On making b the subject , the formula is b = (5/3)a .
in the question ,
it is given that
the formula is a = 3(2a-b), where the subject is a ,
we have to rewrite the formula with b as the subject .
So, the given formula is
a = 3(2a-b)
simplifying the RHS , we get
a = 3*2a - 3*b
a = 6a - 3b
on re arranging the terms , we get
3b = 6a - a
3b = 5a
Dividing both sides by 3 ,we get
3b/3 = 5a/3
Cancelling out 3 from LHS , we get
b = 5a/3
b = (5/3)a
Therefore , On making b the subject , the formula is b = (5/3)a .
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The table below shows the gender and type of movies they prefer to watch.MaleFemale829418464891Horror MoviesSuspense MoviesComedy MoviesWhat is the approximate probability that a person will be a female and prefer suspense movies?
First, we must find the total of females, it will be
[tex]T=94+46+91[/tex]Now we must look at the table how many females prefer suspense movies, it's
[tex]S=46[/tex]Now we do the quotient between the females that prefer suspense by the total of females:
[tex]\begin{gathered} P=\frac{46}{94+46+91} \\ \\ P=\frac{46}{231} \\ \\ P=0.199134199 \end{gathered}[/tex]Rounding it, we can say that approximately,
[tex]P\approx0.2[/tex]Or 20% of the females prefer suspense movies
a laboratory worker finds that 3% of his blood samples test positive for the hiv virus. in a random sample of 70 blood tests, what is the mean number that test positive for the hiv virus? (round your answer to 1 decimal place)
In linear equation ,The mean number that the test positive for the HIV virus is 2.1 .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let x be the number of blood samples test positive for the HIV virus in a sample of 70 blood test.
Here X ~ Binom( n = 70, p = 0.03)
Using binomial distribution property , the mean of X is
μ = ηp
= 70 * 0.03 = 2.1
The mean number that the test positive for the HIV virus is 2.1 .
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Tyler has 500 counters in a bag.
He gives
15 of the counters to Sam
52 of the counters to Peter
43 of the counters to Lakhdar
What fraction of the 500 counters is left in Tyler's bag?
Give your fraction in its simplest form.
Write an equation and the answer.
A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number. What was the original number?
Write in this format:
If the original number is x, the equation will be _; x=_.
I hope this was helpful.
The original number is 0.8.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number be x.
A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number.
So, the mathematical expression is
1/2( 5x- 3) = x- 0.3
Now, solving for x
Multiply both side by 2
5x-3 = 2x- 0.6
5x- 2x= -0.6 + 3
3x= 2.4
Divide both side by 3
3x/3 = 2.4/3
x= 0.8
Hence, the original number is 0.8.
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17. Scarlet made a dive off a 10-ft platform. Her height above the surface of the pool t
seconds after leaving the platform can be modeled in the graph shown. Which of these
statements is NOT true about Scarlet's dive?
A. After 1 second, her height is 42 meters.
B. She reaches her maximum height at 1.5
C. Her maximum height is 46 meters.
D. She hits the water at 3 seconds.
O A
OB
O C
OD
40
30
20
10
1
2
3
Given the attached graph, the statement that is NOT true about scarlet's dive is that "She hits the water at 3 seconds." (Option D) See the explanation below.
What is a graph?In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.
In this scenario, the relationship represented is between Scarlet's descent from a 10-foot platform and the time it takes her to complete the trajectory from point of dive to point of reaching the water.
Hence, it is clear from the graph attached that Scarlet hits the water at 3.25 seconds.
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The equation y = 9x represents the liters of water a baseball team drinks each practice. This equation shows that after four practices, the team will have consumed 36 liters of water.
Determine the constant of proportionality.
36
9
4
0.25
The constant of proportionality of y = 9x is 9.
i.e y ∝ x and y = 9x
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
y = 9x
y = liters of water the baseball team drinks each practice
x = number of practice
We have an equation that after four practices, the team will have consumed 36 liters of water.
y = 36
9x = 38
x = 4
The equation can be written with a constant of proportionality as:
y ∝ x
y = 9x
So,
9 is the constant of proportionality.
Thus,
The constant of proportionality of y = 9x is 9.
i.e
y ∝ x
y = 9x
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Answer: The constant of proportionality of y = 9x is 9
Hamza is graphing the parabola represented by this equation. 3x-6y^2+6y=0
The answer is below!!!
Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right
The given equation is 3x-6y²+6y=0.
What is the parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Right
Vertex: (-1/2, 1/2)
Focus: (-3/8, 1/2)
Axis of symmetry: y=1/2
Directrix: x=-5/8
The coordinate points to plot (-1/2, 1/2), (0.5, 1.21), (0.5, -1.21), (1.5, 1.5) and (1.5, -0.5).
Therefore, Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right.
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I need help asap!!!!
The answer is -1 and 5
What is the equation in slope-intercept form of the line that passes through the point (−3,0) and is parallel to the line represented by y=3.2x+7.3
The equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6
The equation of the line that parallel to the line
y = 3.2x+7.3
Slope intercept form of the line
y = mx+b
y is the y coordinate
x is the x coordinate
m is the slope of the line
b is the y intercept
Compare it with the equation
The slope of the line m = 3.2
Point slope form of the line passing through the points (-3,0) with the slope of the line 3.2
[tex]y-y_{1}=m(x-x_{1} )[/tex]
Substitute the values in the equation
y-0 = 3.2(x-(-3)
y = 3.2(x+3)
y = 3.2x+9.6
Hence, the equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6
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Find the circumference of the circle. Use 3.14 for x
17 ft
The circumference of the circle with a radius of 7 ft is 106.76 ft
What is circumference?The circumference of a circle is the perimeter of the circle
How to calculate the circumference?The given parameters are
Radius = 17 ft
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 17
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 17
So, we have the following equation
C = 2π * 17
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 * 17
Evaluate the products
So, we have the following equation
C = 6.28 * 17
Evaluate the products
So, we have the following equation
C = 106.76
Hence, the circumference is 106.76 ft
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Identify the vertex of the quadratic function given by the equation f(x) = -x² + 8x - 14.
Answer: (4, 2)
Step-by-step explanation:
1) Identify the values of a, b, and c.
a = -1
b = 8
c = -14
2) Use the vertex formula to find the x-value of the vertex.
[tex]{\displaystyle x={\frac {-b}{2a}}}[/tex]
[tex]{\displaystyle x={\frac {-8}{2(-1)}}}[/tex]
[tex]{\displaystyle x={\frac {-8}{-2}}}[/tex]
[tex]{\displaystyle x=4[/tex]
3) Plug the value into the original equation to get the y value.
f(x) = -x² + 8x - 14
f(x) = -(4)² + 8(4) - 14
f(x) = -(16) + 32 - 14
f(x) = 2
3) Put it in an ordered pair
(4, 2)
How long is the hypotenuse?
The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.
How to determine hypotenuse?To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).
The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
a² + b² = c²
⇒ c = √(a² + b²)
Where, a = 30 and b = 40, then
substitute the values in the above equation, we get
30² + 40² = c²
900 + 1600 = c²
2500 = c²
50 = c
Therefore, the hypotenuse exists c = 50.
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what is 6000 divided by 40
Answer:
150
Explanation:
Alright so basically, 150 x 40 = 6000, right? So you want to find out how to find it using the division process. It is a whole number with no fractional part. As division with remainder the result of 6000 ÷ 40 = 150 R 0.
6000 divided by 40 ⇒ 150.
Here given that,
6000 is divisible by 40
since we know that,
Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.
6000 is divisible by 40 we get,
⇒ 6000/40
⇒ 150
So, the quotient is 150
Hence,
After dividing 6000 by 40 we get 150.
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Oscar
and maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles one entry in the table paired 152 km with 95 miles if k represents the number of kilometers and m represents the number of miles who wrote the correct equation that would relate kilometers to miles
The answer to the given question is Oscar wrote the correct equation that would relate kilometers to miles.
Calculation and Parameters1. Table
km miles
152 95
2. Set the proportion with / and solve for k
/ = 152 km / 95 miles
/ = 1.6 km / 1 miles
= 1.6 , where 1.6 / 1 represents kilometers per mile.
So, Oscar is right.
Maria is wrong because:
If we solve the proportionality:
/ = 152 km / 95 miles
/ = 95 miles / 152 km
= 0.625 , where 0.625 represents miles per kilometer
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The complete question is:
"Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If represents the number of kilometers and represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.
Oscar wrote the equation = 1.6, and he said that the unit rate 1.6 / 1
represents kilometers per mile.
Maria wrote the equation = 0.625 as her equation, and she said that 0.625 represents kilometers per mile."
PLEASE HELLLLP ME, SAT PREP QUESTION
Answer: It would be D. 22.5°
Have a nice day!
write 2 quadratic equations (of any form) that are not equivalent, each with a vertex of (4,5)
Answer:
[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]
Step-by-step explanation:
Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)
So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]
we can change the function by changing the value of the constant "a".
we can use two arbitrary values, but in this example I'll use -1 and 1.
this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]
these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.
In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form
[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]
We can also expand the other function similarly.
[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]
Please help me with this math problem!! Will give brainliest!! :)
Answer: 1/2
Step-by-step explanation:
Answer:
The correct answer seems to be 1/2
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y
=
−
16
x
2
+
170
x
+
61
Answer:
10.97 seconds
Step-by-step explanation:
You want to know when a rocket will hit the ground if its height is given by y = -16x² +170x +61, where x is seconds after launch.
Quadratic FormulaThe formula for the solutions of a quadratic equation is ...
[tex]\text{for }ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
When we apply this to the equation y=0, we have ...
[tex]x=\dfrac{-170\pm\sqrt{170^2-4(-16)(61)}}{2(-16)}=\dfrac{170\pm\sqrt{32804}}{32}\\\\x\approx 10.97\quad\text{seconds}[/tex]
The rocket will hit the ground after about 10.97 seconds.
<95141404393>
Calculate the pay for the following day of a
weekly time card given a wage of $12/hr.
Name
Week of:
Morning
Afternoon
In
Out
In
Out
Monday 08:15
12:15
13:00
17:30
pay = $[?]
Round your answer to the nearest hundredth.
The pay for the given weekly time is, $102.
What is the pay wage?
The key distinction between a salary and wages is that wage earners are compensated by the hour, whereas salaried employees receive set payments every pay period.
In the given example the total time for the morning and the afternoon is given.
The total time for the morning is 4 hours and the total time for the afternoon is 4.5 hours.
So, the total number of hours are 4 + 4.5 = 8.5 hours.
The wage of each hour is $12.
So, the wage of 8.5 hours is,
8.5 x $12 = $102.
Therefore, the pay for the given day of a weekly time card given a wage of $12/hr is $102.
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pls help!
9. From a standard deck, how many five-card
hands contain the following?
a) only black cards
b) all face cards
c) no hearts
d) two red and three black cards
e) one face card
which value of V makes 12 equals 12 + V - 8 / 2 a true statement
To determine the value of v that makes the equation true, we have to solve the equation and obtain the value of v
[tex]\begin{gathered} 12\text{ = 12+}\frac{v-8}{2} \\ \text{subtract 12 from both sides} \\ 0=\frac{v-8}{2} \\ \text{cross multiply} \\ 0=\text{ v-8} \\ \text{add 8 to both sides} \\ 8=v \\ or\text{ } \\ v=8 \end{gathered}[/tex]The value of v that makes the equation true is v=8
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 4500 pounds on Planet A, find the elephant's weight on Planet B.
Based on the ratio of the weights of objects in Planet A to Planet B, an elephants weighing 4,500 pounds on Planet A would weigh 135 pounds on Planet B
How to find the weight?The ratio of the weight of an object in Planet A is 100 to 3 on Planet B. This means that every 100 pounds on Planet A is 3 pounds on Planet B.
If an elephant on Planet A is 4,500 pounds, on Planet B it would weigh:
Weight on Planet B = (4,500 x 3) / 100
Weight on Planet B = 13,500 / 100
Weight on Planet B = 135 pounds
In conclusion, the weight of the elephant on Planet B would be 135 pounds.
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One spring day, Grayson noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 58° F. For the next 5 hours, the temperature rose 1° per hour. For the next 3 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 4 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 63° at midnight. On the set of axes below, graph Grayson's data.
On the graph that is included with the solution, the temperature fluctuations are depicted.
A graph is a representation of the relationship between two variables, often measured along one of two right-angled axes each.
It is 56° at 6 a.m.
It rises to 61° for the next 5 hours because it is increasing by 1° per hour, and after another 4 hours it will rise to 69° because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it fell for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.
It is 56° at 6 a.m. The temperature rises to 61° for the next 5 hours because it is increasing by 1° per hour, and then after 4 hours it will rise to 69° again because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it dropped for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.
The final graph is shown in the below attached figure.
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3) Identify the following by using the given figure
a) Two pairs of adjacent angles
b) Two pairs of supplementary angles
c) Linear pairs
Step-by-step explanation:
a) angles that share 1 side and are next to each other
<DBA, <ABE
<ABE, <EBC
b) two angles whose measures add to 180°
<ABE, <EBC
<ABD, <DBC
c) two adjacent angles whose noncommon sides lie on a line
<ABE, <EBC
<ABD, <DBC
♾️ How is the infinite possible? Has anyone ever counted numbers their whole life?
Answer: False, not possible.
The human was never meant to calculate or go beyond their fingers in search of great numbers, taking count for themselves, giving them names, appropriating. If you wanted to go higher for a laugh, it was called guessing. "Give me ZERO of this, give me 14,739,628,837 of that" are words that nobody says and words that stand behind delusion.
The only "anyone" to be counting their whole life is a divine. Keep math, numbers, and geometry sacred.
a geneticist is interested in the proportion of african males who have a certain minor blood disorder. in a random sample of 100 african males, 24 were found to be afflicted. (a) compute a 99% confidence interval for the proportion of african males who have this blood disorder. (b) what sample size (i.e., the number of african males) is needed if we wish to construct the 99% confidence interval of the proportion of african males with this blood disorder to be 0.20?
a) The confidence interval is (0.13, 0.35) for the males who have this blood disorder.
b) The number of African males or the sample size is 88 for the value of P to be 0.20
It is mentioned that a geneticist is interested in the proportion of the African males who have a certain minor blood disorder. In a random sample of 100 males, 24 were found to be afflicted.
So we have,
n (total males) = 100
X (afflicted males)= 24
Let P be the sample porportion,
P = X/ n
∴ P = 24 / 100 = 0.24
a) Here it is given to find the confidence interval if the proportion of males is 99% who have this blood disorder so,
c = 99 % = 0.99
∴ α = [tex]1 -[/tex] c = 1 - 0.99 = 0.01
⇒ α/2 = 0.01/2 = 0.005
Using Z table,
Z of α/2 = [tex]Z_{0.005}[/tex] = 2.576
Margin of error E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]
= 2.576 x [tex]\sqrt{\frac{0.24(1-0.24)}{100} }[/tex]
= 0.11
Now, 99 % confidence interval is P ± E
P-E < P < P +E
0.24 - 0.11 < P' < 0.24 + 0.11
P' = (0.13, 0.35) is the required confidence interval.
b) It is given to find the the number of African males when
P = 0.20
Z = 2.576
E = 0.11
Now E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]
⇒ 0.11 = 2.576 x [tex]\sqrt[2]{\frac{0.20(1-0.20)}{n} }[/tex]
⇒ 0.0427 = [tex]\frac{0.4}{\sqrt{n} }[/tex]
⇒ [tex]\sqrt{n}[/tex] = 9.37
⇒ n = [tex](9.37)^{2}[/tex]
⇒ n = 87.7969
Hence the approximate number of males is 88 for the proportion of males with this blood disorder to be 0.20
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7 x - 7; x = 4!!!???
Answer: 21 x=4
Solve the system of equations
Steps:
Evaluate
{ 7x−7 x=4
Calculate
{ x=4 21
Solution
{ 21 x=4
Pls tell me the answer thank you
Answer:
Third option
Step-by-step explanation:
The intercept x-intercept of f¹(x) is 1 and y-intercept of f(x) is also 1.
a magician charges a $30 fee to cover travel and expenses, plus $19.99 per hour. write an equation to represent the relationship between h, the number of hours, and t, the total charge for the magician.
Answer:
t = 19.99h + 30
Step-by-step explanation:
t is the total cost and h is the hourly charge. The 30 is a one time fee.
The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.
A.-4
B.25
C.-18
D.0
In the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.
What is a quadratic function?f(x) = ax² + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" shape.So, there are no x-intercepts on the graph of a particular quadratic function.
As is common knowledge, if a graph lacks an x-intercept, it will either end above or below the x-axis.This quadratic function has imaginary zeros.Discriminant= D
y = ax² + bx + cD = b² - 4acFor imaginary zeros, D must be negative.
The given option (A) and (C) which are -4 and -18 are negative and hence are the Discriminant with no x-intercepts.
Therefore, in the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.
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