Answers
Answer:
[tex]\large\boxed{Q1.\ A=\dfrac{5}{6}x^2}\\\boxed{Q2.\ 250m^{12}n^{-3}=\dfrac{250m^{12}}{n^3}}\\\boxed{Q3.\ \dfrac{81x^{16}y^{36}}{16z^{28}}}\\\boxed{Q5.\ y^\frac{1}{2}=\sqrt{y}}[/tex]
Step-by-step explanation:
[tex]Q1.\\\\\text{The formula of an area of a triangle:}\\\\A_\triangle=\dfrac{bh}{2}\\\\b-\ \text{base}\\h-\text{height}\\\\\text{We have}\ b=\dfrac{5}{3}x,\ h=x.\ \text{Substitute:}\\\\A_\triangle=\dfrac{\left(\frac{5}{3}x\right)(x)}{2}=\dfrac{5x^2}{(3)(2)}=\dfrac{5}{6}x^2[/tex]
[tex]Q2.\\\\2(5m^4n^{-1})^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=2(5^3)(m^4)^3(n^{-1})^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(2)(125)(m^{4\cdot3})(n^{-1\cdot3})\\\\=250m^{12}n^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{250m^{12}}{n^3}[/tex]
[tex]Q3.\\\\\left(-\dfrac{3x^4y^9}{2z^7}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{3^4(x^4)^4(y^9)^4}{2^4(z^7)^4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{81x^{4\cdot4}y^{9\cdot4}}{16z^{7\cdot4}}=\dfrac{81x^{16}y^{36}}{16z^{28}}[/tex]
[tex]Q4.\\\\\left(x^0y^{\frac{1}{3}\right)^\frac{3}{2}\cdot x^0\qquad\text{use}\ a^0=1\ \text{for any value of}\ a\ \text{except}\ 0\\\\=\left(1\cdot y^\frac{1}{3}\right)^\frac{3}{2}\cdot1\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=y^{\left(\frac{1}{3}\right)\left(\frac{3}{2}\right)}\qquad\text{cancel 3}\\\\=y^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\=\sqrt{y}[/tex]
Related Questions
Sixty-two desks can be assembled in 108.5 hours. At this rate, about how many desks can be assembled in 250 hours? Round to the nearest whole number.
Answers
Answer:
143 desks
62 desks
108.5 hours
=
x desks
250 hours
15500 = 108.5x
142.8 = x
Round to 143
Step-by-step explanation:
Answer:
In 250 hours 143 seats can be assembled.
Step-by-step explanation:
62 desks can be assembled in 108.5 hours.
In 108.5 hours 62 desks can be assembled.
In 1 hour [tex]\dfrac{62}{108.5}[/tex] seats can be assembled.
In 250 hours [tex]\dfrac{62}{108.5}\times 250[/tex] seats can be assembled.
In 250 hours 142.86 seats can be assembled.
Hence, In 250 hours 143 seats can be assembled. (Round to nearest whole number)
find the equation of each line from the given information. write the equation in standard Form. show your work for. The line contains the points (3.0) and (4,6)
Answers
Answer:
y=6x-18
Step-by-step explanation:
To find the standard equation of a linear relationship given two points, you need to find the slope and y intercept.
slope is change in y divided by change in x.
(6-0)/(4-3)
(6)/(1)
The slope of the line is 6.
We can plug this in along with x and y values from a given coordinate into the standard equation format to solve for b, the y intercept.
y=mx+b
y=0
x=3
m=6
0=6(3)+b
0=18+b
b=-18
now we know that the y intercept is (0,-18). The standard equation would be y=6x-18
What is the probability that the student attended the jazz concert given that student is a junior
Answers
Answer: C. 0.60
Step-by-step explanation:
From the given table , the number of students are junior : 60
The total number of students = 137
The probability of selecting any junior is given by :-
[tex]\text{P(Junior)}=\dfrac{60}{137}[/tex]
The number of juniors which who attended Jazz = 36
Then , the probability of selecting a students is junior and attends jazz is given by :-
[tex]\text{P(Junior and Jazz)}=\dfrac{36}{137}[/tex]
Now, the conditional probability that the student attended the jazz concert given that student is a junior will be :-
[tex]\text{P(Jazz}|\text{Junior)}=\dfrac{\dfrac{36}{137}}{\dfrac{60}{137}}\\\\\\=\dfrac{6}{10}=0.60[/tex]
Answer: it’s 0.60
(I just took it)
22n=418
what is the vaule of n.
Answers
Answer:
n = 19
Step-by-step explanation:
22n = 418
Divide both sides by 22.
n = 19
Divide $414 into three parts such that first one is two-third of the second and the ratio between second and third is 5 : 7.
Answers
Answer:
$90, $135, $189
Step-by-step explanation:
Since the first part of the ratio is two- thirds of the second, then
first part = [tex]\frac{2}{3}[/tex] × 5 = [tex]\frac{10}{3}[/tex]
The ratio is then
[tex]\frac{10}{3}[/tex] : 5 : 7
Sum the 3 parts of the ratio
[tex]\frac{10}{3}[/tex] + 5 + 7 = [tex]\frac{46}{3}[/tex]
Divide the amount to be shared by the sum to find the value of one part of the ratio.
$414 × [tex]\frac{3}{46}[/tex] = $27 ← value of 1 part of the ratio, then
[tex]\frac{10}{3}[/tex] × $27 = $90
5 × $27 = $135
7 × $27 = $189
The 3 parts are $90, $135, $189
Need correct answer ASAP please
Answers
Answer:
C = 16pi
Step-by-step explanation:
Since we are evaluating for the circumference, we plug in the r. Since r=8, we get 2*pi*8 or 16pi.
answer should be C gl btw
Anyone know the answer? Much appreciate the help!!
Answers
Answer:
[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex] and [tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]
Step-by-step explanation:
we have
[tex]L=\frac{1} {\sqrt{x^2-6x + 5}}[/tex]
Solve for x
That means-----> isolate the variable x
squared both sides
[tex]L^{2} =(\frac{1} {\sqrt{x^2-6x + 5}})^{2}\\ \\L^{2}=\frac{1} {{x^2-6x + 5}}\\ \\x^2-6x + 5=\frac{1}{L^{2}}\\ \\x^2-6x=\frac{1}{L^{2}}-5\\ \\x^2-6x+9=\frac{1}{L^{2}}-5 +9\\ \\x^2-6x+9=\frac{1}{L^{2}}+4\\ \\(x-3)^2=\frac{4L^{2}+1}{L^{2}}[/tex]
Take the square root both sides
[tex](x-3)=(+/-)\sqrt{\frac{4L^{2}+1}{L^{2}}}\\ \\x=3(+/-)\frac{\sqrt{4L^{2}+1}}{L} [/tex]
therefore
[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex]
[tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]
Write an equation for the line parallel to the given line that contains C.
Cleft parenthesis 3 comma 6 right parenthesis; y equals negative 4 x plus 5
Answers
ANSWER
[tex]y= - 4x + 18[/tex]
EXPLANATION
The given line has equation;
[tex]y = - 4x + 5[/tex]
The slope of this line is
-4
The given line is parallel to this line so it has the same slope:
[tex]m = - 4[/tex]
The equation of this line is in the form:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the slope and the point:
(3,6)
[tex]y-6= - 4(x-3)[/tex]
[tex]y= - 4x + 12+ 6[/tex]
[tex]y= - 4x + 18[/tex]
Please help and thank you
Answers
Answer:
(3, 2)
Step-by-step explanation:
Given a graphical representation of a system of equation then the solution is at the point of intersection of the 2 lines, that is
solution is ( 3, 2)
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
Answers
I think this is the answer X = 3 + 1/2y
The solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
To solve the system of equations[tex]\(x^2 + y^2 = 6\)[/tex] and [tex]\(x^2 - y = 6\)[/tex], we can use substitution or elimination method. Let's solve it using the substitution method:
Given equations:
1.[tex]\(x^2 + y^2 = 6\)[/tex]
2.[tex]\(x^2 - y = 6\)[/tex]
From equation 2, we can express [tex]\(x^2\) as \(y + 6\):[/tex]
[tex]\[x^2 = y + 6\][/tex]
Now, substitute [tex]\(x^2 = y + 6\)[/tex] into equation 1:
[tex]\[y + 6 + y^2 = 6\][/tex]
Rearrange this equation:
[tex]\[y^2 + y + 6 = 6\][/tex]
Subtract 6 from both sides:
\[y^2 + y = 0\][tex]\[y^2 + y + 6 = 6\][/tex]
Factor out y:
[tex]\[y(y + 1) = 0\][/tex]
So, either [tex]\(y = 0\)[/tex] or [tex]\(y + 1 = 0\)[/tex] , which means[tex]\(y = 0\)[/tex] or [tex]\(y = -1\).[/tex]
Now, substitute these values of y back into equation 2 to find the corresponding values of x.
For [tex]\(y = 0\):[/tex]
[tex]\[x^2 - 0 = 6\][/tex]
[tex]\[x^2 = 6\][/tex]
[tex]\[x = \pm \sqrt{6}\][/tex]
For [tex]\(y = -1\):[/tex]
[tex]\[x^2 - (-1) = 6\][/tex]
[tex]\[x^2 + 1 = 6\][/tex]
[tex]\[x^2 = 5\][/tex]
[tex]\[x^2 = 5\][/tex]
So, the solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
The system has four solutions: [tex]\((\sqrt{6}, 0)\), \((- \sqrt{6}, 0)\), \((\sqrt{5}, -1)\), and \((- \sqrt{5}, -1)\).[/tex]
Complete question:
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
Reduce to simplest form. -3/5 + 1/3=
Answers
Answer:
-4/15 (Fraction form) -0.26... (Decimal form)
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
when you add the numerators which are, -3 and 1, you'd end up with -2.
when you add the denominators which are, 5 and 1, you'd end up with 6.
so that would give you -2/6.
when you simplify that you end up with -1/3.
Over the weekend, Brady and Jack drove to Key West to go scuba diving. Novw they're preparing to go home. Brady needs gas for his jeep, which gets 21 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.40 per gallon
Answers
Answer:
(I'm guessing the question is asking how much money Brady needs to pay.)
Step-by-step explanation:
21-5
(the original amount minus the 5 gallons he already has)
= 16.
so Brady needs 16 gallons.
and every gallon is 1.4
so 16 * 1.4
= 22.40
So brady needs 22.40 dollars.
The total cost of 16 gallons of gas is $22.4.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 21 miles per gallon for gas mileage.
When he stops at the gas station, he already has 5 gallons of gas in his tank.
So, 21-5=16 miles
He buys gas for $1.40 per gallon
Now, total cost = 16×1.40
= $22.4
Therefore, the total cost of gas is $22.4.
To learn more about the unitary method visit:
brainly.com/question/22056199.
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A sphere has a volume of 500/3 π cubic centimeters. What is the total surface area , in square centimeters, of the sphere
Answers
Answer:
[tex]\large\boxed{S.A.=100\pi\ cm^3\approx314\pi\ cm^2}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have
[tex]V=\dfrac{500}{3}\pi\ cm^3[/tex]
Substitute and solve for R:
[tex]\dfrac{500}{3}\pi=\dfrac{4}{3}\pi R^3[/tex] divide both sides by π
[tex]\dfrac{500}{3}=\dfrac{4}{3}R^3[/tex] multiply both sides by 3
[tex]500=4R^3[/tex] divide both sides by 4
[tex]125=R^3\to R=\sqrt[3]{125}\\\\R=5\ cm[/tex]
The formula of a Surface Area os a sphere:
[tex]S.A.=4\pi R^2[/tex]
Substitute:
[tex]S.A.=4\pi(5^2)=4\pi(25)=100\pi\ cm^2[/tex]
[tex]\pi\apprx3.14\to S.A.\approx(100)(3.14)=314\ cm^2[/tex]
ebony wants to buy a dvd player and dvds the equation relates the total cost for dvds and dvd player and N dvds is p=20n+200 what does the number 200 in the equation represent
Answers
____________________________________________________
Answer:
It represents the cost of the DVD player.
____________________________________________________
Step-by-step explanation:
The reason why it represents the cost of the DVD player is because in the question, it doesn't mention anything about buying multiple DVD players. Ebony would need to buy many DVD's, but doesn't need many DVD players because ebony could use one for all of the DVD's. If you noticed in the question, it says "a DVD player," what this means is that Ebony is only going to buy one DVD player, since it's singular (without and s at the end).
The equation is saying that she starts off with buying 1 DVD player for 200 dollars; and, she is buying n (number of DVDs) for 20 dollars each.
This shows that the 200 in the equation in the question represents the cost of the DVD player.
____________________________________________________
A talk driver charges $3.50 per mile driver gives a 10mile ride a 5.5 mile ride and a 19 mile ride.he then spends $50 to fill up the gas tank before giving a final ride of 26 miles write a numeric expression to represent the dollar in amounts the driver had after each action in order.then find out how much money he had after the last ride if he started with $0
Answers
Answer:
3.50×10 +3.50×5.5 +3.50×19 -50 +3.50×26$161.75Step-by-step explanation:
You want an expression representing the cash flow of a taxi driver after giving three rides, filling the gas tank, then giving one more ride.
Income per rideAt $3.50 per mile, the driver will have income that is $3.50 multiplied by the number of miles for the ride. These income amounts are added.
OutflowA payment of $50 for gas is subtracted from the driver's income.
Net incomeThe desired expression is ...
3.50×10 +3.50×5.5 +3.50×19 -50 +3.50×26
The value of the expression is $161.75.
The driver had $161.75 after the last ride.
Which reason for step 4 completes the proof?
Prove: -(a + b) + a = -b
Answers
Answer:
Identity Property of Addition.
Answer:
Reason which completes the proof of step 4 is:
Identity property of addition
Step-by-step explanation:
-(a+b)+a= -b
= -a+ (-b)+a (distributive property)
= -a+a+(-b) (Commutative property of Addition)
= 0+ (-b) (Additive inverse property)
= -b (Identity property of addition)
(Identity property of addition says that if 0 is the identity element and a is any element
Then, a+0=0+a=a)
So, reason which completes the proof of step 4 is:
Identity property of addition
Evaluate the expressions for x=6 3x +5= ? X^3-10=?
Answers
Answer:
x^3-10 is greater
Step-by-step explanation:
3(6)+5=18+5=23
6^3-10=206
206>23
determine where f(x) = g(x) by graphing HELP PLEASE!!
Answers
Answer:
C: x=-4
Step-by-step explanation:
I would suggest using the website desmos.com to help you graph your equations.
As shown on the graph I posted, f(x)=g(x) at x=-4
Answer:
Step-by-step explanation:
Given are two functions f(x) and g(x)
[tex]f(x) = \frac{2}{x+3} +1\\[/tex]
and
[tex]g(x) = -|x+3|[/tex]
The two would be equal if
[tex]\frac{2}{x+3} +1=x+3 or -x-3\\\frac{2}{x+3} =x+2 /-x-4\\2=x^2+5x+6/-(x^2+7x+12)\\x^2+5x+6=0 / x^2+7x+14=0[/tex]
x=-4 or -1
Of these x=-4 is consistent as when x=-4, x<-3 hence
|x+3|= 1
So answer is -4
1 3/5(t-6)=-0.4 solve the equation
Answers
To solve the equation 1 3/5(t-6)=-0.4, first distribute 1 3/5 to the terms inside the parentheses. Then, multiply both sides of the equation by the reciprocal of 8/5 to isolate the variable t. Finally, simplify the equation to find the solution t = 5.75.
Explanation:To solve the equation 1 3/5(t-6)=-0.4, we can follow these steps:
Distribute 1 3/5 to the terms inside the parentheses. This gives us 8/5(t-6)=-0.4.Multiply both sides of the equation by the reciprocal of 8/5, which is 5/8, to cancel out the coefficient on the variable. This gives us t-6 = -0.4 * 5/8.Simplify the equation by multiplying and dividing as necessary. This gives us t-6 = -0.25.Add 6 to both sides of the equation to isolate the variable t. This gives us t = -0.25 + 6.Simplify the equation to find the final solution. This gives us t = 5.75.Therefore, the solution to the equation is t = 5.75.
Final answer:
To solve the equation 1 3/5(t-6)=-0.4, distribute the 1 3/5 first and then simplify the equation by adding and subtracting terms to isolate t. The final solution is t = 2.
Explanation:
To solve the equation 1 3/5(t-6)=-0.4, we can begin by distributing the 1 3/5 to the terms inside the parentheses:
1 3/5(t-6) = 1 3/5 * t - 1 3/5 * 6 = 8/5t - 18/5
Now, we can rewrite the equation as:
8/5t - 18/5 = -0.4
Next, we can get rid of the fraction by multiplying both sides of the equation by 5:
5(8/5t - 18/5) = 5(-0.4)
After simplifying, we get:
8t - 18 = -2
Now, add 18 to both sides of the equation:
8t - 18 + 18 = -2 + 18
Simplifying further, we have:
8t = 16
Finally, divide both sides of the equation by 8 to solve for t:
t = 16/8
Therefore, the solution to the equation is t = 2.
The line plot shows amount of miles students ran in a week. What is the difference in the lowest miles and the highest miles run in a week? A) 1 1/2 B) 1 1/4 C) 1 3/4 D) 3/4
Answers
Answer:
C
Step-by-step explanation:
There are 4 lines in between 2 consecutive integers, so each division is:
1/4 = 0.25
As we see from the graph, the highest miles is at the division before 2, which is 1.75
Also, the lowest miles is at 0.
Hence, difference in highest and lowest is 1.75 - 0 = 1.75
In fraction, [tex]1.75=1\frac{3}{4}[/tex]
correct answer C
Write all the factors of 35
.
Use commas to separate them.
Answers
Factors of 35 :
1, 5, 7, 35
Answer:
1,5
Step-by-step explanation:
Identify the length of line BP
A) 9.75
B) 6.75
C) 15.75
D) 9
Answers
Answer:
I believe the answer is c because 4.5 can fit in BP almost 4 times so it is most accurate sorry if I'm wrong
What is formula for following geometric sequence -5,-10,-20,-40
Answers
Answer:
x = -5 * (2)^(n-1)
Step-by-step explanation:
If we look a the supplied n elements of the sequence, and we divide each of them by -5.
1 = -5, -5/-5 = 1
2 = -10, -10/-5 = 2
3 = -20, -20/-5 = 4
4 = -40, -40/-5 = 8
We realize that we have all the powers of 2 there.
So the formula will start with -5 (the first element), then multiplied by a power of 2.
[tex]x = -5 (2)^{n-1}[/tex]
We can verify for the 4th element, where n = 4:
[tex]x = -5 (2)^{n-1} = -5 (2)^{4-1} = -5 (2)^{3} = -5 * 8 = -40[/tex]
Answer:
x = -5 * (2)^(n-1)
Step-by-step explanation:
The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. When this is true, you can use the formula for a sphere to find their volume.
The green turtle lays eggs that are approximately spherical with an average diameter of 4.1 centimeters. Each turtle lays an average of 113 eggs at one time. Find the volume of one egg, rounding your answer to the nearest tenth of a cubic centimeter. Then find the total volume of these eggs, to the nearest tenth of a cubic centimeter
Answers
The eggs are approximately 2.1 and which each turtle does not lay 113 they lay 123 eggs each year around which you subtract it all up and it comes out to 120.9.then the you divide all up which gives you your answer to your problem.
Final answer:
The volume of one spherical green turtle egg with a diameter of 4.1 cm is approximately 36.2 cubic centimeters. The total volume of 113 such eggs is about 4091.6 cubic centimeters when rounded to the nearest tenth.
Explanation:
To calculate the volume of one green turtle egg, we use the formula for the volume of a sphere, which is V = 4/3 πr³, where r is the radius of the sphere. Since the egg has a diameter of 4.1 centimeters, the radius is half of that, which is 2.05 centimeters. Plugging this value into the formula gives us V = 4/3 π(2.05 cm)³ ≈ 36.2 cubic centimeters when rounded to the nearest tenth.
Next, we calculate the total volume of eggs laid by one turtle. Since each turtle lays 113 eggs, the total volume is 113 × 36.2 cm³ = 4091.6 cm³, which rounds to 4091.6 cubic centimeters.
Solve the inequality. Graph the solution . -1.6 < m/-2.5
Answers
Required sοlutiοn of inequality οf -1.6 < m/-2.5 is m < 4
Here given,
We can begin by multiplying bοth sides οf the inequality by -2.5:
[tex]$-1.6\lt \sm < {\frac{m}{-2.5}}$[/tex]
Sο the sοlutiοn tο the inequality is m < 4.
[tex]$\begin{array}{l}{{\rm -1.6 < \dfrac{m}{-2.5}}}\\\\ {{\rm -1.6\times\left(-2.5\right) \gt > m}}\\\\ {{\rm 4\gt > m}}\end{array}$[/tex]
Tο graph this sοlutiοn, we can plοt a number line with an οpen circle at 4, since m is nοt equal tο 4. Then we shade the part οf the number line tο the left οf 4, indicating all values οf m that satisfy the inequality.
The graph shοws that all values οf m tο the left οf 4, including 4 itself, satisfy the inequality.
Learn more about Inequality :
brainly.com/question/30238989
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To solve the inequality -1.6 < m/-2.5, we multiply both sides by -2.5 and reverse the inequality sign, resulting in m being less than 4. This solution can be graphed on a number line with an open circle at 4 and shading to the left.
Explanation:To solve the inequality -1.6 < m/-2.5, we need to manipulate the inequality to isolate the variable m.
First, multiply both sides of the inequality by -2.5 to get m by itself. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. So:
The inequality now reads as m is less than 4.To graph this solution, draw a number line and make an open circle at 4, indicating that 4 is not included in the solution. Then, shade everything to the left of 4 to represent all the numbers that are less than 4.
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 35 years old, with a standard deviation of 10 years.
If you were to take a sampling of 10 employees, what is the probability your mean age will be at least 37? Round to the nearest percent.
Answers
Answer:
The probability your mean age will be at least 37 is approximately 26%
Step-by-step explanation:
Let X denote the ages of all new employees hired during the last 10 years , then X is normally distributed with;
a mean of 35
a standard deviation of 10.
The sample size obtained is 10 employees. This implies that the sampling distribution of the sample mean will be normal with;
a mean of 35
a standard deviation of [tex]\sqrt{10}[/tex]
The sample mean is a statistic and thus has its own distribution. Its mean is equal to the population mean, 35 and its standard deviation is equal to [tex]\frac{sigma}{\sqrt{n} }[/tex]
where sigma is the population standard deviation, 10 and n the sample size which in this case is 10. [tex]\frac{10}{\sqrt{10} }=\sqrt{10}[/tex]
We are required to find the probability that this sample mean age will be at least 37;
P(sample mean ≥ 37)
Since we know the distribution of the sample mean we simply standardize it to obtain the z-score associated with it;
P(sample mean ≥ 37)
=[tex]P(Z\geq \frac{37-35}{\sqrt{10} })=P(Z\geq0.6325)=1-P(Z<0.6325)[/tex]
=1 - 0.7365 = 0.2635
=26%
A logarithmic function is an appropriate model because, for evenly spaced y-values, the ___ of consecutive x-values is constant.
Answers
Answer:
Ratio.
Step-by-step explanation:
A logarithmic function is an appropriate model because, for evenly spaced y-values, the ratio of consecutive x-values is constant. This is the correct answer to your question.
Hope this helps!!!
Kyle.
Answer:
Step-by-step explanation:
Whenever a function is logarithmic function, we get for evenly spaced y,
say y = log x
y+d = log x1
y+2d = log x2
We get
d = [tex]log \frac{x_1}{x} =log \frac{x_2}{x_1}[/tex]
In other words we get the ratios of consecutive x values is constant equal to the difference in consecutive y's.
The seniors on the student council bought a total of 36 plants to use in landscaping the front of the school. They bought some azaleas that cost $6 each and some lilies that cost $5 each. They spent a total of $196 on these plants. How many azaleas did the students buy?
a.) 18
b.) 16
c.) 20
d.) 5
Answers
Answer: B
Step-by-step explanation:
y = azaleas
x = lilies
6y + 5x =196 total cost
y + x = 36 total number of items
y = 36 – x
6(36 -x ) +5x =196
216 – 6x + 5x = 196
-x = 196 – 216
-x = -20
Divide by -1
X = 20 lilies
Plug into y equation
Y = 36 – 20
Y= 16 azaleas
To check
6(16) + 5(20) = 196
96 + 100 = 196
The answer is b 16 because you add the variables into the end of the numbers to identify you answer
Which number is an irrational number?
Answers
Answer
Square root 15
Step-by-step explanation:
When you square root the number 15 it will give you a decimal number with a lot of numbers that can't be rationalized. However the square root of 25 can be seen as 5, 1.15 is a rationalized number, 4th option can be seen 1.255555555... which is still rational.
express with positive exponents
Answers
Answer:
2b^2
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5a^4
Step-by-step explanation:
2a^-4
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5b^-2
Negative exponents go to the denominator when they are in the numerator
and to the numerator when they are in the denominator
a^-4 becomes 1/a^4
1/b^-2 becomes b^2
2/5 * 1/a^4 * b^2
2*b^2 * 1/5a^4
Rewriting
2b^2
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5a^4