dictionary entries, which focus on linguistic information about words, such as their derivation, meaning, pronunciation, use, and grammatical forms.

Width of bookrack = 61 1/4 inches

Width of an encyclopedia = 1 3/4 inches

no. of encyclopedias to be fit = (61 1/4)/(1 3/4)

                                                  = (245/4)/(7/4)

                                                  = 245/7

                                                  = 35

Hence, 35 encyclopedias can be fit on the bookrack.

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The mark up is $30.

As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.

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Given the volume of the box is 100 cm^3

And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.

so, the height of the box = 4 cm

so, the volume = height * area of the base

100 = 4 * area of the base

Area of the base = 100/4 = 25 cm^2

so, the side length of the base of the box =

so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm

Answer:

Explanation: The product has two square-roots being multipled together, the inside of each of the root must be greater than or equal to zero, this in Mathematics can be written as follows:

Therefore, applying the condition leads us to the following conclusion:

Therefore it follows that x must be:

Answer:

Step-by-step explanation:

[tex]\displaystyle\\(64x^\frac{2}{3})^{-\frac{1}{3}} =\\\\(4^3x^\frac{2}{3})^{-\frac{1}{3}}=\\\\ 4^{3*(-\frac{1}{3})}x^ {\frac{2}{3}*(-\frac{1}{3} )}=\\\\ 4^{-1}x^{-\frac{2}{9} }=\\\\\frac{1}{4} x^{-\frac{2}{9} }=\\\\\frac{1}{4} (\frac{1}{x^\frac{2}{9}} } )=\\\\\frac{1}{4\sqrt[9]{x^2} }[/tex]

The friend's explanation is not correct.

They are mixing up x and y intercepts.

To find the y intercept, plug in x = 0 to find y.

To find the x intercept, plug in y = 0 and solve for x.

Answer:

Step-by-step explanation:

1slice=280 and 6 slices so 280x6 so 0x6=0 then 80x6=6+6x4=48x10=480
then 200x6= 6x2=12x100=1200

add all 0+480+1200=1680

sry i'm not used to showing work i usually do it all in my head

Answer:[tex]\sqrt{36} > 5 \\[/tex]

Step-by-step explanation:

because [tex]\sqrt{36} =6[/tex]

Therefore  6 > 5

Answer:

3

Step-by-step explanation:

We need to isolate x in order to solve it:

First, subtract 4 from both sides

15 - 3x = 2x

Add 3x to both sides

15 = 5x

Divide each side by 5 to get x

x = 3

The segment AB = AC is proved for the given line AC.

For the given question;

AC = AB + AB

This can be written as;

AC = 2AB

or AB = (1/2)AC

It means, B is the mid point of AC

So, B will also divide the complete line segment AC into two equal halves.

AB = AC

Thus, the segment AB = AC is proved for the given line AC.

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Answer:

A

Step-by-step explanation:

x² - 2x + y² + 6y - 4 = 0 ( add 4 to both sides )

x² - 2x + y² + 6y = 4

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

= x² + 2(- 1)x + 1 + y² + 2(3)y + 9 = 4 + 1 + 9

(x - 1)² + (y + 3)² = 14 ← in standard form

Answer:

Step-by-step explanation:

See screenshot
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lol I'm improve my rank so brainliest would help a lot :]

The following must be true:

SU + UT = RT

By dividing the base's length by its height, one may calculate any quadrilateral's surface area. We can conclude that all of the sides are the same length because the shape is square. Using the square root of the area to determine the length of one side, we can then work backwards from this information. A square has four sides, thus to determine the length of one side, divide the perimeter by 4. Assumed Area: Since s2 is the formula for a square's area and that number corresponds to one of its sides, you must get the square root of the area. A side is the line segment that connects two vertices of a shape or two-dimensional figure according to the definition of geometry.

Length of SU

= RS - RT - TU

= 24 - 12 - 6

= 24 - 1

= 6

Thus, the length of the US is 6 units.

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Answer:

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

the perpendicular bisector of AB passes through the midpoint of AB at right angles.

find the midpoint using the midpoint formula

with A (- 2, 0 ) and B (0, 6 )

midpoint = ( [tex]\frac{-2+0}{2}[/tex] , [tex]\frac{0+6}{2}[/tex] ) = ( [tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )

find the gradient m of AB using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (0, 6 )

m = [tex]\frac{6-0}{0-(-2)}[/tex] = [tex]\frac{6}{0+2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

given a line with gradient m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex]

the equation of a line in gradient- slope form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = - [tex]\frac{1}{3}[/tex] , then

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 1, 3 ) into the partial equation

3 = [tex]\frac{1}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{1}{3}[/tex] = [tex]\frac{8}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of perpendicular bisector

Answer:

6y + 3x + 9

Step-by-step explanation:

→ Combine all equivalent terms

4y + 2y + 3x + 6 + 3

→ Simplify

6y + 3x + 9

Answer:

3x + 6y + 9

Step-by-step explanation:

Combine like terms.

4y + 2y = 6y

6 + 3 = 9

3x does not have a like term.

6y + 3x + 9

Order the variables in alphabetical order. (In this case, x goes before y.)

Simplify.

3x + 6y + 9

Answer:11

Step-by-step explanation:

Using angle sum property we found that ∠ x = 113°, ∠y = 67°  and ∠z = 49°

The angle sum property of triangle states that the sum of all the interior angles of a triangle is 180°.

If ΔABC is a triangle then,

m ∠A + m ∠B + m ∠C = 180°

Given from the figure in the question that 28°, 39° and x° are interior angles of a triangle, then using angle sum property:

28° + 39° + x° = 180°

⇒ 67° + x° = 180°

⇒ x° = 180° - 67° = 113°

∠x and ∠y are on the same line same point therefore their sum will be 180°

⇒ x° + y° = 180°

⇒ 113° + y° = 180°

⇒ y° = 180° - 113° = 67°

Also an exterior angle of a triangle is equal to sum of interior opposite angles.

∴ y ° = 28° + 39° = 67°

Now, 64° , y° and z° are interior angles of same triangle from the figure in the question.

∴ Using angle sum property,

64° + y° + z° = 180°

⇒ y ° + z° = 180° - 64° = 116°

⇒ y° + z° = 116°

⇒ z° = 116° - y° = 116° - 67°  = 49°

Therefore ∠x, ∠y , ∠z are 113° , 67° and 49° respectively

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Answer:

61 degrees

Step-by-step explanation:

Bro its that easy

Answer:  You are correct

The decreasing interval is (-3, infinity)

This is the same as writing [tex](-3, \infty)[/tex]

===============================================

Explanation:

If a < b and f(a) > f(b), then the function is decreasing.

Visually this means that if the graph is going downhill when moving to the right, the function is decreasing.

The graph shown goes downhill throughout its entire domain of (-3, infinity)

Answer:

y=3 / y=6

x=0 / x=3

Step-by-step explanation:

Follow the steps given in the picture attached above.

Answer: 2.5 inches

Step-by-step explanation: 3*5/6= 2.5

The sets of number to which - 2/5 belongs is a rational number.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.

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He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit and the maximum profit is [tex]\$18,200[/tex].

A Virginia Beach farmer has [tex]480[/tex] acres of land on which to grow either corn or soybeans.

He has labor available during the crucial summer [tex]=800[/tex] hours

The farmer can expect a profit of [tex]\$40[/tex] per acre on corn.

The farmer can expect a profit of [tex]\$30[/tex] per acre on soybeans.

The corn requires hours to raise [tex]=2[/tex] hours per acre.

The soybeans requires hours to raise [tex]=1[/tex] hours per acre.

We have to find how many acres of each should he plant to maximize profit and his maximum profit.

To solve the question we let he plant [tex]x[/tex] acres of corn and [tex]y[/tex] acres of soybeans.

Total land is available for grow either corn or soybeans is [tex]480[/tex] acre.

So the equation should be

[tex]x+y\leq 480\dots\dots Equation (1)[/tex]

He requires [tex]2[/tex] hours to raise corn per acre and [tex]1[/tex] hours to raise soybeans per acre and he has 800 hours of labor available during the crucial summer season.

So the equation should be

[tex]2x+y\leq 800\dots\dots Equation (2)[/tex]

He expect a profit of [tex]\$40[/tex] per acre on corn and [tex]\$30[/tex] per acre on soybeans.

So profit equation should be

[tex]P=40x+30y[/tex]

Now the subject of constraints

[tex]x+y\leq 480[/tex]

[tex]2x+y\leq 800[/tex]

[tex]x,y\geq 0[/tex]

Now solving the equation [tex]1[/tex] and [tex]2[/tex] to find the value of [tex]x[/tex] and [tex]y[/tex].

Multiplying the equation [tex]1[/tex] by [tex]2[/tex].

After multiplying with [tex]2[/tex] the equation [tex]1[/tex]

[tex]2x+2y\leq 960\dots\dotsEquation (3)[/tex]

Now subtracting Equation [tex](3)[/tex] and Equation [tex](2)[/tex].

[tex]2x+2y-(2x+y)\leq 960-800[/tex]

[tex]2x+2y-2x-y\leq 960-800[/tex]

[tex]y\leq 160[/tex]

Now putting the value of [tex]y[/tex] in Equation [tex](1)[/tex]

[tex]x+160\leq 480[/tex]

Subtract [tex]160[/tex] on both side

[tex]x+160-160\leq 480-160[/tex]

[tex]x\leq 320[/tex]

He raise corn in [tex]320[/tex] acres and soybeans in [tex]160[/tex] acres to maximize profit.

The maximum profit

[tex]P=40x+30y\\P=40\times320+30\times180\\P=12,800+5400\\P=18,200[/tex]

The maximum profit is [tex]\$18,200[/tex].

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The probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.

For the given question;

The data for the ball bearing is given as-

Z-score = (x - μ)/σ

Put the values;

z = (152 - 139)/36

z = 0.36

P(x > 125) = P(z > 0.36), see p values from z table for 0.36.

P(x > 125) = 0.6405

P(x > 125) = 64.05%

Thus, the probability that the diameter of a selected bearing is greater than 152 millimeters is 64.05%.

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In linear equation, You are the only person in the garden at the time the 34 people.

What in mathematics is a linear equation?

You are the only person in the garden at the time the 34 people are on their homicidal spree.

Alternatively, if the backyard and garden are in the same place, then there are no longer any individuals in the garden because you would officially count as one of the 34 people who are all killed.

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I think your answer is 10 minutes and 30 seconds. . .

What I did was I took 6 and 7 and multiplied them together, then i divided 42 by 4, and got 10.5. which would give you 10 minutes and 30 seconds.

6*7=42/4=10.5 (aka 10min 30sec)

Applying the scale factor the actual dimension of the ramp in the blueprint Mark was looking at was found to be 0.158 inches

Scale factor represent the amount the image is increased or reduced in the map.

information from the question include

the scale on the blueprint is 1 inch: 6 feet

the ramp's length that is 11.4 inches

finding the scale factor

1 inch ⇒ 6feet = 72 inches

the scale factor is 1/72

finding the actual dimension

1 inch ⇒  72 inches

? = 11.4 inches

cross multiplying gives

72 * ? = 1 * 11.4

? = 1/72 * 11.4

? = 0.158 inches

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A lift ratio of 1.52 implies that identifying a person who purchases coffee and a breakfast sandwich is 52% better than guessing that a random person will purchase a breakfast sandwich.

Stronger relationships are indicated by higher lift values.We divide the confidence ratio by the support of the consequent to arrive at the lift ratio.

Lift ratios greater than one are typically thought to imply a significant link between the components. Lift ratios below 1 indicate that a purchase of the items is unlikely. Lift is simply the ratio of target response divided by the average response.

Carmen analyzed data from the month of March to see if there was a link between coffee and breakfast sandwich purchases. She calculated the lift ratio to be 1.52 after running confidence and expected confidence calculations.

In this case, she wants to know the association between coffee and breakfast sandwich purchases. There's 52% better off than a random individual.

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40% of 8 is 3.2

hope this helped