The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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2. Lyda is taking a test worth 50 points. Her goal is to score 80%.
Write a proportion to figure out how many points she needs to accomplish her goal.
Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.
score / total points = percentage / 100
To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:
score * 100 = percentage * total points
We know that percentage=80 and total points =50, so we can substitute these values:
score * 100 = 80 * 50
score = (80*50) / 100 = 40
So Lyda needs to score 40 points to accomplish her goal of 80%.
The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10
It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.
Step-by-step explanation:
Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart. A linear model of this situation contains the values (25 , 1,167) and (41 , 1,407), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year. What is the flat fee for the annual golf pass? A. $15 B. $1,032 C. $792 D. $807
To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.
Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.
The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.
Two groups of students were asked how far they lived from their school. The table shows the distances in miles: Group A (distance in miles) 1 1.5 8 9.2 6.8 4.5 4.8 2.5 0.76 Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8 Which statement best compares the mean distances for the two groups
Mean distance for group A = 6.01 miles and for group B = 2.17 miles.
What is mean value?In statistics, the mean is the average of all data values given in a data set.
Mean is calculated by adding all the data value and then divided the sum by the total amount of data.
How to calculate the mean distance?distance in miles for Group A distance in miles for group B
11.5 2
8
2.5
9.2 3.23
6.8 1.3
4.5 1.8
4.8 2.4
2.5 3
0.76 1.5
1.8
now mean value for group A = sum of data value/ number of data value
mean distance = (11.5 + 8 +9.2 +6.8 +4.5+ 4.8+2.5+0.76) / 8
mean distance for group A = 6.01 miles
mean distance for group B = (2+2.5+3.23+1.3+1.8+2.4+3+1.5+1.8)/ 9
mean distance = 2.17 miles
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Estimate number of jelly beans in 1 litre jar.
5x/2 +2/3 plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
Solutions given:
[tex] \frac{5x}{2} + \frac{2}{3} [/tex]
Taking L.C.M
[tex] \frac{15x + 4}{6} [/tex] is a right answer.
WILL GIVE BRAINLIEST TO CORRECT ANSWER
What graph shows the line of best fit?
Answer:
Graph C (third one down)
Step-by-step explanation:
The line of Graph C is going through closest to the middle, taking all points into account.
Write a STORY PROBLEM for the following equation: 4x+(-3)=-11
Answer:
X = - 2
John had solve the equation 4x+(-3)=-11, he said's his answer is x = 2.
Is he wrong or correct? If wrong plz show the steps on how to get the right answer.
Step-by-step explanation:
4x+(-3)= -11
-11 + 3
= -8
We got x by itself
now solve for x
4x = -8
Solution
X = -2
Help please??!!!!!!!!!
Answer:
c
Step-by-step explanation:
the answer is c
hope it helps
Two piecewise functions are shown below. What is the value of 3h(2) + 4g(1)?
Answer: In order to calculate the value of 3h(2) + 4g(1), we would need to know the specific functions h(x) and g(x) that you are referring to. Without more information, it is not possible to determine the value of the expression.
Typically, piecewise functions are defined by several different expressions, each defined over a different interval of the input variable x. To evaluate a piecewise function at a specific value of x, we must first determine which interval that value of x falls into, and then use the corresponding expression for that interval to find the output value.
Are you able to provide the piecewise functions, or are you just using them as an example?
Also, in case if you want to describe the functions in words, please let me know.
Step-by-step explanation:
Please find the perimeter of this irregular shape
Answer:
30
Step-by-step explanation:
i’ll give brainliest please help
Answer:
m=4
Step-by-step explanation:
Answer:
m= 4
Step-by-step explanation:
i hope this helps :)
Round your answer to the nearest hundredth.
?
B
С
50°
7
9514 1404 393
Answer:
BC ≈ 5.87
Step-by-step explanation:
The law of sines is applicable.
a/sin(A) = 7/sin(50°)
Angle A is the complement of angle B, so we have ...
a = 7(sin(40°)/sin(50°))
a ≈ 5.8736974
The length of BC is about 5.87 units.
Find the quartiles and interquartile range of the following data. 6, 15, 8, 13, 3, 18, 0, 5, 5, 12
Answer:
Q1 - 5
Q3 - 12.75
Interquartile Range = 7.75
(i think)
Step-by-step explanation:
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
Option D. {7 + i√71 / 20, 7 – i√71 / 20}
Step-by-step explanation:
10m² – 7m + 3 = 0
Using formula method, the solution to equation can be obtained as follow:
10m² – 7m + 3 = 0
Coefficient of m² (a) = 10
Coefficient of –7m (b) = –7
Constant (c) = 3
m = –b ±√(b² – 4ac) / 2a
= – –7 ±√((–7)² – 4 × 10 × 3) / 2 × 10
= 7 ±√(49 – 120) / 20
= 7 ±√(–71) / 20
Recall:
–17 = –1 × 17
Thus,
7 ±√(–71) / 20 = 7 ±√(–1 × 71) / 20
Recall:
√–1 = i
Thus,
7 ±√(–1 × 71) / 20 = 7 ± i√71 / 20
= 7 + i√71 / 20 or 7 – i√71 / 20
Therefore, the solutions to the equation are:
{7 + i√71 / 20, 7 – i√71 / 20}
what is the answer to 4^43
Answer:
7.737
Step-by-step explanation:
Find the break - even points for company X, which sells all it produces, if the variable cost per unit is $3, fixed costs are $2 and YT R = 5√q, where q is the number of thousands of units of output produced.
Given:
The variable cost per unit is $3, fixed costs are $2.
The revenue function is:
[tex]Y_{TR}=5\sqrt{q}[/tex]
where q is the number of thousands of units of output produced.
To find:
The break - even points for company X.
Solution:
The variable cost per unit is $3, fixed costs are $2.
So, the cost function is:
Total cost = Fixed cost + Variable cost × Quantity
[tex]Y_{TC}=2+3q[/tex]
The revenue function is:
[tex]Y_{TR}=5\sqrt{q}[/tex]
At break - even points the profit is zero. It means the cost and revenue are equal.
[tex]Y_{TC}=Y_{TR}[/tex]
[tex]2+3q=5\sqrt{q}[/tex]
Squaring both sides, we get
[tex](2+3q)^2=(5\sqrt{q})^2[/tex]
[tex]2^2+2(2)(3q)+(3q)^2=25q[/tex]
[tex]4+12q+9q^2-25q=0[/tex]
[tex]4-13q+9q^2=0[/tex]
Splitting the middle term, we get
[tex]4-4q-9q+9q^2=0[/tex]
[tex]4(1-q)-9q(1+q)=0[/tex]
[tex](4-9q)(1-q)=0[/tex]
Using zero product property, we get
[tex]4-9q=0[/tex] and [tex]1-q=0[/tex]
[tex]q=\dfrac{4}{9}[/tex] and [tex]q=1[/tex]
[tex]q\approx 0.444[/tex] and [tex]q=1[/tex]
Therefore, the break even points are 0.444 and 1.
will mark u brainliest
Answer:
( - 7, - 1, 1, 4 )
Step-by-step explanation:
( x, y )
where,
x is Domain
y is Range
Hence,
Domain is ( - 7, - 1, 1, 4 )
Find what’s missing exponent.
32=2?
Answer:
1/5
Step-by-step explanation:
32^1/5 = 2
Answer:
5
Step-by-step explanation:
2x2x2x2x2 = 2⁵ = 32
Hope this helps :)
Can x = 2i be a "solution" for (x+3)^2 =5
Answer:
the x =2 cant be a solution for (x+3)^2 =5.
hope it helps.
some one plz help me and no scam links plz and if u do i will report and just no scam links :( look at the pic for the work
Answer:
LOOK BELOW: USE FORMULA WHL WIDTH X HEIGHT X LENGTH
Step-by-step explanation:
4 IN, 3IN, 6IN =72 IN CUBED
6IN, 3IN, 2IN= 36 IN CUBED
4IN, 5IN, 4IN= 80 IN CUBED
2IN, 9IN, 3IN= 54 IN CUBED
PLS HELP I HAVE NO IDEA
Complete the remainder of the table for the given function
y=x/2 + 5
Answer:
Step-by-step explanation:
(-2,4)
(0,5)
(2,6)
(4,7)
Answer: 4, 5, 6, 7,
Step-by-step explanation: From the formula y = x / 2 + 5
substitute x with the value -2
It becomes -2 / 2 + 5
that equals 4
then do the same for the rest
when x = 0
y = 0 / 2 + 5
y = 5
when x = 2
y = 2 / 2 + 5
y = 1 + 5
y = 6
when x = 4
y = 4 / 2 + 5
y = 2 + 5
y = 7
I hope this was helpful
pls help me, i need to get my grade up as soon as I can
Answer:
106 and 93
Step-by-step explanation:
The whole thing has to add up to 360
The rectangular floor of a classroom is 36 feet in length and 27 feet in width.A scale drawing of the floor has a length of 12 inches.What is the area, in square inches, of the floor in the scale drawing?
The area of the scale drawing is 108 square inches.
I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108
The first rule is add 4 starting from 2. The second rule is subtract 4 starting from 28. What is the second ordered pair using the terms in each sequence? A (2, 28) B(6, 24) C (14, 16) D (10, 20)
The second ordered pair using the terms in each sequence is B (6, 24).
THE SEQUENCE PAIRThe first rule says to add 4 to the first term of the ordered pair, starting from 2. So the first term of the second ordered pair would be 2+4 = 6.The second rule says to subtract 4 from the second term of the ordered pair, starting from 28. So the second term of the second ordered pair would be 28-4 = 24.
Therefore, the second ordered pair using the terms in each sequence is B (6, 24).
The third ordered pair using the terms in each sequence would be C (14,16) and the fourth ordered pair would be D (10,20)This is because:
C (14,16) can be obtained by adding 4 to first term of B(6,24) which is 6+4 = 10 and subtracting 4 from second term of B(6,24) which is 24-4=20.
D (10,20) can be obtained by adding 4 to first term of C(14,16) which is 14+4 = 18 and subtracting 4 from second term of C(14,16) which is 16-4=12.
So the sequence list of ordered pair would be:
First order: A (2,28)
Second order: B(6,24)
Third order: C (14,16) D (10,20)
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5) Samantha uses 14 gallons of gas for every 110 miles she drives. How
many gallons does she use if she drives 215 miles?
What is an example of ordered pair function?
An ordered pair function is a type of mathematical function that associates certain pairs of elements (called ordered pairs) with a single output. For example, the function f(x,y) = x+y associates the ordered pair (2,3) with the output 5.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions such as print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This is because 2+3 = 5. Another example is the function f(x,y) = x×y,
which associates the ordered pair (3,4) with the output 12, since 3×4 = 12.
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What is the Pythagorean triplet of 12 and 16?
"20" is the Pythagorean triplet of 12 and 16.
A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a,b, and c such that a right triangle exists with legs a,b, and hypotenuse c.
By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying a²+b²=c²
The simplest Pythagorean triple is the set “3,4,5.”
Now, substitute the values in the above equation:
=) x² = 12² + 16²
=) x² = 144 + 256
=) x² = 400
=) x = √(400)
=) x = 20.
Therefore, (12,16,20) is a Pythagorean triplet.
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math. f(x)=8x-7;f(x)=9
Answer:
65
Step-by-step explanation:
We are given f(x) = 9
Substitute 9 for x in f(x) = 8x - 7
f(x) = 8 (9) - 7
f(x) = 72 - 7
f(x) = 65
On Monday, Lexi rode 3 miles on a bike. On Tuesday, she rode 3 times more than she did Monday. On Wednesday, she rode an additional 4 miles.
How many miles has Lexi ridden so far this week?
Answer:
she has rode 16 miles this week
Step-by-step explanation:
3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up
3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale
sorry for my speling erros
She rode a total distance of 16 miles this week.
An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
The distance rode by Lexi per day is mentioned below -
Monday - Lexi rode 3 miles on a bike.
Tuesday - Lexi rode 3 times more than she did Monday.
Wednesday - Lexi rode an additional 4 miles.
We can write the expression to find the total distance in miles covered by Lexi as -
d = d{M} + d{T} + d{W}
d = 3 + (3 + 3) + 4
d = 3 + 6 + 4
d = 13 miles
Therefore, she rode a total distance of 16 miles this week.
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Find the area of the shaded region
On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Total Surface Area = 2(lw + bw + lb)
Total Surface Area = [tex]2(24 + 30 + 20)[/tex]
Total Surface Area = [tex]148cm^2[/tex]
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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²
what is surface area ?
An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Total Surface Area = 2(lw + bw + lb)
Total Surface Area = - 148cm²
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