Answer:
√27
3√3
Step-by-step explanation:
The expression is equal to the square root of 3 cubed, so:
*The bottom of the power fraction is the root, and the top of the power is the power for the base.
√3³
√27
Answer:
Step-by-step explanation:
3^3/2 =
Change the fraction into a radical form
[tex]\sqrt{3^3} = \sqrt{27}[/tex]
the solution is d
6x - 2y = 18
3x + 4y= -6
Which of the following ordered pairs (x, y) is the
solution to the system of equations shown above?
A. (-3,2)
B. (-2,3)
C. (2, -3)
D. (3,-2)
Answer:
C. (2, -3)
Step-by-step explanation:
Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.
Subtract -1/2n - (-1/2n)
Marissa needs to determine the height of a tree. Holding a drafter's 45° triangle so that one leg
is horizontal, she sights the top of the tree along the hypotenuse, as shown. If she is 6 yards
from the tree and her eyes are 5 feet from the ground, find the height of the tree. Remember: 3
feet in a yard.
Answer:
23 ft
Step-by-step explanation:
Sorry it is late
Find the measure of angle d when angle a is 128 angle b is 126 and angle c is 54
Step-by-step explanation:
sum of four angles=360°
a=128
b=126
c=54
d=?,let d=x
128+126+54+x=360°
308+x=360
find like terms
x=360-308
x=52°
Evauluate 37/100+3/10
Answer:
67/100
Step-by-step explanation:
Find common denominators, note that what you do to the denominator, you must do to the numerator.
The common denominator is 100:
(3/10)(10/10) = (3 * 10)/(10 * 10) = 30/100
Add:
37/100 + 30/100 = 67/100
67/100 is your answer.
~
Answer:
67/100
Step-by-step explanation:
37/100+3/10
Get a common denominator
37/100 + 3/10 *10/10
37/100+30/100
67/100
WHY CAN'T ANYONE HELP ME? Find an equation of the line described. Write the equation in slope-intercept form when possible. Through (-5,-3), perpendicular to the y-axis.
Answer:
y=-3
Step-by-step explanation:
If the line is perpendicular to the y- axis, that means that it must be a horizontal line. Any horizontal line must be in the form y=b. Since the y-value of the point is -3, the equation of the line must be y=-3
Answer:
y = -3
Step-by-step explanation:
A line perpendicular to the y-axis is a horizontal line.
The equation of a horizontal line is of the form
y = k,
where k is the y-coordinate of all points on the line. Since point (-5, -3) is on the line, then the y-coordinate of all points on the line is -3.
Answer: y = -3
Solve the system by using the inverse of the coefficient matrix. -3x + 9y = 9 3x + 2y = 13 Group of answer choices
Answer:
x= 3
y=2
Step-by-step explanation:
-3x + 9y = 9 ----------- equation 1
3x + 2y = 13--------------- equation 2
In Matrix Form
[tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right][/tex]
Let A = [tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right][/tex] X = [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] and B = [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Then Mathematically AX= B
or X= A⁻¹ B
Where A⁻¹ = Adjacent A/ mod of A
Adjacent A = [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex]
Mod Of A= -6 - (27) = -33 which is not equal to zero
so Putting These values in the given formula
X= 1/-33 [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex] [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Now Multiplying Rows and Columns
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right][/tex]
Solving the Matrix we get
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}-99\\-66\end{array}\right][/tex]
From Here we find x= 99/33 or 3
and y = 66/33= 2
which of the following describes an irrational number?
A. a repeating and non-terminating decimal.
B. a fraction
C. a terminating decimal
D. a non-terminating and non-repeating decimal
Answer:
A.
Step-by-step explanation:
B is wrong because irrational numbers can include pie.
C and D are wrong because irrational numbers don't get a whole number, and instead gives a decimal numbers.
solve p varies directly as the square of s and inversely as r, when s=6,r=3,and p=48 find the value of p when s =10and r=5
Answer:
see explanation
Step-by-step explanation:
Given that p varies directly as s² and inversely as r then the equation relating them is
p = [tex]\frac{ks^2}{r}[/tex] ← k is the constant of variation
To find k use the condition when s = 6, r = 3 and p = 48, that is
48 = [tex]\frac{6^2k}{3}[/tex] ( multiply both sides by 3 to clear the fraction
144 = 36k ( divide both sides by 36 )
4 = k , thus
p = [tex]\frac{4s^2}{r}[/tex] ← equation of variation
When s = 10 and r = 5 , then
p = [tex]\frac{4(10)^2}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80
Please help me. Please....
Answer:
20
Step-by-step explanation:
1/2(a+b)=180
1/2(6+12)=18
1/2(18)=180
9/9=180/9
=20
How many triangles exist with the given side lengths? 3 cm, 5 cm, 9 cm A. Exactly one unique triangle exists with the given side lengths. B. More than one unique triangle exists with the given side lengths. C. No triangle exists with the given side lengths.
Answer:c is the correct ans
Step-by-step explanation:
Feel pleasure to help u
Answer:
B-. More than one unique triangle exists with the given side lengths.
Step-by-step explanation:
according to to tringle inequality theorem he sum of the length of two sides of a triangle should be greater than the third side”. In order to verify the mentioned theorem, some cal. are preforemed below
12+15>18
15+18>12
If In(y - 40) = 5x, then y =
(a)
[tex] {e}^{5x} + 40[/tex]
(b)
[tex] {e}^{5x} - 40[/tex]
(c)
[tex]5 ({e}^{x} + 40)[/tex]
(d)
[tex]5 {e}^{x} - 40[/tex]
(e)none
If [tex]\ln(y-40)=5x[/tex] then [tex]y=e^{5x}+40[/tex].
Hope this helps.
Answer:
a e^(5x) +40
Step-by-step explanation:
In(y - 40) = 5x
Raise each side to base e
e^In(y - 40) = e^5x
y - 40 = e^5x
Add 40 to each side
y - 40 +40 = e^5x+40
Rafael is saving money to buy a game. So far he has saved $30, which is five-sixths of the total cost of the game. How much does the game cost?
Answer:
$36
Step-by-step explanation:
30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.
If we add another sixth, we get 36, which will be the total cost of the game.
Licence plates in Costa Rica are made up of 6 one-digit number. How many license plates can be made if the numbers can be repeated? (Probability unit grade 12 data management)
Answer:
There are 10 digits and 6 numbers so the answer is 10 * 10 * 10 * 10 * 10 * 10 = 10⁶ = 1,000,000.
Ross needs to buy a countertop for a laundry room. He calculated the area to be 12 square feet. The actual area is 11.8 square feet. What is Ross's percentage error? a.1.02% b.1.69% c.20% d.98%
Answer:
b. 1.69
Step-by-step explanation:
So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>
to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->
now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169
--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69
Hope this helps!
Answer:
B. 1.69%
Step-by-step explanation:
If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!
In order to solve this question,
1) We need to create proportions:
Ross' calculations x
______________ = _________
actual area 100
x represents the percentage error.
100 is the total percentage.
2) Now we plug in the numbers:
We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:
12 x
______ = _______
11.8 100
3) Time for cross multiplication:
12 times 100 is 1,200
11.8 times x is 11.8x
So,
1,200 = 11.8x
4) Now we divide:
1,200 divided by 11.8 equals to 101.69 %
5) We are not done! We still have to subtract:
101.69
-100.00
_______
1.69
Finished!!
Our answer is 1.69%, which is B.
Hope this was helpful !!!
help pleaseeeeeeeeee
It's Class B:
[tex]32\% \text{ of } 50 = 32\%\cdot50=\dfrac{32}{100}\cdot50 = \dfrac{32}{2}=16[/tex]
pat and tim work together at a pizzeria, Pat can fold 30 pizza boxes per minute and tim can fold 20 pizza boxes per minute. Working together, how many SECONDS will it take them to fold 200 boxes? plz help will give everything
Step-by-step explanation:
1 min = 60 sec
Boxes both can fold per min = 30 + 20 = 50
No of boxes to fold = 200
Time taken in sec = 200 ÷ 50 = 4 min = 60 x 4 = 240 sec
Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 7 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Sloth CW Ratios
1.5
1.09
0.98
1.42
1.49
1.25
1.18
Fill in the blank for a with the estimate of the standard deviation of this measurement in three-toed sloths to two decimals, and include the leading zero
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero)
Does this interval include the value obtained from other species? (answer yes or no in blank d)
Answer:
Step-by-step explanation:
Hello!
Given the variable
X: Ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloth.
The researcher's claim is that the ratio of the SC of the sloths is more variable than in other animal species that are more active.
For more active species the standard deviation of the ratio is σ= 0.09
1)
To calculate the sample standard deviation you have to calculate the sample variance first:
[tex]S^2= \frac{1}{n-1} [sumX^2-\frac{(sumX)^2}{n} ][/tex]
n=7; ∑X= 8.91; ∑X²= 11.8599
[tex]S^2= \frac{1}{6} [11.5899-\frac{(8.91)^2}{7} ]= 0.0287= 0.029[/tex]
S= √S²= √0.029= 0.169≅ 0.17
The sample standard deviation of the ratio is 0.17
2)
The parameter of interest is the population standard deviation. To calculate a confidence interval for the standard deviation of a population you have to estimate the population variance first. Then calculate the square root of both limits of the interval for the variance to obtain the interval for the standard deviation.
The statistic to use is the Chi-Square and the formula for the interval is:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{6; 0.025}= 1.2373[/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{6; 0.975}= 14.449[/tex]
[tex][\frac{6*0.029}{14.449} ;\frac{6*0.029}{1.2373} ]\\[/tex]
[0.0120; 0.1406]
Using a 95% confidence level you'd expect the interval [0.0120; 0.1406] to include the true value of the population variance of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
Now you have to calculate the square root of each limit:
[√0.0120; √0.1406]
[0.1097; 0.3750]
Using a 95% confidence level you'd expect the interval [0.1097; 0.3750] to include the true value of the population standard deviation of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
3)
As you can see the calculated interval doesn't include the value obtained for the other species.
I hope this helps!
Members of a gymnastics team are traveling to a tournament. They must pay $250 for a bus plus $40 per athlete to register for the tournament. What is the average total cost per athlete if 20 gymnasts attend? Do not include the dollar sign ($) in your answer.
Answer:
1050 in total, 52.50 for each athlete
Step-by-step explanation:
We can start by writing an equation with x as the number of athletes
250+40x= Total cost
Now we can substitute 20 for x
250+40(20)
250+800
1050
The total cost is 1050
If you need the amount that each athlete is paying individually, just divide it by 20
1050/20=52.50
52.50 for each athlete
A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why
Answer:
Statistic, because it is a property of a sample and not the population.
Step-by-step explanation:
The difference between a parameter and an statistic is that the parameter is a property of a population distribution and an statistics is referred to a sample property.
For example, a sample mean is a statistic while a population mean is a parameter.
In t his case, the proportion is referring to the sample of 481 customers, so it is not a property of the population (altough we can use it to infere about the population), so this proportion (79%) is an statistic.
What is the simple interest earned on
$300 over 6 years at 4% interest?
Answer:
$72
Step-by-step explanation:
I = Prt
I = ($300)(0.04)(6)
I = $72
A spring has natural length 24 cm. Compare the work W1 done in stretching the spring from 24 cm to 34 cm with the work W2 done in stretching it from 34 to 44 cm. (Use k for the spring constant) So:W1= ? W2:=? These answers must be written in terms of k. How are W2 and W1 related? W2 = ? W1
Answer:
From the analysis W1=W2.
they are directly related
Step-by-step explanation:
the work-done in stretching a spring can be expressed as
[tex]W=\frac{1}{2}kx^2[/tex]
where k= spring constant
x= change on length of spring
Hence for W1
Given data
x= 34-24= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k[/tex]
Hence for W2
Given data
x= 44-34= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k[/tex]
Joel is fertilizing an irregularly shaped garden. the grid has squares with side lengths of 2 m. Estimate the area of the garden. Given that the price of the fertilizer is $2.99 per square meter, find the cost of the fertilizer
Answer:
34.99
Step-by-step explanation:
P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?
Answer: Q(x) = x² - 4x + 2
Step-by-step explanation:
P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)
R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2
I will use synthetic division (but you can also use long division).
-2 | 1 -2 -6 4
| ↓ -2 8 -4
1 -4 2 0 ← remainder
The reduced polynomial is: x² - 4x + 2
Robert wants to arrange the books for statistics, calculus, geometry, algebra, and trigonometry on a shelf. In how many arrangements can he keep them on the shelf such that the algebra and trigonometry books are not together?
Answer: 72 arrangements
Step-by-step explanation:
The books are:
Statistics, calculus, geometry, algebra, and trigonometry.
So we have 5 books.
We want that algebra and trigonometry are not together.
Suppose that we have 5 positions:
Now, we can start with algebra in the first position.
Now, we have 3 positions for trigonometry (3rd, 4th and 5th).
Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.
The number of combinations is equal to the number of options in each selection:
3*(3*2*1) = 18
Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)
and for the other 3 books again we have 3*2*1 combinations:
the total number of combinations is:
2*(3*2*1) = 12
If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)
For the other 3 books, we have 3*2*1 combinations.
The total number of combinations is:
(3*2*1)*2 = 12
in the fourth position is the same as the second position, so here we have again 12 combinations.
For the fifth position is the same as for the first position, so we have 18 combinations.
The total number of combinations is:
C = 18 + 12 +12 +12 +18 = 72
Triangle ABC is a right triangle. The sides measure AB = 3 and BC = 4. Use the Pythagorean theorem to find CA. A. CA = 25 B. CA = 2.5 C. CA = 20 D. CA = 5
Answer:
CA = 5
Step-by-step explanation:
Since the sides are 3 and 4, we recognize this as a 3:4:5 right triangle, with CA = 5. Using the Pythagorean theorem confirms this:
CA² = AB² +BC²
CA² = 3² +4² = 9 +16 = 25
CA = √25
CA = 5
Answer:
D. CA = 5
Step-by-step explanation:
The Pythagorean Theorem states that given a right triangle with legs a and b and hypotenuse (longest side) c:
a² + b² = c²
Here, the legs are 3 and 4, so a = 3 and b = 4. Plug these in to find c:
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25 = 5
The answer is thus D.
~ an aesthetics lover
A salesperson found that there was a 1% chance of a sale from her phone solicitations. Find the probability of getting 5 or more sales for 2000 telephone calls.
Answer:
P(X ≥ 5) = 0.99972
Step-by-step explanation:
From the given data;
[tex]X \sim B(n = 2000 ;p = 0.01)[/tex]
Mean [tex]\mu = np[/tex]
Mean [tex]\mu = 2000 \times 0.01[/tex]
Mean [tex]\mu = 20[/tex]
Standard deviation [tex]\sigma = \sqrt{np (1-p)}[/tex]
[tex]\sigma = \sqrt{2000 \times 0.01 (1-0.01)}[/tex]
[tex]\sigma = \sqrt{20(0.99)}[/tex]
[tex]\sigma = \sqrt{19.8}[/tex]
[tex]\sigma =[/tex] 4.44972
P(X ≥ 5) ; The discrete distribution by continuous normal distribution for P(X ≥ 5) lies between 4.5 and 5.5. Hence, Normal distribution x = 4.5 since greater than or equal to is 5 relates to it.
Now;
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{4.5 - 20}{4.4972}[/tex]
[tex]z = \dfrac{-15.5}{4.4972}[/tex]
z = −3.45
P(X > 4.5) = P(Z > -3.45)
P(X > 4.5) = 1 - P (Z < - 3.45)
From Normal Z tables;
P(X > 4.5) = 1 - 0.00028
P(X > 4.5) = 0.99972
P(X ≥ 5) = 0.99972
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc) estimate Create a t-chart to graph the coordinates Find the 0's of the function Solve for y and use the slope-intercept form
Answer:
creat a t-chart to graph the coordinates.
2. If x=2, y=3 find
value of
x²-5y+2
Answer:
-9
Step-by-step explanation:
Substitute the give values into the correct place in the equation.
Since x=2, y=3,
Place "2" in the x of the equation, and "3" into the y of the equation.
x²-5y+2
= 2² - 5(3) + 2
= 4 - 15 + 2
= -9
Answer:
-9
Step-by-step explanation:
x² - 5y + 2 when x = 2 and y = 3
→ Substitute in x = 2 and y = 3
x² - 5y + 2 ⇔ (2)² - (5 × 3) + 2
→ Simplify
(2)² - (5 × 3) + 2 ⇔ (4) - (15) + 2
→ Simplify further
(4) - (15) + 2 ⇔ 4 - 15 + 2
→ Simplify further
4 - 15 + 2 ⇔ -11 + 2
→ Work out -11 + 2
-11 + 2 = -9
To determine if a particular predictor in a regression analysis is statistically significant, which statistic should one interpret
Answer:
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Step-by-step explanation:
The general form of a regression equation is:
[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]
Here,
α = y-intercept
βi = regression coefficients, (i = 1, 2, ..., n)
A regression analysis is performed to determine whether the predictor variables are statistically significant or not.
The output of the regression analysis consists of two tables.
One is the regression output and the other is the ANOVA table.
The regression output table is used to display which predictor variables are statistically significant and which are not.
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
And the ANOVA table displays overall regression analysis.
The F-test statistic is used to for the overall regression analysis.
Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]