The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
The samples, each comprised of 15 observations, were taken from the four populations.
How to find the degrees of freedom?The determine the degrees of freedom for the numerator and denominator for the critical value of F is given below:
k = 4
n = 15
Total degree of freedom;
= nk - 1
= 59
For numerator, it is
= k -1
= 4 - 1
= 3
For denominator it is
= T - (k -1 )
= 59 - 3
= 56
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
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Does anybody know this? The quotient of -45 and -5 is
Write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 5 0, t ≥ 5
The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
Given,
[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]
Write the function in unit step function.
[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]
= [tex]t(1-u_{5}(t))[/tex] ∵[tex]u_{0} (t)=1[/tex]
= [tex]t-tu_{5} (t)[/tex]
[tex]f(t)=t-tu_{5} (t)[/tex]
In order to make it easier to take the Laplace transform of the function, we can follow the steps:
[tex]f(t)=t-tu_{5} (t)[/tex]
= [tex]t-(t-5+5)u_{5} (t)[/tex]
= [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
We need to find the Laplace transform of f(t).
Apply Laplace transform on both sides,
£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]
= [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]
= [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
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Find the Perimeter of the figure below, composed of a parallelogram and one
semicircle. Rounded to the nearest tenths place
4
14
The perimeter of the figure to the nearest tenth is 44.6 units
Perimeter of a figure?The perimeter of a figure is the sum of the whole sides.
Therefore,
A parallelogram has opposite sides equal to each other.
Therefore, the perimeter of the figure is as follows;
The figure combines a parallelogram and a semi circle.
Therefore,
perimeter of the figure = 4 + 14 + 14 + πr
perimeter of the figure = 32 + 3.14 × 4
perimeter of the figure = 32 + 12.56
perimeter of the figure = 44.56
perimeter of the figure ≈ 44.6 units
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The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Question 4 (Essay Worth 10 points)
(05.07 HC)
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
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The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm
There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.
The function that best fits the data is y = 3x + 4.
The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
What is a Scatter Plot?The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.
A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.
The function is y = 3x + 4
When x = 0, y = 3(0) + 4 = 4.
In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
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If f(x)=3x, g(x)=x+2 and fog(x)=18, find the value of x.
solve this
Answer: 4
Step-by-step explanation:
f(g(x)) = f(x+2) = 3(x+2) = 18
x + 2 = 6
x = 4
Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?
The height of the second square base prism is 50 cm.
How to find volume of a square base prism?The volume of the first square base prism is represented as follows:
v = ha²
where
h = heighta = side length of the baseTherefore, the height of the prism is 10 cm.
v = 10a²
Hence, the volume of the initial prism is 5 times the volume. Therefore,
v = 5(10a²)
v = 50a²
Therefore,
50a² = ha²
divide both sides by a²
50a² / a² = ha² / a²
50 = h
h = 50 cm
Therefore, the height of the second square base prism is 50 cm.
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Find where the sequence converges
Answer: [tex]\\ \lim\limits_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]
Step-by-step explanation:
[tex]\displaystyle\\ \lim_{k \to \infty} (1+\frac{4}{k})^k \\x=\frac{x}{4} *4\\So,\ \lim_{k \to \infty} (1+\frac{4}{k})^\frac{k}{4}*4 \\ \lim_{k \to \infty} ((1+\frac{4}{k})^\frac{k}{4} )^4.\\Use\ the\ second\ wonderful\ limit:\\\boxed { \lim_{x \to \infty} (1+\frac{1}{x})^x=e },\\\\So,\\ \lim_{k \to \infty} (1+\frac{4}{k})^k =e^4.[/tex]
We can also apply l'Hôpital's rule by first rewriting the limit as
[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp\left(\ln \left(1 + \frac4k\right)^k\right) = \exp\left(\lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k}\right)[/tex]
Applying the rule gives
[tex]\displaystyle \lim_{k\to\infty} \frac{\ln\left(1+\frac4k\right)}{\frac1k} = \lim_{k\to\infty} \frac{\left(-\frac4{k^2}\right)/\left(1+\frac4k\right)}{-\frac1{k^2}} = 4 \lim_{k\to\infty} \frac1{1 + 4k} = 4[/tex]
so that the overall limit is
[tex]\displaystyle \lim_{k\to\infty} \left(1 + \frac4k\right)^k = \lim_{k\to\infty} \exp(4) = \boxed{e^4}[/tex]
4a. In a cookie mix, we find no-bake cookies, vanilla cookies, and cinnamon cookies in a ratio of 2 2 2 If a bag of the mix contains 40 no-bake cookies, how many vanilla cookies are there? please help
Answer:
40 vanilla cookies
Step-by-step explanation:
Lets say that
N = No-bake cookies
V = Vanilla cookies
C = Cinnamon cookies
If the ratio is 2 : 2 : 2
And there are 40 no-bake cookies
It would be 40 vanilla cookies and 40 cinnamon cookies because the ratio is all the same
( N : V : C )
( 40 : 40 : 40 )
Hope this helps (๑ > ᴗ <)وxx
( I am so sorry if this is wrong!!)
A basketball player averages 12.5 points per game. There are 24 games in a season. At this rate, how many points would the player score in an entire season?
In the entire season, the basketball player would score
point
Answer:
300 points
Step-by-step explanation:
Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:
[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
help math related pleaseee
[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]
[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]
Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity. 9 times the square root of quantity 3 x end quantity 9 times the square root of quantity 6 x end quantity 19 times the square root of quantity 3 x end quantity 19 times the square root of quantity 9 x cubed
The square root of the quantity x plus 7 end quantity minus 1 equals x=2.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. Square root of, end square root is the symbol for square root. Finding an integer's square root is the inverse of squaring a number.To find the square root:
√(x + 7) − 1 = x√(x + 7) = x + 1x + 7 = (x + 1)²x + 7 = x² + 2x + 10 = x² + x − 60 = (x + 3) (x − 2)x = -3 or 2Check for extraneous solutions:
√(-3 + 7) − 1 = -3√4 − 1 = -32 − 1 = -31 = -3x ≠ -3√(2 + 7) − 1 = 2√9 − 1 = 23 − 1 = 22 = 2x = 2Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.
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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x
Pls Help!!!!! I will give brainliest!!!!!
Answer:
Step-by-step explanation:
The equation of a circle in standard form is (x - h)² + (y - k)² = r² ,
where (h, r) are coordinates of a center of a circle and "r" is a radius of a circle.
a² ± 2ab + b² = (a ± b)²
~~~~~~~~~~
x² + y² - 2x - 10y + 17 = 0
To rewrite the equation in standard form, need to group terms with the same variables, move the constant to the right side and complete the square for each grouping:
(x² - 2x) + ( y² - 10y) = - 17
( x² - 2x + 1 ) + ( y² - 10y + 25 ) = - 17 + 1 + 25
( x - 1 )² + ( y - 5 )² = 9
( x - 1 )² + ( y - 5 )² = 3²
The center of the given circle is
( 1 , 5 )
The radius of the given circle is
3 units
Which graph shows the image of ABCD? On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (0, 3), (0, negative 1.2), (negative 2, 1). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (negative 2, 1), (0, negative 1), (0, 3). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (3, 0), (negative 1.5, 0), (0.5, 2). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (1, 2), (negative 1.5, 0), (2.8, 0).
A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.
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What is the solution set 5.5x+15.5>32
Answer:
(3, ∝) or all values of x greater than +3
Step-by-step explanation:
The inequality is [tex]5.5x + 15.5 > 32[/tex]
Subtracting 15.5 from both sides yields
5.5x > 32 - 15.5 or 5.5x > 16.5
Dividing by 5.5 on both sides yields
x > 16.5/5.5 or x > 3
This means the inequality is valid for all values of x > 3
The solution set is the interval (3, ∝ )
Alexa is a basketball player at East High. At a recent game, she made some three point shots and some two point shots. Alexa scored a total of 18 points and made 3 times as many two point shots as three point shots. Determine the number of three point shots Alexa made and the number of two point shots she made.
Answer:
6 2 point shots 2 3 points
Step-by-step explanation:
3 two point shot 1 3 point shot = 9
6 two point shot 2 3 point shot =18
Circle A has center of (2, 3) and a radius of 5, and circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B? (5 points) Dilate circle A by a scale factor of 2. Translate circle A using the rule (x + 1, y − 1). Rotate circle A 180° about the center. Reflect circle A over the y-axis.
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
How to prove that two circles are similar
Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following rigid transformation:
Translating the circle from A to B.Enlarging the circle A by a dilation factor.Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).
(x, y) = (2, 3) + (- 1, 1)
(x, y) = (1, 4)
Step 2 - Dilate the circle by a factor of 2.
r = 2 · 5
r = 10
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
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c= 6x+100 and c=10x+80
what number does x have to be for c to be the same on each equation?
Answer:
x= 5 , for c to be same on each eqn
My Uncle ordered 5 Pizzas, we were 20 people in all. I was just thinking how many pieces of
Pizza will each one of us will get if divided equally? (Each Pizza has 8-pieces)
How do you graph x < 5 on a number line and is the circle open or not? Where's the number line going? Thanks!
The inequality sign < means "less than." If there is a line underneath the inequality sign that means "less than or equal to."
To graph x < 5, we first need to understand what the inequality is saying. In this case, x must be less than 5. So, a number that will make this inequality true will be less than, but not equal to, 5.
Start by putting an open circle on the number 5. An open circle indicates that 5 is not a value that works in this inequality. Then, we know that our values that make this inequality true are less than 5, so we'll draw an arrow from the circle to the left as numbers to the left of 5 are less than it.
Hope this helps!
11%
5. The grid shows how many eggs Ms. Benton bought.
eggs she
The shaded boxes represent the number of
used to make the cookies. What percent and fraction
of the eggs bought were not used to make the cookies?
Show your work in the space below. Remember to
check your solution.
Answer:
36
Step-by-step explanation:
don't know but let me check right quick
1. How many quarters are in 12 1/4
2. How many ninths are in 6 1/9
3. How many eighths are in 5 3/4
. An ant is standing at the center of a perfectly circular plate. If the ant crawled in a straight line, he would have to crawl 6 inches to reach the edge of the plate. How many inches would he crawl if he crawled a full circle around the edge of the plate?
The size around the circular edge of the plate is 37.68 inches
How to find the circumference of a circle?The circumference of a circle can be solved as follows:
The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .
The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.
Hence, the distance around the edge of the plate is the circumference of the plate.
Therefore,
circumference of the circular plate = 2πr
circumference of the circular plate = 2 × π × 6
circumference of the circular plate = 12π
circumference of the circular plate = 12 × 3.14
circumference of the circular plate = 37.68 inches
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From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
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A base- three-digit number is selected at random. What is the probability that the base- representation and the base- representation of are both three-digit numerals
The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
How to determine the probability?To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:
The smallest 3-digit base 11 number in base 10The largest 3-digit in base 9 in base 10 with 3 digits The count of base 10 3-digit numbersThe smallest 3-digit base-11 number is 100
When converted to base 10, the equivalent number is 121
The largest 3-digit base-9 number is 888
When converted to base 10, the equivalent number is 728
So, the total number of possibilities is:
Possibilities = 728 - 121 + 1
Possibilities = 608
The count of base 10 3-digit numbers is
Count = 999 - 100 + 1
Count = 900
The required probability is:
P = 608/900
Evaluate
P = 0.6753
Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
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Complete question
A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals
Determine whether the geometric series is convergent or divergent. if it is convergent, find the sum. (if the quantity diverges, enter diverges. ) 7 − 8 64 7 − 512 49
The sum of the given series is 49 and it converges to infinity.
According to the statement
we have given that a series which is 7, -8, 64/7, 512/49
And we have to find that the series is converges or diverges.
So, For this purpose,
The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:
So,
[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]
[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]
[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]
And so on then
Sum of the series become to the nth partial sum
[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]
Multiplying both sides by -8/7 gives
[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]
and subtracting this from [tex]S_{N}[/tex] gives
[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]
[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]
Now the sum of the series is 49 and the it converges to infinity.
So, The sum of the given series is 49 and it converges to infinity.
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x² + y² if x = 7 and y = 5. What is the solution to this??
Step-by-step explanation:
x = 7
y = 5
[tex] = {x}^{2} + {y}^{2} [/tex]
[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]
= 7 × 7 + 5 × 5
[tex] = 49 + 25 [/tex]
[tex] = 74[/tex]
Hey there!
x^2 + y^2
= 7^2 + 5^2
= 7 * 7 + 5 * 5
= 49 + 25
= 74
Therefore, your answer should be: 74
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
At a football game
number of men : number of women : number of children = 13:5:7
There are 4152 more men then women.
Work out the number of children at the game
Answer:
Step-by-step explanation:
let the ratio of men women and children be 13x 5x and 7x
now
13x + 5x + 7x = 4152
25x = 4152
x = 4152/25
x = 166.08
Solve the que in the given picture!
Answer:
a) 20
Step-by-step explanation:
when we have an exponent of an exponent, we simply multiply them for the overall exponent.
so, we actually have
a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000
let's find the prime factors of 5000 :
5000 ÷ 2 = 2500
2500 ÷ 2 = 1250
1250 ÷ 2 = 625
625 ÷ 3 no
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
so,
5000 = 2³ × 5⁴
so, a = 2, b = 5
a²b = 2²×5 = 4×5 = 20
