Four spheres of radius 10 sit on a flat table. Each sphere touches two of the other spheres, and the centres of the four spheres form a square. A fifth sphere of radius r is sitting on the table; it touches the table at a point directly beneath the centre of the square formed by the four other spheres. If the sphere of radius r touches each of the four other spheres, determine the value of r.

The slope-intercept form of this table is y = 3x - 10.

In Mathematics, the point-slope form of any straight line can be determined by using the following mathematical expression:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex] or y - y₁ = m(x - x₁)

Where:

At point (25, 65), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

[tex]y - 65 = \frac{(68- 65)}{(26 - 25)}(x - 25)[/tex]

y - 65 = 3(x - 25)

y = 3x - 75 + 65

y = 3x - 10.

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this table in slope-intercept form is y = 3x - 10.

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Equation for the line passing through the point (-3, -1) is:

c. y = -1

Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.

Now in the question here,

The line passes through the point (-3, -1).

So, the equation that satisfies the point is: y = -1.

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Answer: 6

Step-by-step explanation:

When x=-3, y=6

You can count it, 1,2,3,4,5,6.

Hope you found that helpful!

Answer:

(x+1)(x-6)

Step-by-step explanation:

two number that times to make -6 and add to make-5

these are : -6 and +1

(x+1)(x-6)

when u expand it

x^2-6x+x-6

=x^2-5x-6

"To solve this problem, we can use the Law of Cosines. Let's call the distance the pilot travels before the course correction d1 and the distance she travels after the course correction d2. We want to find the distance between her starting position and ending position, which we can call D.

First, let's find d1:

d1 = (720 mph) * (90 min / 60 min) = 1080 miles

Next, let's find d2:

d2 = (720 mph) * (100 min / 60 min) = 1200 miles

Now we can use the Law of Cosines:

D² = d1² + d2² - 2d1d2*cos(20°)

D² = 1080² + 1200² - 210801200*cos(20°)

D ≈ 1169 miles

Therefore, the pilot is approximately 1169 miles from her starting position." (ChatGPT, 2023)

Answer:

B

Step-by-step explanation:

the metal is a conductor

The prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4  is 1/2.

In science, the prοbability οf an event is a number that indicates hοw likely the event is tο οccur. It is expressed as a number in the range frοm 0 and 1, οr, using percentage nοtatiοn, in the range frοm 0% tο 100%. The mοre likely it is that the event will οccur, the higher its prοbability.

space οf twο-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 ?

here are a tοtal οf 16 pοssible οutcοmes in the sample space, as shοwn in the tree diagram. Out οf these 16 pοssible οutcοmes, 8 οf them cοntain the digit 1 οr 4 (i.e., 14, 17, 19, 41, 44, 71, 74, 91).

Therefοre, the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is:

P(1 οr 4) = 8/16 = 1/2

Sο the prοbability is 1/2.

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Accοrding the given questiοn 0.16 is 0.4 Percentage οr % οf 40

A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, multiply it by 100 and divide it by the tοtal. Sο, a part per hundred is what the percentage refers tο. Percent means fοr every 100. The symbοl "%" is used tο denοte it.

Percentages have nο dimensiοn. Hence it is called a dimensiοnless number. If we say, 50% οf a number, then it means 50 per cent οf its whοle.

0.4% is equivalent tο 0.4/100 = 0.004 as a decimal.

Tο find οut what number (a) is 0.4% οf 40, we can use the fοllοwing fοrmula:

a = 0.004 x 40

a = 0.16

Therefοre, 0.4% οf 40 is 0.16.

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The total cost of the camera with sales tax included is $976.68

The listed  price of the camera = $891.95

The sales tax rate = 9.5%

The amount of tax = The listed  price of camera × (The sales tax rate / 100)

Substitute the values in the equation

The amount tax = 722.95 × (9.5 / 100)

Divide the terms first

= 891.95 × 0.095

Multiply the terms

= $84.735

The cost of the camera including tax = The listed  price of camera + The amount of tax

Substitute the values in the equation

= 891.95 +84.735

= $976.68

Hence, the total cost of the camera with sales tax included is $976.68

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Answer:

Step-by-step explanation:

well, 2 and 1/2 is just 2 + 1/2 or just 2.5, so 2.5%.

[tex]~~~~~~ \stackrel{ \textit{\LARGE 8 years} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$250\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (250)(0.025)(8) \implies I = 50[/tex]

how about after 1 year?  well, we simply set t = 1, so (250)(0.025)(1) = 6.25.

would the interest for t = 2 be the same as for t = 1, if t = 2 is calculated, anyhow, the wording is a bit poor, let me reword it.

after the 1st year, she has an accumulated amount of 250 + 6.25 = 256.25.

now, if for the 2nd year we use the same 2.5% rate BUT we use the accumulated amount of $256.25 to get the interest, instead of the initial $250, will they be the same?

well, hell no, because (250)(0.025)(2) using the inital amount

is not the same as (256.25)(0.025)(2).

bear in mind that simple interest is calculated for each year using the initial amount or deposit, not the accumulated amount thus far.

The correct answer is answer choice- A.

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

See the attached worksheet. The use of a filled or unfilled circle on a number indicates whether that actual number is included (solid circle) or not included (empty circle)  A solid bar between two points telss us these points are all included.  

 -3<x<3 does not have an equality ("=") for ether +3 nor -3.  The the line between those points would be solid (all points are allowed).  Either 3 would be an empty circle.  

Option A seems to have these features.

The numerical coefficient of  [tex]\frac{2b}{3}[/tex]   is [tex]\frac{2}{3}[/tex] . So here we know how to find numeric coefficient.

A numerical coefficient is defined as a fixed (stable) number that is multiplied to a variable.

When an algebraic expression consists of several (various) parts, each part that is added called a term. The numerical part of a term is called as its numerical coefficient (or coefficient).

Variable, It is a symbol that represents (means) a mathematical object. A variable may represent(mean) a number, a matrix, a function, a vector, the argument of a set, a function, or an element of a set.

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Answer:

add 3

Step-by-step explanation:

adding 3 to each number for next erm

Podemos utilizar la ley de cosenos para aproximar la distancia entre las cometas. Primero, necesitamos encontrar la longitud de la tercera cuerda, que conecta los puntos donde se cruzan las dos cuerdas que sostienen las cometas. Podemos usar trigonometría para encontrar la altura de este triángulo.

El ángulo opuesto a la altura es de 30°, por lo que podemos calcular la altura como:

Ahora podemos usar la ley de cosenos para encontrar la longitud de la tercera cuerda:

Entonces, la distancia entre las cometas es aproximadamente de 380 pies.

The optimal number of TVs to sell in order to achieve the highest profit are 24 and 48, respectively

Given the question, the objective function can be stated as follows.

P(n, m) = 175b + 205m

The given values for the constraints and the result of evaluating them are provided as

After analyzing the above values, we have identified the highest value as

Maximum = 14040

These values are at

b = 24 and m = 48

Hence, the number of TV to be sold are 24 and 48, respectively

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Answer:

Step-by-step explanation:

To have the product of three integers be negative, we must have an odd number of negative integers. This is because when two negative integers are multiplied, the result is positive, and when an odd number of negative integers are multiplied, the result is negative. Therefore, we need at least one negative integer to produce a negative product, and then either one or three negative integers depending on whether the other two integers are positive or negative.

Here are two groups of three integers whose product is negative:

Group 1: {-1, 2, 3}

Product = (-1) x 2 x 3 = -6

In this group, there is one negative integer and two positive integers, which gives us an odd number of negative integers and a negative product.

Group 2: {-2, -3, 4}

Product = (-2) x (-3) x 4 = 24

In this group, there are two negative integers and one positive integer, which gives us an even number of negative integers and a positive product.

Note that there are infinitely many groups of three integers that can produce a negative product, as long as there is an odd number of negative integers in the group.

Answer:

The coordinates are (-2, 4)

The last option

Step-by-step explanation:

When you rotate 90 degrees clockwise, the coordinates change from (x,y) to (y, -x) so you just substitute the numbers to get the answer.

The allowed housing expense for the year is $38,582.01.

The minimum realized income per month is $1,774.53.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

1 ) p = 7.65 + 11.5 + 9 = 28.15 %

$53,698.00 · ( 1 - 0.2815 ) =

= $53,698.00 · 0.7185 = $38,582.01

The allowed housing expense for the year is $38,582.01.

2 ) $1,275.00 : 0.7185 = $1,774.53

The minimum realized income per month is $1,774.53.

The complete question is-

1.) You (or your parents) earn $53,698.00/yr and you have deductions of FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (9%). How much is the allowed housing expense for the year? (1 point)

$ /year

2.) You (or your parents) plan to pay $1,275.00/month for a mortgage. How much is the minimum realized income per month to the nearest penny

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Therefore , the solution of the given problem of probability comes out to be there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.

The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.

Here,

To resolve this issue, we can use the conventional normal distribution. First, we must standardise the 96 number using the following equation:

=> z = (x - μ) / σ

where the mean is, the standard deviation is, and x is the number we're interested in. When we enter the numbers, we obtain:

=> z = (96 - 85) / 4.6 = 2.3913

The area to the right of z = 2.3913 can then be determined using a calculator or a conventional normal distribution table.

The area to the right of 2.39, according to a standard normal distribution chart, is 0.0084. (rounded to four decimal places).

As a result, there is a 0.0084 percent chance that a raw number chosen at random will be higher than 96.

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The lateral surface area of the cube shaped Paco is 45.6 square inches.

In a cube, all six faces are identical squares, so there is no distinction between the lateral surface area and the total surface area. The surface area of a cube can be found by adding up the areas of all six faces.

If s represents the length of each edge of the cube, then the surface area S can be calculated using the formula: S = 6s²

So the lateral surface area of a cube with edge length s is simply 6 times the area of one of its faces, which is just the area of a square with side length s.

The Lateral surface area of a cube = 6s²

or we can say that, Lateral surface area = 6×(area of one face of a cube)

Given that the area of one face of a cube shaped Paco is 7.6 square inches.

Lateral surface area = 6×(7.6) = 45.6 square inches

Therefore, the lateral surface area of the cube shaped Paco is 45.6 square inches.

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The length of JL can be found by subtracting the length of ML from the sum of LK and LN. Therefore, JL = 28 + 16 - 12 = 32.

To find the length of JL, first we can add the lengths of LK and LN. LK = 28 and LN = 16, so 28 + 16 = 44. Then, we can subtract the length of ML from the sum of LK and LN. ML = 12, so 44 - 12 = 32. Therefore, JL = 32.

This can be done by visualizing the diagram. The length of JL can be found by adding the lengths of LK and LN, which can be seen as the two sides of the right triangle that form the line MN. Then, the length of ML can be subtracted from the sum of LK and LN to get the length of JL. This is because the length of JL is equal to the length of LK plus the length of LN minus the length of ML.

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Answer:

[tex]\boxed{k=\frac{p}{r \ s} }[/tex]

Second option is correct.

Step-by-step explanation:

We have been given that p varies jointly with r and s.

Thus, we can write it mathematically as

[tex]p=krs[/tex]

Here, k is the constant of variation.

Now, we have to find the value of k.

Divide the above equation by rs

[tex]\dfrac{p}{r \ s}=\dfrac{kr\ s}{rs}[/tex]

[tex]k=\dfrac{p}{r s}[/tex]

Hence, the value of k is [tex]k=\dfrac{p}{r s}[/tex]

Second option is correct.

Answer:

B

Step-by-step explanation:

edge 23

Answer and Step-by-step explanation:

Based on the evidence provided, Gary is most likely to make the conjecture that the store expects high demand for mountain bikes in the spring compared to racing bikes. Another conjecture that could be made is that mountain bikes will most likely sell better than racing bikes. This is because the manager has ordered 50 mountain bikes, which is five times more than the number of racing bikes ordered. This suggests that the store is anticipating greater demand for mountain bikes than for racing bikes in the spring season.

Satoko play the most number of times with her tokens is KOF. The correct answer is A.

A line graph is a type of chart that displays data as a series of points connected by a line. Line graphs show the relationship between two variables. The equation of each line can be obtained from the graph given regarding the game played by satoko.

Let us first derive the equation of first line Claw. This line goes from (0,0) to (5,20) so, the equation is y = 4x. The unit price is 4.

Next, the equation of DDR line. This line is from (0,0) to (5, 10). so, the equation is y = 3x. The unit price is 3.

The equation of line KOF goes from (0,0) to ( 5, 10). The equation of line is y = 2x. So, the unit price is 2.

Here, 4 greater than 3, and 3 is greatter than 2. so the correct answer is choice A, KOF.

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Answer: A

Step-by-step explanation:

i just know because i got it right.

Answer: Jalen wants the post to be perpendicular to the ground, which means the angle between the post and the ground should be 90 degrees. If the protractor showed the angle to be 82 degrees, then the post is leaning towards the ground. To make the post perpendicular, the angle needs to be decreased. Jalen incorrectly concluded that he needed to increase the angle by 12 degrees, which would make the angle 94 degrees, still not perpendicular.

To make the post perpendicular, Jalen needs to decrease the angle by 8 degrees (90 - 82 = 8). Therefore, the correct answer is D: The angle needs to be increased by 8 degrees to get to a 90 degree angle.

Step-by-step explanation:

Answer:

(3)(x)(z)

Step-by-step explanation:

Answer: $2,750

Step-by-step explanation:

Answer: Find the square root of 60i-11

Step-by-step explanation:

i is imaginary number

you can't find the square root of i because i is an imaginary number unless you put sqrt(i)