Answers
Answer:
12a^3 b^4 c^5
Step-by-step explanation:
First you rewrite 144a^6 b^8 c^10 as (12a^3 b^4 c^5)^2.Pull terms out from under the radical, assuming positive real numbersRelated Questions
Two cylinders, a and b are created cylinder a has volume v culinder b has the same height as a cylinder be has half the width of cylinder a write an expression that represents the volume of cylinder b in terms of v
Answers
Answer:
v/4
Step-by-step explanation:
Volume of cylinder a = v
Let the height of cylinder a is h and its radius is r. The volume of cylinder a will be:
[tex]v=\pi r^{2}h[/tex]
Height of cylinder b is same as cylinder a. So height of cylinder b is h.
Radius of cylinder b is half of radius(width) of cylinder a. So radius of cylinder b will be r/2
The volume of cylinder b will be:
[tex]v^{'}=\pi (\frac{r}{2} )^{2}h\\\\ v^{'}=\pi(\frac{r^{2}}{4})h \\\\ v^{'}=\frac{\pi r^{2}h}{4} \\\\ v^{'} = \frac{v}{4}[/tex]
Thus the volume of cylinder b will be v/4
Answer:
The volume of cylinder A is four times the volume of cylinder B.
Step-by-step explanation:
count me brainliest
what are the domain and range of the function?
y=2√3x+4-5
A. x ≥ -4/3; y ≥ -5
B. x ≥ 4/3; y ≥ - 5
C. x ≤ -4/3; y ≤ -5
D. x ≥ -4/3; y ≤ -5
Answers
√(3x+4)≥0 (otherwise it becomes imaginary)
3x+4≥0
3x≥-4
x≥-4/3
Y=2(0)-5 (it's the lowest x value, and that means it will limit y)
Y=-5
As x can be > -4/3, let's try for another Y value
Y=2√(3(5/3)+4)-5
Y=2√9-5
Y=6-5
Y=1
1>-5
So, Y≥-5
Answer is A
The school fun fair made $ 1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales
Answers
Simplify the expression. 5 + 10 – 2 • 3 9 39 29 19
Answers
Answer:
9
Step-by-step explanation:
Orders of operation tells us we have to multiply or divide first, whichever one comes first from left to right; then we add or subtract from left to right. It looks like we have a 2*3 which is 6. That changes our expression to
5 + 10 - 6,
which is 15 - 6 which is 9
All of the angles are exterior angles EXCEPT:
Answers
Answer:
Step-by-step explanation:
XYZ
The first one
I hope I helped you.
In the figure, is tangent to the circle at point U. Use the figure to answer the question.
Describe the relationship among the lengths of the segments formed by the secant RT, and the tangent Suppose RT=16 in. and ST=4 in. Find the length of . Show your work.
Answers
Answer:
The length of TU is [tex]8\ in[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem states that, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
in this problem
[tex]TU^{2}=RT*ST[/tex]
we have
[tex]RT=16\ in[/tex]
[tex]ST=4\ in[/tex]
[tex]TU^{2}=(16)(4)[/tex]
[tex]TU^{2}=64[/tex]
[tex]TU=8\ in[/tex]
Suppose x has a distribution with μ = 40 and σ = 12. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μ x = 40 and σ x = 0.8. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 3. No, the sample size is too small. Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 40 and σ x = 3. Yes, the x distribution is normal with mean μ x = 40 and σ x = 12. Yes, the x distribution is normal with mean μ x = 40 and σ x = 0.8.
Answers
Answer:
a: no the sample size is too small
b: Yes, the distribution is normal with a mean of 40 and standard deviation of 12
Step-by-step explanation:
a: If n < 30, we need to know that the sample is normally distributed or else we can't determine anything. When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed
b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population
Dylan work for 4 hours and is paid 17.50 per hour he must pay 15% in income taxes what amount does he earn after taxes
Answers
Dylan earns $17.50 per hour for 4 hours, yielding a total income of $70. After deducting 15% of his total earnings ($10.50) for income taxes, Dylan's earnings reduce to $59.50.
Explanation:To answer this question, we first need to calculate Dylan's total earnings before taxes. He earned $17.50 per hour for 4 hours, so his total earnings would be 4 hours * $17.50/hour = $70.
Next, we determine the amount of income tax. Dylan's income tax rate is 15%, so he would pay 15% of his total earnings in taxes: 15/100 * $70 = $10.50 in taxes.
Finally, we calculate Dylan's net earnings after tax by subtracting the tax amount from his total earnings: $70 - $10.50 = $59.50. Therefore, Dylan will earn $59.50 after taxes for 4 hours of work.
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Dylan earns $59.50 after taxes.
Explanation:To calculate the amount Dylan earns after taxes, we need to first find out his total earnings before taxes.
Dylan works for 4 hours and is paid $17.50 per hour, so his total earnings before taxes are 4 hours multiplied by $17.50, which is $70.
Next, we need to calculate the amount of income tax Dylan needs to pay. He must pay 15% of his total earnings as income taxes, which is 15% of $70, which is $10.50.
To find out how much Dylan earns after taxes, we subtract the income tax amount from his total earnings,
so $70 - $10.50 = $59.50.
Therefore, Dylan earns $59.50 after taxes.
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Two small pizzas with diameter 10 cost $15, while a large pizza with diameter of 16 cost $17 which pizza is less expensive per square inch
Answers
Answer:
The larger pizza is less expensive per square inch
Step-by-step explanation:
we know that
The area of a circle (pizza) is equal to
[tex]A=\pi r^{2}[/tex]
step 1
Find the area of the smaller pizza
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(5)^{2}=78.5\ in^{2}[/tex]
Find the price per square unit
Remember that
The price of one smaller pizza is [tex]\$15/2=\$7.5[/tex]
so
[tex]\frac{7.5}{78.5}\frac{\$}{in^{2}}=0.10\frac{\$}{in^{2}}[/tex]
step 2
Find the area of the larger pizza
we have
[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=(3.14)(8)^{2}=200.96\ in^{2}[/tex]
Find the price per square unit
so
[tex]\frac{17}{200.96}\frac{\$}{in^{2}}=0.08\frac{\$}{in^{2}}[/tex]
Therefore
The larger pizza is less expensive per square inch
Use the limit theorem and the properties of limits to find the limit.
Answers
Answer:
The answer is √3/4 ⇒ answer (d)
Step-by-step explanation:
∵ [tex]\lim_{n \to \infty} \frac{\sqrt{3x^{2}+2} }{4x+1}[/tex]
* By using the limit theorem: divide up and down by x
∵ x = √x²
∴ [tex]\sqrt{\frac{3x^{2} }{x^{2}}+\frac{2}{x^{2}}[/tex] =
[tex]\sqrt{3+\frac{2}{x^{2}}[/tex] ⇒ numerator
∵ [tex]\frac{4x}{x}+\frac{1}{x}=4+\frac{1}{x}[/tex] ⇒ denominator
∵ x →∞ ⇒ ∴ 2/x² = 2/∞ = 0 and 1/x = 1/∞ = 0
∴ [tex]\lim_{x \to \infty}\frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}=\frac{\sqrt{3}}{4}[/tex]
∴ The answer is √3/4 ⇒ (d)
The answer is: [tex]d.\frac{\sqrt{3} }{4}[/tex]
Why?Since the degree of both numerator and denominator are the same, the result will be a number different of zero, so the first given option (a) it's incorrect.
We need to "break" the indeterminate form of the limit in order to find the correct answer.
To solve this limit, we must divide each term by the largest degree term, for this case is "x" since the numerator is inside of a square root.
So, doing it we can solve the limit:
[tex]\lim_{x \to \infty}\frac{\sqrt{\frac{3x^{2} }{x^{2} }+\frac{2}{x^{2}}}}{\frac{4x}{x}+\frac{1}{x}}\\\\ \lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}[/tex]
Then, before evaluating the limit, we must remember that any number divided by infinity will give as result zero (0), so:
[tex]\lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{(infinity)^{2}}}}{4+\frac{1}{infinity}}\\\\\lim_{x \to \infty} \frac{\sqrt{3+0}}{4+0}=\frac{\sqrt{3} }{4}[/tex]
So, the correct option is: [tex]d.\frac{\sqrt{3} }{4}[/tex]
Have a nice day!
You choose at random from letters a,b,c, and d, and you roll a number cube once. What are your chances you get a and 5
Answers
Answer:
your answer is 10! please mark brainliest :))))))
Step-by-step explanation:
The volume of a rectangular prism has a volume of 42 cubic units the length is 3 units the width is 2 units what is the height
Answers
Answer: the answer is 7
Step-by-step explanation: 42/3=14 14/2=7 hope this helps
The value of the height will be 7 units.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The volume of a rectangular prism = 42 cubic units
And, The length is 3 units ,the width is 2 units.
Now,
Since, We know that;
⇒ Volume of rectangle = Length x Width x Height
Let height of a rectangular prism = x
Hence, we get;
⇒ Volume of rectangle = Length x Width x Height
⇒ Volume of rectangle = 3 × 2 × x
⇒ 42 = 6x
⇒ x = 42 / 6
⇒ x = 7 units
Thus, The value of the height will be 7 units.
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Use the graph of the function f to determine the given limit
Answers
Answer: b. 3
Step-by-step explanation:
The limit of the function as it approaches -3 from the left is 3.
The limit of the function as it approaches -3 from the right is 3.
Since the limit from the left equals limit from the right, then the limit of the function exists and is 3.
Answer: 3, or b
Step-by-step explanation:
The rule that it comes from both the right and the left and meets at a common point verifies this.
Tell whether this set of numbers is a Pythagorean Triple. (6, 9, 12) Yes or no?
Answers
No it’s not a Pythagorean triple
Team A has nine more points than team B. Team A has four times as many points as team B. Dose anyone know the answe?
Answers
Team A is the correct answer
Answer:
Team A has 12 points , Team B has 3
Step-by-step explanation:
The price of a hat is $27.When it goes on sale, it wll be 1/3.How much would you save if you were to buy ti on sale
Answers
Answer:
You would save $18
Step-by-step explanation:
(27/3)*2 = $18
Which quadrilateral with side lengths shown will have a perimeter of 20 meters? 6 m, 5 m, 4 m, 6 m 7 m, 4 m, 4 m, 6 m 3 m, 7 m, 3 m, 7 m 6 m, 3 m, 5 m, 5 m NEXT
Answers
Answer:
3 m, 7 m, 3 m, 7 m
Step-by-step explanation:
The perimeter is the sum of the side lengths, so the perimeters of your quadrilaterals are ...
6 m + 5 m + 4 m + 6 m = 21 m . . . . ≠ 20 m
7 m + 4 m + 4 m + 6 m = 21 m . . . . ≠ 20 m
3 m + 7 m + 3 m + 7 m = 20 m . . . . . This is it!
6 m + 3 m + 5 m + 5 m = 19 m . . . . ≠ 20 m
The quadrilateral with side lengths of 3 m, 7 m, 3 m, and 7 m will have a perimeter of exactly 20 meters, as the sum of these side lengths is 20 meters.
To determine which quadrilateral with the given side lengths will have a perimeter of 20 meters, we need to add the lengths of all the sides for each option and see which one totals 20 meters.
For the first option (6 m, 5 m, 4 m, 6 m), the sum is 6 + 5 + 4 + 6 = 21 meters.
The second option (7 m, 4 m, 4 m, 6 m), the sum is 7 + 4 + 4 + 6 = 21 meters.
The third option (3 m, 7 m, 3 m, 7 m), the sum is 3 + 7 + 3 + 7 = 20 meters.
The fourth option (6 m, 3 m, 5 m, 5 m), the sum is 6 + 3 + 5 + 5 = 19 meters.
Therefore, the quadrilateral with sides measuring 3 m, 7 m, 3 m, and 7 m will have a perimeter of 20 meters.
Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)
Answers
Answer: Option a.
Step-by-step explanation:
To solve the given exercise, you must keep on mind the law of logarithms shown below:
[tex]log(a)-log(b)=log(\frac{a}{b})[/tex]
Therefore, by applying the law , you can rewrite the expression given, as following:
[tex]log(\frac{5}{7})=log(5)-log(7)[/tex]
You know that:
[tex]log5=0.6990\\log7=0.8451[/tex]
Then, when you substitute values, you obtain:
[tex]0.6990-0.8451=-0.1461[/tex]
Use the quotient rule [ [tex]\text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay[/tex] ] to simplify.
[tex]\text{log}\frac{5}{7} = \text{log}(5)-\text{log}(7)[/tex]
Simplify using the given values.
0.6990 - 0.8451
-0.1461
Therefore, [tex]\text{log}\frac{5}{7}=-0.1461[/tex]
Best of Luck!
The angle of elevation from a soccer ball on the ground to the top of the goal is 38 degrees. If the goal is 8 feet tall, what is the distance from the ball to the goal?
Answers
Answer:
The distance is 10.24 feet ( to the nearest hundredth).
Step-by-step explanation:
Use trigonometry of a right angled triangle:
The angle = 38 degrees, opposite side = 8 ft, we require the adjacent side: We have opposite / adjacent side so we need the tangent.
tan 38 = 8 / a
a = 8 / tan 38
= 10.24 feet.
Please help me out :)
Answers
180-124=56
56/2=28
Ans 28
B is the midpoint of AC if AB equals X +5 and BC equals 2X -11 find the measure of AB
Answers
Answer:
AB = 21
Step-by-step explanation:
The midpoint divides the segment into two congruent parts, so you have ...
AB = BC
x +5 = 2x -11 . . . substitute the given expressions for AB and BC
16 = x . . . . . . . . add 11-x
Then the measure of AB is ...
AB = x +5 = 16 +5 = 21
A chef used 1/9 of a bag of potatoes for a meal. If the potatoes fed 5 people. What fraction of the bag did each person get
Answers
1/9 has to be divided by 5 if it is shared by others.
1/9 divided by 5 is 1/45 and each person would have 1/45
Answer is 1/45
Leslie needs 48 ounces of charcoal for her grill.How many pounds of charcoal should she buy?
Answers
Leslie needs to divide 48 ounces by the conversion factor of 16 ounces per pound to find out she needs 3 pounds of charcoal for her grill.
Leslie is seeking to understand how much charcoal she should purchase in pounds if she needs 48 ounces for her grill. Since the question involves converting ounces to pounds, we can use the conversion factor that 1 pound is equal to 16 ounces. To find out how many pounds are in 48 ounces, we divide 48 by 16.
48 ounces divided by 16 ounces per pound equals 3. Therefore, Leslie will need to buy 3 pounds of charcoal for her grill.
What is the value of X in the triangle below? if the answer is not an integer, leave it in simplest radical form
Answers
Answer:
[tex]x=\frac{13\sqrt{2} }{2}[/tex]
Step-by-step explanation:
We can use the sine ratio to find the value of [tex]x[/tex].
Recall the mnemonics SOH; which means sine is Opposite over Hypotenuse.
[tex]\sin(45\degree)=\frac{x}{13}[/tex]
This implies that;
[tex]x=13\sin(45\degree)[/tex]
[tex]x=\frac{13\sqrt{2} }{2}[/tex]
What is the equation of a circle whose center is begin ordered pair negative 4 comma 6 end ordered pair and whose radius is 9 cm? Question 1 options: open parentheses x minus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 81 open parentheses x plus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 3 open parentheses x plus 4 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 81 open parentheses x minus 4 close parentheses squared plus open parentheses y plus 6 close parentheses squared equals 3
Answers
Answer:
[tex](x+4)^2+(y-6)^2=81[/tex]
Step-by-step explanation:
We want to find equation of a circle with center (-4,6) and radius 9cm.
The equation of a circle with center (h,k) and radius [tex]r[/tex] units is given by;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the radius and the center to obtain;
[tex](x+4)^2+(y-6)^2=9^2[/tex]
The required equation is:
[tex](x+4)^2+(y-6)^2=81[/tex]
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit?
Answers
Answer:
a) 11.51%; b) 13 minutes
Step-by-step explanation:
We will use a z score to answer these questions. The formula for a z score is
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For part a, X is 20, the mean is 17 and the standard deviation is 2.5:
z = (20-17)/2.5 = 3/2.5 = 1.2
Using a z table, we see the area to the left of, or less than, this value is 0.8849; this means the area to the right of, or greater than, is 1-0.8849 = 0.1151. This means 11.51% of people have a time greater than 20 minutes and get half off.
For part b, we start out in the z table finding values as close to 5%, or 0.05, as possible. There are two possibilities, 0.0505 (z=-1.64) and 0.0495 (z=-1.65). Since they are equally distant from the desired value, we will use -1.645 for z. Our values for the mean and standard deviation are the same:
-1.645 = (X-17)/2.5
Multiply both sides by 2.5:
2.5(-1.645) = ((X-17)/2.5)(2.5)
-4.1125 = X-17
Add 17 to each side:
-4.1125+17 = X-17+17
12.8875 = X
This means the garage should make the guaranteed time no more than 13 minutes.
Which two points are on the graph of y=x - 4?
(1, -3), (-1, -5)
(1, 5), (0, -4)
(0, -4), (4, 1)
(4, 0), (1, 3)
Answers
Replace x with the value in the answers and solve for Y to see which ones match.
y = 1-4 = -3
y = -1-4 = -5
(1,-3), (-1,-5) is the answer.
The length of a rectangle is three times it's width. If the perimeter of the rectangle is 64, find its length and width
Answers
set up an equation for the perimeter
l = length w = width
2l + 2w = 64
set up another equation as you know the length is 3 times the width
w = 3l
subsitute w = 3l into the 2l + 2w = 64
2l + 2(3l) = 64
solve for l
2l + 6l = 64
8l = 64
length = 8
subsitute into w = 3l
w = 3(8)
width = 24
Adam says that the expression 52 - 3y is equal to 20 when y = 2 explain why Adams awnswe is incorrect
Answers
Answer:
y=10.33333333333
Step-by-step explanation:
52-3y=20
52-20=3y
3y=32
y=10.3333
In london, 1 litre of petrol costs 108.9p In Ney York, 1 US gallon of petrol costs $2.83 1 US gallon = 3.785 litres ?1= $1.46 In which city is petrol better value for money, London or New York? You must show your working.
Answers
Answer:
In London it cost $ 6.017 while in Newyork it cost $2.831
so NewYork is cheaper
Step-by-step explanation:
As we know, 1 US gallon = 3.785 liters
so,converting liters into gallon = 1.089 * 3.785
= 4.121 per gallon
Cost of 4.121 gallon petrol in dollars = 4.121 * 1.46
= $ 6.017
In London it cost $ 6.017 while in Newyork it cost $2.831
so NewYork is cheaper
Final answer:
Petrol is better value for money in New York, where it costs approximately £0.512 per litre after converting from USD to GBP and gallons to litres, compared to £1.089 per litre in London.
Explanation:
To determine where petrol is better value for money, we need to compare the cost per litre in both London and New York, taking into account the exchange rate and units of measure. First, let's convert the cost of petrol in New York from gallons to litres:
The cost of 1 US gallon of petrol in New York is $2.83.1 US gallon is equivalent to 3.785 litres. So to find the cost per litre we divide $2.83 by 3.785 litres: $2.83 / 3.785 litres = $0.748 per litre.Next, we'll convert the cost from dollars to pounds using the given exchange rate of £1 = $1.46. So $0.748 multiplied by the exchange rate: $0.748 / $1.46 = £0.512 per litre.Now, let's compare it to the cost in London:
The cost of petrol in London is 108.9p per litre, which is equivalent to £1.089 per litre.Comparing the two:
London: £1.089 per litreNew York: £0.512 per litreTherefore, the petrol is better value for money in New York as £0.512 per litre is less than £1.089 per litre.