The radius of the fifth sphere or the value of r is 14.14
In order to determine the value of the radius r of the fifth sphere, we must first calculate the side length of the square that the four spheres of radius 10 form.
Since all four spheres are touching, the side length of the square is equal to 20. Thus, the area of the square is equal to 400. Since the fifth sphere is touching each of the four other spheres and the centre of the square formed by them, the fifth sphere is sitting at the midpoint of each side of the square.
Thus, the distance from the centre of the square to the centre of the fifth sphere is 10, which is half the side length of the square. Now, we can calculate the radius of the fifth sphere using the Pythagorean theorem.
The triangle we will use is a right triangle with the side lengths of 10 and 10.
Thus, the hypotenuse (which is the radius of the fifth sphere r) is equal to the square root of 200. Therefore, the radius of the fifth sphere is approximately 14.14.
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Find the angle of elevation that a 30-foot ladder, leaning against a wall, if the bottom
of the ladder is 9 feet from the base of the wall.
Answer:
Step-by-step explanation:
im struggling a lot with this question have good day
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.
Gary works at a bicycle store in Vancouver. For the start of spring, the manager of the store has ordered 50 mountain bikes and 10 racing bikes.
Which conjecture is Gary most likely to make from this evidence?
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.
The tree diagram shows the sample space of two-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the probability of choosing a number from the sample space that contains 1 or 4 ?
The prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is 1/2.
What is prοbability ?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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Factorise the following
[tex] {x}^{2} - 5x - 6[/tex]
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
brainliest, 100 points, and multiple choice!!!!!!
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.
Pls answer thiss
give ismple working out
Answer:
add 3
Step-by-step explanation:
adding 3 to each number for next erm
Un niño está haciendo volar dos cometas al mismo tiempo; tiene 380 pies de cuerda a una de las cometas y 420 pies para la otra. Él estima que el ángulo entre las dos cuerdas es de 30°. Aproxime la distancia entre las cometas.
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:
sin(30°) = altura / 200altura = 100 piesAhora podemos usar la ley de cosenos para encontrar la longitud de la tercera cuerda:
d^2 = 380^2 + 420^2 - 2(380)(420)cos(30°)d^2 = 144400d ≈ 380 piesEntonces, la distancia entre las cometas es aproximadamente de 380 pies.
Given the expression
Choose all the equivalent expressions as your answer.
Answer:
(3)(x)(z)
Step-by-step explanation:
How many integers must be negative for the product of three integers to be negative? Explain. Find two different groups of three integers whose product is -12. Show your work.
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.
I NEED HELP ON THIS QUICKLYYY, WILL GIVE BRAINLIESTT!
The optimal number of TVs to sell in order to achieve the highest profit are 24 and 48, respectively
What is the optimal number of TVs to sell in order to achieve the highest profit?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
P(0, 0) =175(0) + 205(0) = 0 P(0, 64) =175(0) + 205(64) =13,120 P(24, 48) =175(24) + 205(48) =14,040 P(72, 0) =175(72) + 205(0) = 12,600After 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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PLEASE HELP!!!!!!!!!!!!
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!
One face of a cube shaped Paco has an area of 7.6 square inches. What is the lateral surface area of the package
The lateral surface area of the cube shaped Paco is 45.6 square inches.
What is the lateral surface area of cube shape?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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How much is the allowed housing expense for the yr if u earn 53698. 00 a yr?
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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A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
prs
StartFraction p Over r s EndFraction
StartFraction r s Over p EndFraction
p + r + s
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
Jalen was repairing the post on his mailbox. He wanted the post to be
perpendicular to the ground, but his protractor showed that the post was at an
82 degree angle with the ground. He incorrectly concluded that he needed to
increase the angle by 12 degrees. What should Jalen have concluded?
A.The angle needs to
be increased by 10
degrees to get a 90
degree angle.
B.The angle needs to
be decreased by 28
degrees to get a 180
degree angle.
C.The angle needs to
be decreased by 98
degrees to get a 180
degree angle.
D.The angle needs to
be increased by 8
degrees to get to a
90 degree angle.
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:
A HORIZONTAL line passes through point (-3, -1) Responses A x = 1x = 1 B x = 3x = 3 C y = -1y = -1 D y = 1
Equation for the line passing through the point (-3, -1) is:
c. y = -1
What is slope intercept?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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A pilot flies in a straight path for 90 minutes. She then makes a course correction, heading 20° to the right of her original course, and flies 100 minutes in the new direction. If she maintains a constant speed of 720 miles per hour, how far is she from her starting position? Round your answer to the nearest mile.
"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)
PLEASE HELPPPPP im struggling
Answer: $2,750
Step-by-step explanation:
In the diagram below, MN is parallel to JK. If ML = 12, LK = 28,
JK 14, and LN 16, find the length of JL. Figures are not necessarily
drawn to scale.
N
M
K
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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A camera has a listed price of $891. 95 before tax. If the sales tax rate is 9. 5%, find the total cost of the camera with sales tax included
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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You have given an exam for which :
μ=85
σ=4.6
What is the probability that a randomly selected faw score will be greater than 96 ? ANSWER: 0.0084
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.
What is probability exactly?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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Satoko has 30 tokens to spend at an arcade. The three lines represent the cost of playing Satoko's three favorite games for various numbers of times. Which game can Satoko play the most number of times with her tokens? Choose 1 answer: (Choice A) KOF (Choice B) DDR (Choice C) Claw
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.
What number (a) is 0.4% of 40?
Accοrding the given questiοn 0.16 is 0.4 Percentage οr % οf 40
What is Percentages ?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 table shows a function. Is the function linear or nonlinear?
X
3
6
9
y
19
12
2
linear
nonlinear
In the following term, give the numerical coefficient of the variable.
2b/3
The numerical coefficient of 2b/3 is ____.
The numerical coefficient of [tex]\frac{2b}{3}[/tex] is [tex]\frac{2}{3}[/tex] . So here we know how to find numeric coefficient.
What is Numerical 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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find the slope-intercept form of this table
The slope-intercept form of this table is y = 3x - 10.
What is the point-slope form?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:
m represent the slope.x and y represent the points.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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Please help will mark brainliest please!!!
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)
12.5 points
Question at position 4
Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.
Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.
A. The battery will die.
B. The light bulb will light up.
C. The light bulb will break.
D. The paper clip will turn black.
Answer:
B
Step-by-step explanation:
the metal is a conductor
Please help
Graph the inequality
-1
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.