The fraction 3/2 and square root of 2 are not equivalent because their decimal approximations (1.5 and about 1.41 respectively) are not the same.
Explanation:To determine if a fraction like 3/2 is equal to the square root of 2, we would need to compare their decimal values.
First, divide 3 by 2 to get the decimal value for the fraction, which is 1.5.
For the square root of 2, we can use a calculator and find that its approximate decimal value is 1.41.
Therefore, since 1.5 is not equal to 1.41, the fraction 3/2 is not equivalent to the square root of 2.
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The fraction 3/2 is not equal to the square root of 2. By comparing the values directly or using fractional exponents, we can see that squaring 3/2 gives us 9/4, which is not equal to 2, and numerically the square root of 2 is approximately 1.414.
To determine if the fraction 3/2 is equal to the square root of 2, we can compare them directly or convert them into the same format. Recall that fractional exponents serve as another way to represent roots. Specifically, an exponent of 1/2 equates to taking the square root of a number. Thus, [tex](3/2)^{2}[/tex] would equal 3/2 multiplied by itself, which is 9/4, and that is not equal to 2. Therefore, 3/2 is not the square root of 2. We can also numerically evaluate the square root of 2, which is approximately 1.414, and see that it does not equal 3/2, which is 1.5.
Another consideration is that the square root of any number x can be expressed as [tex]x^{1/2}[/tex]. For instance, [tex](\sqrt{2})^2[/tex] = 2 because [tex](2^{1/2})^2[/tex] equals [tex]2^{1/2 * 2}[/tex] = 2. When we do this with 3/2, we would have [tex](3/2)^{1/2} * (3/2)^{1/2}[/tex] = 3/2, which does not satisfy the equation for the square root of 2. Therefore, 3/2 is not equal to the square root of 2.
What is the probability that a red 10 is drawn in a regular deck of cards?
Answer:
1/26 or 1 out of 26
Step-by-step explanation:
only 2 red tens
52 cards in a deck
2/52=1/26
there were 100 questions on the social studies test. Arpan answered 97 of the questions Correctly. what fractions and demical presents the fraction of questions Arpan answered correctly?
Answer:
97/100 i think
Step-by-step explanation:
The difference between two numbers is greater than the first number and the sum of
the two numbers is greater than 21. Find the system of inequalities representing the
given situation.
Answer:
Step-by-step explanation:
let the numbers be x and y
x-y>x
or -y>0
or y<0
and x+y>21
or if we want to solve further then
y<0
and x+y>21
or y>21-x
or 21-x<y <0
so 21-x<0
or 21<x
or x>21
Final answer:
The system of inequalities for the given situation is x - y > x and x + y > 21, where x represents the first number and y represents the second number.
Explanation:
System of Inequalities:
x - y > x
x + y > 21
Here, x represents the first number and y represents the second number.
find the exact length of the third side
Answer: 30
Step-by-step explanation:
I’m big smart
Answer:
30
Step-by-step explanation:
24^2 + 18^2 = c^2
(576 + 324 = c)
900 = c^2
[tex]\sqrt{900}[/tex] = 30
c = 30
What is the sum of the first five terms of the geometric sequence in which
a1 = 3 and r= 1/3?
Express your answer as an improper fraction using the slash (/) key and no
spaces.
Final answer:
The sum of the first five terms of the geometric sequence with a1 = 3 and r = 1/3 is 121/81.
Explanation:
The sum of the first five terms of a geometric sequence where a1 = 3 and r= 1/3 is found using the formula for the sum of a geometric series Sn = a1 * (1 - rn) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms. Plugging our values into the formula, we get:
S5 = 3 * (1 - (1/3)5) / (1 - 1/3)
First, we calculate (1/3)5, which is 1/243. Then we can rewrite the equation:
S5 = 3 * (1 - 1/243) / (2/3)
Subtracting inside the brackets gives us 242/243. The division by 2/3 is equivalent to multiplying by 3/2, resulting in:
S5 = 3 * (242/243) * (3/2) = 9/2 * 242/243
Finally, we multiply the fractions:
S5 = 726/486
Reducing this to simplest terms gives:
S5 = 121/81
Final answer:
To find the sum of the first five terms of a geometric sequence with a = 3 and r = 1/3, use the formula for the sum of a geometric series to get 242/81.
Explanation:
The sum of the first five terms of a geometric sequence can be calculated using the formula for the sum of a geometric series.
Given a1 = 3 and r = 1/3, the sum of the first five terms is 3(1 - (1/3)⁵) / (1 - 1/3).
Plugging in the values, the sum is (3 * 242) / 243 = 726 / 243 = 242 / 81.
Create your own equation chain using these numbers for the variables: a = 10, b = 6, c = 18, and d = 3.
Answer:
a + b + d - 1 = c
Step-by-step explanation:
a + b + d - 1 = c
10 + 6 + 3 - 1 = 18
PLSSSSSS HELP
BRAINLIST
Answer:
The step 4 is not what he should have done. But the wrong is step 5, because if he added -2x both sides, it would give the following equation:
[tex]x-12=-4x+6[/tex]
and not [tex]x-12=6[/tex]
Note that in step 4 he should have added 2x and not -2x to both sides, but we still have the equality. The problem is that step 5 is totally wrong.
I don't know what answer is expected to this question, but I would mark step 5, because this is mathematically wrong.
Solving the equation
[tex]3(x-4)=-4-2(x-5)[/tex]
Using distribution
[tex]3x-12=-4-2x+10\\3x-12=-2+6[/tex]
Add [tex]2x[/tex] both sides
[tex]3x-12+2x=-2x+6+2x[/tex]
[tex]5x-12=6[/tex]
Add 12 both sides
[tex]5x-12+12=6+12\\5x=18[/tex]
Divide both sides by 5
[tex]$x=\frac{18}{5} $[/tex]
A tailor pays $10.25 per yard for wool and pays $5.75 per yard for cotton. He bought 4.8 yards of cotton and spent a total of $85.00 on the
two types of fabric.
How many yards of wool did he buy?
A. 4.1 yards
B. 5.6 yards
C. 6.2 yards
D. 8.2 yards
Answer:
A. 4.1 yards
Step-by-step explanation:
Multiply $10.25 by 2 because there is 2 fabrics. You would get 20.5 and divide 20.5 from 85.00 and the answer is 4.1.
He buys 5.6 yards of wool, the correct option is B.
What is the equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
A tailor pays $10.25 per yard for wool and pays $5.75 per yard for cotton.
He bought 4.8 yards of cotton and spent a total of $85.00 on the two types of fabric.
Let x be the yards of wool did he buy.
The yards of wool did he buy is given by;
[tex]\rm 10.25x + 5.75 \times 4.8 = 85\\\\10.25 x=85-27.6\\\\10.25 x=57.4\\\\x=\dfrac{57.4}{10.25}\\\\x=5.6[/tex]
Hence, he buys 5.6 yards of wool, the correct option is B.
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Examine the diagram to answer the question.
A circle with its center at (negative 0, 0) and passing through point (negative 3, negative 4).
What is the equation of the circle?
x2+y2=5
x2+y2=5–√
x2+y2=25
x2+y2=10
Answer:
x^2 + y^2 = 25 (third one)
Step-by-step explanation:
formula is x^2 + y^2 = r^2 (r = the radius)
the radius is 5 so r^2 is 25.
The equation of the circle is x² + y² = 5², is x²+ y² = 25.
To determine the equation of the circle with its center at (-0, 0) and passing through the point (-3, -4), use the standard equation of a circle:
(x - h)² + (y - k)² = r²
Where (h, k) represents the center coordinates of the circle and r represents the radius.
In this case, the center of the circle is (-0, 0), so the equation becomes:
(x - 0)² + (y - 0)² = r²
Simplifying:
x² + y² = r²
to find the radius (r). Since the circle passes through the point (-3, -4), we can use the distance formula to find the radius:
r = √((x2 - x1)²+ (y2 - y1)²)
r = √((-3 - 0)² + (-4 - 0)²)
r = √(9 + 16)
r = √25
r = 5
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17.0027992+z= 35.0780212 I need to solve for z
Answer:
z= 18.075222
Step-by-step explanation:
Z=35.0780212-17.0027992
so z= 18.075222
Answer:
18.075222
Step-by-step explanation:
17.0027992+z=35.0780212
leave z so that it's by itself by subtracting.
z=35.0780212-17.0027992
then solve
z=18.075222
· A store has put a robotics kit on sale for 25% off the original price. If the original price is
$40, what is the soles price?
Answer:
$30
Step-by-step explanation:
50% of $40 would be half of 40 so 50%=20
Half of 50% =25% so half $20 is $10
This means that the discount price is $10 so if we take away the original price ($40) from the discount ($10) that leaves us with the new sale price of $30!
Hope this helps!
Answer:
$30
Step-by-step explanation:
If an item is 25% off of it's original price, off it is 75% of it's original price.
(100-25=75)
So, what we need to do is find 75% of 40.
0.75*40=30
The sales price is $30.
Which value is a solution for the equation cot x/2 =1
Step-by-step explanation:
cot(x/2) = 1
Take inverse of both sides.
tan(x/2) = 1
Solve for x/2.
x/2 = π/4 + kπ
Solve for x.
x = π/2 + 2kπ
Possible values for x are π/2, 5π/2, 9π/2, etc.
Answer:
it's 3pi
Step-by-step explanation:
In the week that ended on January 4, there were 24 cases of flu reported in a city’s hospital. In the 5 weeks that followed, the number of new cases reported each week had grown exponentially and can be modeled by this graph.
Final answer:
The question involves analyzing the exponential growth of influenza cases and understanding historical flu pandemics, from the model of cases' augmentation in the hospital to societal impacts and public health responses, which falls within the field of Biology for High School students.
Explanation:
The discussion around the reported cases of flu, responses to outbreaks, and historical flu data primarily involves understanding trends in influenza incidences and epidemiology, which is a field within Biology. When analyzing how flu cases reported in a hospital grow, utilizing an exponential model suggests a mathematical approach to biological data. This is a common method in epidemiology for tracking the spread of diseases. Moreover, looking at past flu pandemics, the focus shifts to the interaction between the disease and society, and how responses such as quarantine and public health measures impact the containment and eventual decline of a pandemic. Historical data can provide insights into how a disease progresses through a population, the impact on the healthcare system, and how public health responses can mitigate these effects.
For example, during the 2007-2008 influenza season, the United States saw an abnormal increase in emergency department visits for influenza-like symptoms. In the context of the 2009-2010 flu pandemic, which resulted in a significant number of worldwide deaths, we can see the importance of quick response and effective public health strategies in areas like the United States. Data showing the number of cases and deaths over time highlight how the course of an outbreak or a pandemic can change based on these factors and natural disease progression.
All I need to know is if I picked the right one!
Answer:
No! The answer is not zero. There can be infinite solutions for this equation.
Hope it helps!
Answer:
no
Step-by-step explanation:
there can be more solutions ( infinite) as x could be either negative and positive...
Which expression has a lesser value? 1/3 x (492 - 166) or 3 x (492 - 166)
Answer:
1/3x(392-166)
Step-by-step explanation:
1/3x(492-166)
1/3x(326)
=326/3
3x(492-166)
3x(326)
=978
Tip, think of 1/3 and 4 as pizzas. Do you want 1 out 3 pizzas? Or 4 pizzas?
The vertices on the snowflake pictured form what kind of geometric figure?
Answer:
The natural, hexagon geometry of a snowflake
Step-by-step explanation:
Answer:
.
Step-by-step explanation:
if there are 5,280 feet in every mile, then what is the speed of a car that is traveling 35 miles per hour in feet per second.
a) 24
b) 38
c) 44
d) 51
Hey there!
We see that we have 35 miles, and each one is 5,280 feet. Given this, we multiply them together and we see that we have 184800 feet per hour. But, we need feet per second. To do this, we can look at this.
60 seconds=1 minute
60 minutes= one hour
If we use this, we can see that there are 3600 seconds in one hour. We now divide our feet per hour divided by 3600 to get feet per second.
184800/3600= 51 1/3
Therefore, our answer is D) 51.
I hope this helps!
The speed of the car in feet per second should be option D. 51.
The calculation is as follows:We know that
60 seconds=1 minute
60 minutes= one hour
And, in one hour there is 3600 seconds
So,
[tex]= (5280 \times 35) \div 3600[/tex]
= 51
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Which expression shows 2x² + 18 factored completely
Answer:
2(x^2+9)
Step-by-step explanation:
2x^2 +18
Factor out a 2
2(x^2+9)
You get a part time job earning $7.50 hr. Your tips are $2.75 hr on average. Deductions are
FICA (7.65%u federal tax withholding (9.25%), and state tax withholding (6.45%). You work
for 10 hours. What is your gross base pay?
Final Answer:
$75
Explanation:
To calculate your gross base pay, you only need to consider your hourly wage and the number of hours worked. Tips, FICA taxes, federal tax withholding, and state tax withholding are not included since they are either extra income (tips) or deductions (taxes) that do not affect gross base pay.
Your hourly wage is $7.50.
You worked for 10 hours.
To calculate the gross base pay, you multiply the hourly wage by the number of hours worked:
Gross Base Pay = Hourly Wage * Hours Worked
Gross Base Pay = $7.50 * 10
Gross Base Pay = $75.00
Your gross base pay for 10 hours of work is $75.00. This is before any tips and deductions are taken into account.
The gross base pay for 10 hours of work at $7.50 per hour is calculated by multiplying the hourly wage by the number of hours worked.
Gross base pay = Hourly wage × Number of hours worked
Gross base pay = $7.50 × 10 hours
Gross base pay = $75.00
Therefore, the gross base pay is $75.00.
To determine the gross base pay, one only needs to consider the hourly wage and the number of hours worked. The gross base pay does not take into account any deductions or tips; it is simply the total amount of money earned from the hourly wage before any deductions are made. In this case, the hourly wage is $7.50, and the individual worked for 10 hours. By multiplying these two values together, we obtain the gross base pay of $75.00. This is the amount of money the individual earned from their wages alone, prior to any taxes or other deductions being subtracted.
Jen ran for 10 minutes with the speed of 6 mph and then walked for 30 minutes at a speed of 3 miles per hour. What is the total distance covered by Jen?
Answer:
2.5 miles
Step-by-step explanation:
Jen ran for 10 minutes. This is 1/6 of an hour.
1/6*6=1
He covered 1 mile in that 10 minutes.
Jen then walked for 30 minutes. This is 1/2 of an hour.
1/2*3=1.5
He covered 1.5 miles in that 30 minutes.
1+1.5=2.5
The total distance covered by Jen is 2.5 miles.
Answer:
2.5
Step-by-step explanation:
Which functions represent a horizontal translation to the left of the parent function f(x) = In x?
Check all that apply.
g(x) = 3 In(x - 1) + 6
h(x) = 3 In(x + 3) + 1
r(x) = -3 In(x + 1) + 3
s(x) = -3 In(x) - 3
p(x) = In(x + 2) - 2
Answer:
Step-by-step explanation:
Answer:
B,C,E
Step-by-step explanation:
The equation of a circle is x2+y2+10x−4y−20=0 .
What is the radius of the circle?
Enter your answer in the box.
Answer:
7
Step-by-step explanation:
Let's start by converting this to standard form.
[tex]x^2+10x+y^2-4y=20\\(x^2+10x+25)-25+(y^2-4y+4)-4=20\\(x+5)^2+(y-2)^2=49[/tex]
The center of the circle is at (-5,2), and the radius is [tex]\sqrt{49}=7[/tex] units. Hope this helps!
The radius of the circle is r = 7 units
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be r
Now , the equation of circle is
x² + y² + 10x - 4y - 20 = 0
And , standard form of a circle is
( x - h )² + ( y - k )² = r²
We need to complete the square for both the x and y terms in the given equation:
x² + y² + 10x - 4y - 20 = 0
( x² + 10x + 25 ) + ( y² - 4y + 4 ) - 49 = 0
On Adding and subtracting constants to complete the square
( x + 5 )² + ( y - 2 )² = 49
Now we can see that the equation is in standard form.
The center of the circle is at (-5, 2), and the radius is the square root of 49, which is 7
Hence , the radius is 7 units
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To reduce the likelihood of an accident when driving, you should consider how
far your car will travel before safely coming to a stop for the speed at which you
are traveling. Assume you are traveling on a dry road and have an average reaction
time. The formula d = 0.044s + 1.1s gives you a safe stopping distance d in feet,
where s is your speed in mi/h. Make a table of values for speeds of 10, 20, 30, 40,
50, and 60 mi/h. Then, graph the function.
Answer:
10 -- 1.54
20 -- 1.98
30 -- 2.42
40 -- 2.86
50 -- 3.3
60 -- 3.74
Step-by-step explanation:
jus tput the value of x:10,20,30,40,50,60 and calculate y
then plot x and y
Answer:
d = 0.044s + 1.1s
d = 1.144s
s. | d.
10 | 11.44
20 | 22.88
30 | 34.32
40 | 45.76
50 | 57.2
60 | 68.64
For the graph, draw a straight line (only in the first quadrant) connecting:
(0,0) and (50,57.2)
Label the horizontal axis "speed (m/h)" and the vertical axis "distance (m)"
PLEASE HELP I WILL GIVE BRAINLIEST TO WHOEVER SOLVES THIS FIRST ITS A GRADE :)!!
Answer:
B- the volleyball one
Step-by-step explanation:
A negative correlation is a relation where one variable goes up and another variable goes down. One variable in this is the volley ball time. Another is the amount of free time. As the time spent on volley ball goes up, the free time goes down and vice versa.
I think it's option D, let me know if this helps
The first equation from the previous system of
equations is graphed. Graph the second equation to
find the solution of the system of equations.
y = -2x + 4,
y = -5x-1
What is the solution to the system?
Answer:
(x, y) = (-5/3, 22/3)
Step-by-step explanation:
The graph and solution are shown below.
The solution is (-1 2/3, 7 1/3).
Explain how leaders supported writers.
Answer:
It seems there has been an explosion of articles about leading and leadership and what to do to be a great leader. Their suggestions can seem so broad and wide-ranging that it can be difficult to know just what to do next when trying to lead. Some seem so romanticized and idealized that it is hard to imagine anyone being a truly great leader. Yet, there are some practical skills needed in leading, and they can quite different depending on whether you are leading yourself, other individuals, groups or organizations -- and on the situation each is in. This topic provides the resources to develop those skills. However, if you want to truly understand leadership (and this topic assumes that you do), then you should be acquainted with its broad context, including the diversity of theories, models and styles in leadership. This topic mentions all of those, as well.
Step-by-step explanation:
Answer: It seems there has been an explosion of articles about leading and leadership and what to do to be a great leader. Their suggestions can seem so broad and wide-ranging that it can be difficult to know just what to do next when trying to lead. Some seem so romanticized and idealized that it is hard to imagine anyone being a truly great leader. Yet, there are some practical skills needed in leading, and they can quite different depending on whether you are leading yourself, other individuals, groups or organizations -- and on the situation each is in. This topic provides the resources to develop those skills. However, if you want to truly understand leadership (and this topic assumes that you do), then you should be acquainted with its broad context, including the diversity of theories, models and styles in leadership. This topic mentions all of those, as well.
Step-by-step explanation: I got it right
Determine the solutions of the quadratic equation, 2 x squared minus 8 x plus 6 equals 0 using the quadratic formula. x equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a. c and denominator 2 a.
Answer:
1, 3
Step-by-step explanation:
2x^2 - 8x + 6 = 0 -->
x^2 - 4x + 3 = 0
(x-1)(x-3) = 0
x = 1, 3
OR
2x^2 - 8x + 6 = 0 -->
x^2 - 4x + 3 = 0 -->
(-(-4) +-sqrt((-4*-4) -4(1 * 3)))/2 -->
(4 +-sqrt(4))/2 -->
(4 +/-2)/2 -->
6/2 or 2/2 -->
3, 1
Final answer:
The solutions to the quadratic equation 2x^2 - 8x + 6 = 0, found using the quadratic formula, are x = 1 and x = 3.
Explanation:
To find the solutions to the quadratic equation 2x^2 - 8x + 6 = 0 using the quadratic formula, we first identify the coefficients: a = 2, b = -8, and c = 6. Then, we substitute these values into the quadratic formula 'x = (-b ± √(b^2 - 4ac)) / (2a)'. The solutions can be found by carrying out the arithmetic operations.
Plugging the values into the formula gives us:
x = (8 ± √((-8)^2 - 4*2*6)) / (4)
x = (8 ± √(64 - 48)) / (4)
x = (8 ± √(16)) / (4)
x = (8 ± 4) / 4
Therefore, we have two solutions:
x = (8 + 4) / 4 = 12 / 4 = 3
x = (8 - 4) / 4 = 4 / 4 = 1
So, the solutions to the equation 2x^2 - 8x + 6 = 0 are x = 1 and x = 3.
The mean height of a American males is 69.5 inches. The height of the 43 male presidents have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the 43 presidents as a simple random sample , determine if there is evidence to suggest that the us presidents are taller than the average American male .
Answer:
American presidents are taller than the average American man
Step-by-step explanation:
We have to:
H0: m = 69.5
Ha: m> 69.5
Since the population standard deviation is unknown and the hypothesis test of the population mean, the t-test should be used. Here the sample size is large, so we can assume that the sample distribution of the sample mean It is normal.
sd = 2.77, x = 70.78 and n = 43
Then the test statistics will be:
t = (x - m) / (s / n ^ (1/2))
replacing
t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))
t = 3.03
Here the test is correct and the degree of freedom of the test is df = n-1 = 43-1 = 42.
Critical approach:
So
alpha = 0.05, the critical value of the test is 1,682.
Rejection region:
If t> 1,682, reject the null hypothesis.
Since the value of the test statistics is greater than the critical value, we reject the null hypothesis.
P-value approach:
The p-value using the Excel function "= TDIST (3,030,42,1)" is:
p value = 0.0021
Since the p-value is less than α = 0.05, we reject the null hypothesis.
Which means that American presidents are taller than the average American man.
Answer:
American presidents are taller than the average American man
Step-by-step explanation:
Given Data :
sd = 2.77, x = 70.78 n = 43
Test statistics will be:
t = (x - m) / (s / n ^ (1/2))
t = (70.78 - 69.5) / (2.77 / 43 ^ (1/2))
t = 3.03
df = n-1 = 43-1 = 42.
Thus the American presidents are taller than the average American man
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A department store is selling a watch with an initial price of 340. if the price of the watch is marked down by 35%, what is the sale price
Answer:
$221
Step-by-step explanation:
First we need to find what is 35% of 340. To do this, we multiply 340 by 0.35. This gives us 119. Because this is the amount they are taking off, we need to subtract it from the initial price. 340-119=221. Therefore the price after being marked down is $221 :)
Here is a table of values for y = f(x).
x 0 5 10 15 20 25 30 35 40
(x) 5 6 7 8 9 10 11 12 13
Mark the statements that are true.
A. The domain for f(x) is the set {5, 6, 7, 8, 10, 11, 12, 13).
B. f(15) = 8
c. K(5) = 6
D. The range for fx) is all real numbers.
Answer, Step-by-step explanation:
Based on the given table of values for y = f(x), the following statements are true:
A. The domain for f(x) is the set {5, 6, 7, 8, 10, 11, 12, 13). [True]
B. f(15) = 8 [True]
C. f(5) = 6 [True]
D. The range for f(x) is all real numbers [False]
The range for f(x) is not all real numbers, as the table only provides specific values for y = f(x) and does not cover all possible real numbers. The range for f(x) is the set {5, 6, 7, 8, 9, 10, 11, 12, 13}.