Answer:
The answer would be 18484.2883549
Step-by-step explanation:
Firstly, you'll simplify 10².
10²÷0.00541 ---> 100 ÷ 0.00541
Then, you'll divide 100 by 0.00541.
100 ÷ 0.00541 ---> 18484.2883549
Answer:
18484.28835
Hope this helps
-Amelia The Unknown
solve for x: (x-5)^2 = 49
Answer: [tex]x=12, -2[/tex]
Step-by-step explanation:
[tex](x-5)^{2}=49[/tex]
F.O.I.L the binomial
[tex]x^2-10x+25=49[/tex]
Set to 0
[tex]x^2-10x+25_{-49} =49_{-49}[/tex]
[tex]x^2-10x-24=0[/tex]
Factor the polynomial
[tex](x-12)(x+2)[/tex]
Set to 0 and Inverse operations
[tex](x-12)=0\\x=12[/tex]
Set to 0 and Inverse operations
[tex](x+2)=0\\x=-2[/tex]
Answer:
[tex]x=12, -2[/tex]
Which choices are equivalent to the quotient below? Check all that apply. √12/√6
The expression (√12) / (√6) simplifies to √2 by combining square roots and simplifying the fraction. The final simplified form is √2. Here option A is correct.
Given Expression:
(√12) / (√6)
Step 1: Write as Quotient of Square Roots
(√12) / (√6) can be expressed as √(12/6)
We express the division of square roots as the square root of the division of the radicands.
Step 2: Simplify the Quotient Under the Radical
√(12/6)
To simplify the fraction under the square root, divide the numerator by the denominator:
√(12/6) = √2
Step 3: Write the Answer in Simplified Form
√2
Therefore, the given expression (√12) / (√6) simplifies to √2.
We simplified the expression by combining the two square roots into one using the rule for dividing square roots and then simplified the fraction under the square root to arrive at the final answer, which is √2. Here option A is correct.
The correct option is A and C.
The equivalent choices to the given quotient [tex]\(\frac{\sqrt{12}}{\sqrt{6}}\)[/tex] are A [tex](\(\sqrt{2}\))[/tex] and C [tex](\(\frac{\sqrt{4}}{\sqrt{2}}\))[/tex].
The question shows a math problem asking which choices are equivalent to the given quotient:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} \][/tex]
We'll solve this step by step:
1. Simplify the square roots by factoring out squares:
[tex]\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]
[tex]\[ \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3} \][/tex]
2. Write the original quotient with the simplified square roots:
[tex]\[ \frac{\sqrt{12}}{\sqrt{6}} = \frac{2\sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} \][/tex]
3. Cancel out the common terms:
[tex]\[ \frac{2\sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} = \frac{2}{\sqrt{2}} \][/tex]
4. Rationalize the denominator by multiplying the numerator and denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} \][/tex]
5. Simplify the fraction:
[tex]\[ \frac{2\sqrt{2}}{2} = \sqrt{2} \][/tex]
So the simplified quotient is [tex]\(\sqrt{2}\)[/tex]. Now let's check the options in the image to see which ones are equivalent to [tex]\(\sqrt{2}\)[/tex]:
A. [tex]\(\sqrt{2}\)[/tex] - This is the correct simplified form of the given quotient.
B. [tex]\(2\)[/tex] - This is incorrect because it is not the square root of 2.
C. [tex]\(\frac{\sqrt{4}}{\sqrt{2}}\)[/tex] - Since [tex]\(\sqrt{4} = 2\)[/tex], this simplifies to [tex]\(\frac{2}{\sqrt{2}}\)[/tex], which after rationalization becomes [tex]\(\sqrt{2}\)[/tex], so this is also correct.
D. [tex]\(\frac{2}{\sqrt{3}}\)[/tex] - This is incorrect because it does not simplify to [tex]\(\sqrt{2}\)[/tex].
E. [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex] - Since [tex]\(\sqrt{6} = \sqrt{2 \cdot 3}\)[/tex], this simplifies to [tex]\(\sqrt{3}\)[/tex], which is incorrect.
F. [tex]\(\frac{\sqrt{6}}{2}\)[/tex] - This does not simplify to [tex]\(\sqrt{2}\)[/tex] and is therefore incorrect.
The correct answer choices are A and C, which are both equivalent to [tex]\(\sqrt{2}\)[/tex].
The complete question is here:
Find the GCF of 21, 30
Answer:
The GCF of 21 and 30 is 3.
Step-by-step explanation:
Find the prime factorization of 21
21 = 3 × 7
Find the prime factorization of 30
30 = 2 × 3 × 5
To find the gcf, multiply all the prime factors common to both numbers:
Therefore, GCF = 3
Answer:
3
Step-by-step explanation:
Factors of 21: 1, 3, 7, 21
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The GCF is the largest factor they both have.
GCF = 3
A map has a scale of 1 inch =35 miles what is the distance if the distance on the map is 3.5
Answer: 122.5 Miles.
Step-by-step explanation: This is because if you multiply 35 miles by 3.5 inches, you get 122.5 miles.
Hope this helps!
find the equation of a line that passes through (-2,4) and (1,-2)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-6}{1+2}\implies \cfrac{-6}{3}\implies -2[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-2}[x-\stackrel{x_1}{(-2)}]\implies y-4=-2(x+2) \\\\\\ y-4=-2x-4\implies y = -2x[/tex]
For every 6 children there is 1 adult so if there’s 66 children how many adults are there?
Answer:
11
Step-by-step explanation:
6 : 1
66 : X
X/66 = 1/6
X = 11
3 Fred is making a fruit salad. The ratio
of cups of peaches to cups of cherries
is 2 to 3. How many cups of peaches
will Fred need to make 60 cups of
fruit salad?
Answer: 24 cups.
Step-by-step explanation:
Let be "x" the amount of cups of peaches that Fred will need to make 60 cups of fruit salad.
According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:
[tex]2:3[/tex]
Which can also be written as a fraction:
[tex]\frac{2}{3}[/tex]
Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.
Knowing the above, you can set up the following proportion:
[tex]\frac{2}{5}=\frac{x}{60}[/tex]
Now you must solve for "x" in order to find its value. This is:
[tex](60)(\frac{2}{5})=x\\\\x=24[/tex]
a card is randomly chosen from a standard deck of cards. Find each probability.
Answer: The probability is 1/52 or .0192.
Step-by-step explanation:
A standard deck of cards has 52 so the probability of picking 1 card would be 1/52.
(a) The probability of drawing a spade is 1/4.
(b) The probability of drawing a face card (jack, queen, or king) is 3/13.
(c) The probability of drawing a red card is 1/2.
(d) The probability of drawing a card that is not an ace is 12/13.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
(a) The probability of drawing a spade.
There are 13 spades in a standard deck of 52 cards, so the probability of drawing a spade is:
P(spade) = 13/52 = 1/4
(b) The probability of drawing a face card (jack, queen, or king).
There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck of 52 cards, so the probability of drawing a face card is:
P(face card) = 12/52 = 3/13
(c) The probability of drawing a red card.
There are 26 red cards (13 hearts and 13 diamonds) in a standard deck of 52 cards, so the probability of drawing a red card is:
P(red card) = 26/52 = 1/2
(d) The probability of drawing a card that is not an ace.
There are 48 cards that are not aces in a standard deck of 52 cards (there are 4 aces), so the probability of drawing a card that is not an ace is:
P(not ace) = 48/52 = 12/13
Thus,
(a) The probability of drawing a spade is 1/4.
(b) The probability of drawing a face card (jack, queen, or king) is 3/13.
(c) The probability of drawing a red card is 1/2.
(d) The probability of drawing a card that is not an ace is 12/13.
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The complete question:
A card is randomly chosen from a standard deck of cards. Find each probability.
(a) The probability of drawing a spade.
(b) The probability of drawing a face card (jack, queen, or king).
(d) The probability of drawing a card that is not an ace.
mrs.darby works at the local bakery as a cake decorator if it takes her 1 1/3 hours to decorate one cake how many cakes can she dcorate in a 30-hour week
Answer:
22 1/2 cakes
Step-by-step explanation:
1 cake = 1 1/3 hours
Number of cakes in 30-hour week
= 30 ÷ 1 1/3
= 30 ÷ 4/3
= 30 x 3/4
= 90/4
= 45/2
= 22 1/2
Answer: 22 1/2 cakes
Ben goes to the grocery store at a rate of 7 times a week. How many times would he be expected to
go to the grocery store in 17 weeks?
times
Translate to a proportion:
V
weeks
weeks
times in 17 weeks
Answer:
hrhehehehrjejehejrjrjr in graduation in a Raha hai tu kya bolata of infectious agents and managers and managers in mmg of the marks the end of your ad on CL ad and I will send it out here
Step-by-step explanation:
bfyhh a ryagdh a child with hai tu ki baat nahin hota ha ha bol de mon iPhone and I will send you a Raha tha u y ok bye uy y ok bye y ok Sharjah United Arab and I have written to occur
Final answer:
Ben goes to the grocery store at a rate of 7 times a week. To find out how many times he goes in 17 weeks, you multiply 7 by 17, which equals 119. Therefore, Ben is expected to go to the grocery store 119 times in 17 weeks.
Explanation:
To calculate how many times Ben goes to the grocery store in 17 weeks, given that he goes at a rate of 7 times a week, we need to multiply the number of weeks by the frequency of his visits per week. The calculation is as follows:
Multiply the number of visits per week by the number of weeks: 7 visits/week imes 17 weeks. Perform the multiplication: 7 imes 17 = 119. Therefore, Ben is expected to go to the grocery store 119 times in 17 weeks.
As a proportion, this can be represented as:
V
--- =
weeks
7 times/week
-------------- =
1 week
Which can be scaled up to represent the 17 weeks:
119 times
--------------
17 weeks
PAGE 15
1) Describe the relationship shown in the table of values.
X 5 4 0
Y 8 9 13
A Relation only.
B Function only.
C Both relation and function.
D Neither relation nor function.
Answer:
C Both relation and function.
Step-by-step explanation:
This would pass the vertical line test so it is both a relation and a function
A partial
hubcap is shown. Copy and complete the
figure so that the completed hubcap has
rotational symmetry of 90°, 180°, and 270°.
Answer:
just complete the whole drawing
Step-by-step explanation:
y = -8x2 + 665x – 5754
Answer:
Is the -8x2 a -8x squared? Because the answer of this problem can be different.
Step-by-step explanation:
5.4 - 6 - 2 = x
A. (5.4)-6= 2 = x
B. 5.(4-6-2) = x
5.4—(6= 2)= x
5.(4-6)= 2 = x
00
Answer:
[tex]x=-2.6[/tex]
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Which number line represents all of the values of x for the equation x2 = 25?
Answer:
x = 5 and x = -5
Step-by-step explanation:
Given x^2 = 25, we take the square root of both sides. The two solutions are x = 5 and x = -5
The values for x in the equation x2 = 25 are 5 and -5. These solutions are represented on a number line at points 5 and -5.
Explanation:The equation x2 = 25 can be solved by taking the square root of both sides of the equation. When we take the square root of a number, we get two possibilities: a positive and a negative value, since squaring a number always results in a positive number. Therefore, the values for x in the given equation would be x = 5 and x = -5.
On a number line, these points would be represented at the 5 and -5 positions. Therefore the number line that represents all the values of x for the equation x2 = 25 is the one that includes both -5 and 5. Keep in mind that no other numbers would satisfy the equation x2 = 25.
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What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x − 6y = 15?
3
1) y−9=−2(x−6)
2
2) y−9= 3(x−6)
3
3) y+9=−2(x+6)
4) y+9=23(x+6)
Given:
The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]
We need to determine the equation of the line.
Slope:
Let us convert the equation to slope - intercept form.
[tex]-6 y=15-4x[/tex]
[tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]
From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]
Since, the lines are perpendicular, the slope of the line can be determined using the formula,
[tex]m_1 \cdot m_2=-1[/tex]
[tex]\frac{2}{3} \cdot m_2=-1[/tex]
[tex]m_2=-\frac{3}{2}[/tex]
Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;
[tex]y-9=-\frac{3}{2}(x-6)[/tex]
Simplifying the terms, we get;
[tex]2(y-9)=-3(x-6)[/tex]
[tex]2y-18=-3x+18[/tex]
[tex]3x+2y=36[/tex]
Thus, the equation of the line is [tex]3x+2y=36[/tex]
The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).
Explanation:The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.
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Four laps around the track equals one mile. How many miles does sixteen laps equal?
Answer:
It equals 4 miles
Which item has a unit rate of $6.50?
O caps: 4 for $25.00
o posters: 3 for $20.25
o tote bag: 4 for $30.00
O T-shirts: 5 for $32.50
Answer:
T-shirts
Step-by-step explanation:
First, find the unit price for caps. Divide 25 by 4, which equals $6.25. Then, divide 20.25 by 3, which equals $6.75. Next, divide 30 by 4, which equals $7.50. Finally, divide 32.50 by 5, which equals $6.50. To t-shirts have a unit rate of $6.50
i think the answer is t-shirts , hope this helps
=
Initial Knowledge Check
Question 8
A veterinarian treated 7 dogs this morning. The list below gives the weights (in pounds) of each dog.
66, 8, 12, 74, 36, 66, 7
Find the range of the data set.
x
?
The range of the data set is 67 pounds.
Explanation:The range of a data set is the difference between the maximum and minimum values. In this case, the weights of the 7 dogs are 66, 8, 12, 74, 36, 66, and 7 pounds. To find the range, we subtract the smallest value (7) from the largest value (74):
Range = 74 - 7 = 67
So, the range of the data set is 67 pounds.
Solve for 18. will give brainliest to first answer
Answer:
v > -1
Step-by-step explanation:
1/3(v-2) < v
Multiply both sides by 3(from 1/3) to equalize both sides.
This is equal to:
v-2 < 3v
Simplify equation:
v-2 < 3v =
-2 < 3v - v =
-2 < 2v
-1 < v
Swap sides:
v > -1
Therefore v is greater than -1.
Answer:
v > -1
Step-by-step explanation:
Simplify the left side.
Apply the distributive property.
13v+13⋅−2<v
Combine 13 and v
v3+13⋅−2<v
Combine 13 and −2
v3+−23<v
Move the negative in front of the fraction.
v3−23<v
Move all terms containing v to the left side of the inequality.
Subtract v from both sides of the inequality.
v3−23−v<0
Simplify the left side of the inequality.
−2(v+1)3<0
Multiply each term in −2(v+1)3<0 by −1
2(v+1)3>0
Multiply both sides of the equation by 3
2(v+1)>0⋅(3)
and again Simplify the left side.
Apply the distributive property.
2v+2⋅1>0⋅(3)
Multiply 2 by 1
2v+2>0⋅(3)
Multiply 0 by 3
2v+2>0
Subtract 2 from both sides of the inequality.
2v>−2
Divide each term by 2 and simplify.
Getting the conclusion where V is greater than 1
v>−1
Hope this helps
evaluate the following 7 = 5x+y÷3-3y
Answer:
5x + 22y = 21
or
5x + 22y - 21 = 0
Step-by-step explanation:
evaluate 7 = 5x+y÷3-3y
7 = [5x + y]/[3-3y]
Don't forget 7 can also be expressed in form 7/1,
so the step to follow is using a cross multiplication technique.
we have ;
5x + y = 7(3 - 3y)
5x + y = 21 - 21y
Collect the like terms (note when the negative sign crosses over the equal to sign it changes to positive and the same thing applies to positive sign it changes to negative respectively.)
5x + y + 21y = 21
5x + 22y = 21
5x + 22y - 21 = 0
Find a linear function that models the data in the table.
f(x)= *blank* x + *blank*
The linear function that models the data in the table is [tex]\( f(x) = 2x + 3 \)[/tex].
Explanation:To find the linear function, we need two key pieces of information: the slope mn and the y-intercept b. In the given function f(x) = 2x + 3, the coefficient of x (2) represents the slope, and the constant term (3) represents the y-intercept.
The slope m indicates the rate at which the function is changing, and in this case, it is 2. This means that for every unit increase in x, y increases by 2 units. The y-intercept b is the value of y when x is zero, which is 3 in this case. Therefore, the linear function f(x) = 2x + 3 accurately models the relationship between x and y in the given dat x in a linear manner.
In summary, the general form of a linear function is [tex]\(f(x) = mx + b\)[/tex], where m is the slope and b is the y-intercept. The values of m and b can be determined from the data or information provided.
The linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex], where x represents the input and f(x) the output.
To find a linear function that models the data in the table, we can use the slope-intercept form of a linear equation: f(x) = mx + b, where m is the slope and b is the y-intercept.
Let's find the slope (m) first using the given data points (-4, -6) and (3, 7):
[tex]\[m = \frac{\text{change in } y}{\text{change in } x} = \frac{7 - (-6)}{3 - (-4)} = \frac{13}{7}.\][/tex]
Now that we have the slope, we can use any point from the table to find the y-intercept (b). Let's use the point (0, 1):
[tex]\[1 = m(0) + b \implies b = 1.\][/tex]
Now, we can write the linear function:
[tex]\[f(x) = \frac{13}{7}x + 1.\][/tex]
So, the linear function that models the data in the table is [tex]\(f(x) = \frac{13}{7}x + 1\)[/tex].
. Which of the following quartic functions has x = -2 and x=-3 as its only two real zeros?
Answer: b
Step-by-step explanation:
if the cost of goods sold was $42,000 the income from sales was $86,000 and the expenses were $12,000 find gross profit and net profit
Gross profit is $44,000 and Net profit is $32,000
Step-by-step explanation:
Given :
cost of goods sold = $42,000The income or revenue = $86,000expenses = $12,000Gross profit :
Gross Profit = Total income - Cost of goods sold
⇒ $86,000 - $42,000
⇒ $44,000
⇒ Gross profit is $44,000
Net profit :
Net profit = Gross profit – Total Expenses
⇒ $44,000 - $12,000
⇒ $32,000
⇒ Net profit is $32,000
Makoto's summer job is mowing and edging lawns. He charges $20 to mow a lawn and $10 to edge a lawn. Makoto earned $180 mowing some lawns and edging 4 lawns. How many lawns did he mow?
Answer:
7
Step-by-step explanation:
to edge a lawn =10.he edged 4 lawn =10multiplied by 4=40
2nd. total -40=180-40=140
3rd. when he mows 1 lawn he is paid 20 what about when he is paid 140=140 divided by 20 =7
Makoto mowed 7 lawns to earn $180.
Let's denote the number of lawns Makoto mowed as m. Since he edged 4 lawns, that part of the income is 4 times $10, which sums up to $40. The total income from mowing is then $20 times the number of lawns he mowed, which is m. The equation representing Makoto's earnings is:
20m + 40 = 180
Subtracting 40 from both sides gives us:
20m = 140
Dividing both sides by 20 to solve for m gives us:
m = 7
(2x^3+4x^2-3)+(6x^3+4x-4)
Answer:
8x^3 + 4x^2 + 4x -7
Step-by-step explanation:
Add like terms.
Answer: everything is explained in the picture
Step-by-step explanation:
Ariana and two friends decide to split a pizza and garlic bread. If the total cost for the food is $15.33, how much should each person pay?
Answer: $7.665 each, approximately $7.67 each
Step-by-step explanation:
If cost is $15.33
To be sharedby two friends will be the cost/2
15.33/2= $7.665 each
Each person should pay $5.11 to equally split the total cost of the pizza and garlic bread, which is $15.33.
The student is asking how to divide the total cost of a pizza and garlic bread, which is $15.33, evenly among three people. To calculate this, we can use simple division.
Here is the step-by-step calculation:
First, identify the total cost of the food: $15.33.
Next, determine the number of people sharing the cost, which is three.
Divide the total cost by the number of people: $15.33 ÷ 3 = $5.11.
Therefore, each person should pay $5.11 to equally split the cost of the pizza and garlic bread.
Given the parent function, y=2^x, write an equation for a function that has a vertical shift down 5 units.
Answer:
y=2^x - 5
Step-by-step explanation:
"- 5" demonstrates a verical shift 5 units down
what is more 1200cm or 10m
Answer:
1200 cm is bigger. There are 100 cm in a meter. In 10 meters, there are 1000 cm. 1200 cm is longer than 1000 cm (10 meters)
Step-by-step explanation:
Jasmine has a pet rhino that weighs 4,000 pounds. How many tons does Jasmine's pet rhino weigh? Explain
Answer: 2 tons.
Step-by-step explanation:
1 pound = 0.0005 tons.
4,000*0.0005=2
Jasmine's rhino weighs 2 tons
Answer:
2 tons
Step-by-step explanation:
Since 1 ton is 2000 pounds, we can make a proportion:
2000lbs/1ton=4000lbs/xtons
4000lbs=2000lbs*xtons
2=tons
So Jasmine's pet rhino weighs 2 tons