The limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.
When trying to use L'Hospital's Rule to find the limit lim(x→∞) x/√(x^2 + 3), it is important to note that L'Hospital's Rule can only be applied if the function is continuous and differentiable. In this case, the function is continuous and differentiable, but applying L'Hospital's Rule is not necessary as the limit can be evaluated using another method.
First, let's rewrite the given function by dividing both the numerator and the denominator by x:
lim(x→∞) (x/x) / (√(x^2 + 3)/x) = lim(x→∞) 1 / √(1 + 3/x^2)
As x approaches infinity, the term 3/x^2 approaches 0, so the limit becomes:
lim(x→∞) 1 / √(1 + 0) = 1 / √(1) = 1
Therefore, the limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.
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Solve for w. w + –54 = 0
GIVING BRAINLIEST IF YOU SOLVE CORRECTLY WITH EXPLANATION!!!!!!!
(2y-3)(3y-2)
Answer:
16y^2-13y+6
Step-by-step explanation:
(2y-3)(3y-2)
you have to expand the brackets
to do this you have to times each expression by the other bracket
2y×3y=6y^2
2y×-2=-4y
-3×3y=-9y
-3×-2=6
if you put these together u get:
6y^2-4y-9y+6
because there are two pairs containing y we can simplify this
-4y-9y=-13y
so the answer is
6y^2-13y+6
[tex]6y^{2}-13y+6[/tex]
Distribute[tex](2y-3)(3y-2)=\\2y(3y-2)-3(3y-2)[/tex]
Keep distributing [tex]2y(3y-2)-3(3y-2)=\\6y^{2}-4y-3(3y-2)[/tex]Keep distributing[tex]6y^{2}-4y-3(3y-2)\\6y^{2} -4y-9y+6[/tex]
Combine like terms[tex]6y^{2} -4y-9y+6=\\6y^{2}-13y+6[/tex]
Answer:So the answer [tex](2y-3)(3y-2)[/tex] is [tex]6y^{2}-13y+6[/tex]
I hope this helped, if it displeased tell me what I did wrong so I can possibly fix it ૮ ˶ᵔ ᵕ ᵔ˶ ა
A woman rides her bike 16 miles with the wind in the same time she travels 10 miles against the wind. If the speed of the wind is 3 mph, find the speed of the cyclist in still air.
The speed of the cyclist in still air is 13 mph
How to find the speed of the cyclist in still airLet the speed of the cyclist in still air be x mph
when she rides with the wind her speed = (x + 3) mph
when she rides against the wind her speed = (x - 3) mph.
Mathematically we can represent the problem as:
16 / (x + 3) = 10 / (x - 3)
cross multiplying and simplifying
16 (x - 3) = 10 (x + 3)
16x - 48 = 10x + 30
6x = 78
x = 13
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.Which of the following refers to rules of thumb that simplify the process of making decisions?
A. Dialectical inquiry
B. Biases
C. Heuristics
D. Creativity
E. Practical alternatives
Heuristics refers to rules of thumb that simplify the decision-making process. Heuristics are mental shortcuts that help individuals make decisions quickly, often relying on previous experience or intuition rather than a more systematic approach.
While heuristics can be useful, they can also lead to biases and errors in judgment if they are applied too broadly or without careful consideration. It is important to be aware of these heuristics and how they can affect decision-making processes, especially in complex or high-stakes situations where careful consideration is necessary.
The answer is C.
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What percent of 25 is 12
Answer:
48%
Step-by-step explanation:
25 is 100% of 25
so
25----------------100%
12------------------ X
Cross multiplication
25X = 12x100
25X = 1200
X = 48
I makes sense since half (50%) of 25 is 12.5 So 12 is a little less than half
Answer:
48
Step-by-step explanation:
to solve this you would use the [tex]\frac{part}{whole}[/tex] = [tex]\frac{percent}{100}[/tex] equation.
the whole would be 25 as that is what you are taking the percent out of.
the part would be 12, as that is what the percent of the whole equals.
plug those in:
[tex]\frac{12}{25} = \frac{percent}{100}[/tex]
change the percent to an x, as that is what we're solving for
[tex]\frac{12}{25} = \frac{x}{100}[/tex]
cross multiply to get
[tex]25x=1200[/tex]
isolate the variable by dividing by 25 on both sides
[tex]\frac{25x}{25} = \frac{1200}{25}[/tex]
you should get[tex]x=48[/tex]
48 is your answer
Rate of change
y=25(1.071)x
The given exponential function will grow with,
⇒ 7.1%
We have to given that;
The exponential function is,
⇒ y = 25 (1.071)ˣ
Since, We know that;
A relation in between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now, For identify the change represents growth or decay, and determine the percentage rate of increase or decrease as,
Since, We have,
⇒ y = 25 (1.071)ˣ
Clearly, The equation is shows exponential growth because the growth factor is 1.071 which is greater than 1.
And, The general form equation is:
y(x) = a(1 + r)ˣ
Where, r is the growth percent.
Hence,
⇒ 1 + r = 1.071
⇒ r = 0.071 = 7.1%
Therefore, We get;
Rate = 7.1%
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Megan and her family went apple picking at an orchard. She filled one large basket with eight green apples to make a pie. She also filled three small baskets with g green apples each to give to her friends as presents.
Pick all the expressions that represent how many apples Megan picked in all.
A. 11 + G
B. 8 + g + g + g
C. 24g
D. 8 + 3g
Answer:
D. 8+3g
Step-by-step explanation:
We know that Megan filled 1 large basket, L, with 8 green apples.
So L = 8.
We also know that she filled 3 small baskets, S, with the same amount of green apples, g.
This would mean that we could multiply the amount of green apples, g, with the amount of small baskets Megan filled to find the amount of apples Megan picked for the small baskets.
This would mean that S = 3*g. Which could be written also be written as S = 3g.
We want to know how many apples Megan picked overall, so we would add the apples in the large basket and small baskets together to find the total, T.
This would be T = G + S. After plugging in [8] for G and [3g] for S, we would get [8+3g].
Answer: What are all of the Expressions that Represent how Many Apples Megan Picked in All?
Step-by-step explanation:
The expressions that represent how many apples Megan picked in all are:
b.) 8+g+g+g
d.) 8+3g
Expression (a) does not take into account the three small baskets of apples that Megan picked to give to her friends, so it is not correct. Expression (c) multiplies the number of apples in the first basket by the number of baskets Megan picked, but it does not take into account the number of apples in the other three baskets, so it is not correct.
Therefore, the correct expressions are (b) and (d), which count the apples in the large basket and the three small baskets.
{I Hope This Helps! :)}
the normal approximation can be used in a two-sample test of proportions for which one of these sets of values?
The normal approximation can be used in a two-sample test of proportions when the sample sizes are sufficiently large.
The rule of thumb is that each sample should have at least 10 successes and 10 failures. When these conditions are met, the sampling distribution of the difference in sample proportions can be approximated by a normal distribution with a mean equal to the difference in population proportions and a standard deviation calculated from the sample proportions. This approximation allows us to calculate probabilities and make inferences using the standard normal distribution. It is important to note that this approximation may not be accurate for small sample sizes, in which case exact methods such as the Fisher's exact test should be used instead. In summary, the normal approximation can be used in a two-sample test of proportions when the sample sizes are large enough and the conditions are met.
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Abby bought 2/3 pound of seeds for $7. What is the cost of 1 whole pound of seeds?
Answer:
$ 14.50
Step-by-step explanation:
So 2/3 is $7, right?
If we multiply to find how much it would be to get to one pound, you would find that 1.5 would get you to that number.
So, that means two 2/3, and a half, meaning:
7+7+0.5=14.5
Leading to your answer: $ 14.50
Hope this helps :)
can more than one triangle be drawn with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees?
No, it is not possible to draw more than one triangle with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees.
In a triangle, the measure of an included angle between two sides determines the length of the third side. In this case, we have fixed side lengths of 5 inches and 7 inches, and an included angle of 50 degrees.
According to the Law of Sines, the ratio of the length of a side to the sine of its opposite angle is constant in a triangle. Using this law, we can calculate the length of the third side.
Let's denote the unknown side length as "x". Using the Law of Sines:
sin(50°) / 5 = sin(opposite angle) / x
We can solve this equation to find the value of x. However, it's important to note that there will be only one solution for x. This means that there is only one possible triangle that can be formed with the given side lengths and included angle measure.
No,it is not possible to draw more than one triangle with the given specifications.
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PLEASEEEEE HELP!
I have no idea how to do this!
Answer:
Step-by-step explanation:
See image
Find the value of x.
(7x-5)°
(x+3)°
Because the two angles are complementary, the value of x must be 11.5
How to find the value of x?In the image we can see that the two given angles are complementary, which means that their measures add up to 90°, then we can write:
(7x - 5)° + (x + 3)° = 90°
Now we can solve that linear equation to find the value of x, we iwll get:
7x + x - 5 + 3 = 90
8x - 2 = 90
8x = 92
x = 92/8
x = 11.5
That is the value of x.
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On a fruit farm, 1 acre of land produces 2 tons of oranges. How many kilograms of oranges will be produced by 300m of the same farm land
300m of the fruit farm land will produce 300 kilograms of oranges. Given that 1 acre of land produces 2 tons of oranges, we can calculate the equivalent amount of oranges produced on 300m of land.
We know that 1 acre of land produces 2 tons of oranges. To find the equivalent amount of oranges produced on 300m of land, we need to convert the units of measurement.
First, we convert 1 acre to square meters. 1 acre is equal to 4046.86 square meters.
Next, we need to determine the proportion of land used. We have 300m of land, which is equivalent to 300 square meters.
Now we can calculate the amount of oranges produced on 300m of land. Since 1 acre produces 2 tons of oranges, we can set up a proportion:
1 acre / 2 tons = 300 square meters / x kilograms
Cross-multiplying the proportion, we get:
1 acre * x kilograms = 2 tons * 300 square meters
Simplifying the equation, we find:
x = (2 tons * 300 square meters) / 1 acre
x = (2 * 300) kilograms
x = 600 kilograms
Therefore, 300m of the fruit farm land will produce 600 kilograms of oranges.
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AC=A, C, equals Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle A B C is thirty-five degrees. Side A C is unknown. Side A B is five units.
The length of side AC is approximately 2.87 units when rounded to the nearest hundredth.
In a right triangle ABC, where angle ACB is a right angle and angle ABC is 35 degrees, we are given that side AB has a length of 5 units. We need to find the length of side AC.
To find the length of side AC, we can use trigonometric ratios. In this case, we can use the sine function.
The sine of angle ABC is defined as the ratio of the length of the side opposite the angle (AC) to the length of the hypotenuse (AB).
sin(35°) = AC / 5
To find the length of AC, we can rearrange the equation:
AC = 5 * sin(35°)
Using a calculator to find the sine of 35 degrees, we get:
AC ≈ 5 * 0.5736 ≈ 2.868
Therefore, the length of side AC is approximately 2.87 units when rounded to the nearest hundredth.
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Addison left her house at time zero and drove for 7 minutes to the store, at a speed of
2 blocks per minute. Then she stopped and went into the store for 5 minutes. From
there, she drove in the same direction at a speed of 3 blocks per minute until she got
to the bank, which is 6 blocks away from the store. She stopped at the bank for 7
minutes. Then she drove home at a speed of 5 blocks every minute. Make a graph of
showing the number of blocks away from home that Addison is a minutes after she
leaves her house, until she gets back home.
The graph shows that Addison drives away from home, reaches a maximum distance of 20 blocks away from home, and then drives back home, arriving at the same distance of 0 blocks away from home.
A graph of Addison's distance from her home over time, we can plot time on the x-axis and distance on the y-axis.
Here's a step-by-step process to create the graph:
Start by drawing the x-axis and labeling it "Time (minutes)".
Mark the minimum value as 0 and the maximum value as 24 (7 + 5 + 6 + 7 + 7 = 32 minutes total, but we only need to plot until Addison gets home).
Draw the y-axis and label it "Distance from Home (blocks)".
Mark the minimum value as 0 and the maximum value as 13 (7 blocks to the store + 6 blocks to the bank).
Plot Addison's starting point, which is at (0,0).
Addison drives to the store at a speed of 2 blocks per minute, so after 7 minutes she is 14 blocks away from home (7 minutes × 2 blocks/minute = 14 blocks). Plot a point at (7, 14).
Addison stops at the store for 5 minutes, so her distance from home doesn't change during that time.
Draw a horizontal line from the point at (7,14) to (12,14).
Addison drives from the store to the bank at a speed of 3 blocks per minute, so it takes her 2 minutes to travel 6 blocks (6 blocks / 3 blocks/minute = 2 minutes).
After 12 minutes total (7 minutes to the store + 5 minutes at the store), she is 20 blocks away from home (14 blocks + 6 blocks). Plot a point at (12, 20).
Addison stops at the bank for 7 minutes, so her distance from home doesn't change during that time.
Draw a horizontal line from the point at (12,20) to (19,20).
Drives from the bank to home at a speed of 5 blocks per minute, so it takes her 2.6 minutes to travel 13 blocks (13 blocks / 5 blocks/minute = 2.6 minutes).
After 19 minutes total (7 minutes to the store + 5 minutes at the store + 6 minutes to the bank + 1 minute waiting at the bank), she is 13 blocks away from home (20 blocks - 13 blocks). Plot a point at (19,13).
Addison arrives home after 24 minutes (7 minutes to the store + 5 minutes at the store + 6 minutes to the bank + 7 minutes at the bank + 2.6 minutes driving home).
Draw a point at (24,0) to represent her arrival home.
Connect the points with a line to complete the graph:
Distance from Home
^
13 _| •
| |‾‾‾•‾‾‾‾‾‾
12 _| | /
| | /
11 _| | /
| | /
10 _| | /
| |/
9 _|_ ___ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
0 7 12 19 24 → Time
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Please help for it will give you 20 points
Answer: 4.80
Step-by-step explanation:
The wheels on a car have a diameter of 28 inches. How many full revolutions will the wheels need to make to travel 200 feet? OA. 8 revolutions B. 15 revolutions C. 28 revolutions D 88 revolutions
Answer: The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle. In this case, the diameter of the wheels is 28 inches, so the circumference of each wheel is:
C = π(28) = 28π inches
To find how many revolutions the wheels need to make to travel 200 feet, we need to convert 200 feet to inches, and then divide by the circumference of each wheel. There are 12 inches in 1 foot, so 200 feet is equal to:
200 feet × 12 inches/foot = 2400 inches
Dividing 2400 inches by the circumference of each wheel, we get:
2400 inches ÷ (28π inches/revolution) ≈ 85.3 revolutions
Therefore, the car's wheels need to make approximately 85.3 full revolutions to travel 200 feet. Since the question asks for the number of full revolutions, we can round down to the nearest whole number to get:
Answer: D. 88 revolutions.
The graph of line m is shown. Use the similar slope triangles to compare the slope of segment AD, the slope of segment DF, and the line of m
By use the similar slope triangles, the slope of segment AD, segment DF, and the line of m are all equal.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of side JL and side MP are equal;
Slope of segment AD = AB/BD
Slope of segment DF = DE/EF
Slope of line m = DE/EF = AB/BD
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Solve the right triangle. If two sides are given, give angles in degrees and minutes.
A = 12° 33', c = 283 ft
Round side lengths to two decimal places.
In a purely inductive AC circuit as shown in the figure, ΔVmax = 100 V. uploaded image(a) The maximum current is 8.00 A at 80.0 Hz. Calculate the inductance L. H (b) At what angular frequency ω is the maximum current 1.50 A? rad/s
To calculate the inductance L in the circuit, we can use the formula for the maximum current in an inductive circuit:
Imax = ΔVmax / (ωL)
where Imax is the maximum current, ΔVmax is the maximum voltage, ω is the angular frequency, and L is the inductance.
The inductance L is 0.15625 H (or 156.25 mH).
Given that Imax = 8.00 A, ΔVmax = 100 V, and ω = 80.0 Hz, we can rearrange the formula to solve for L:
L = ΔVmax / (Imax * ω)
Substituting the given values:
L = 100 V / (8.00 A * 80.0 Hz)
L = 0.15625 H (or 156.25 mH)
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a survey found that the american family generates an average of 17.2 pounds of glass garbage each year. assume the standard deviation of the distribution is 2.5 pounds. find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds. why can the central limit theorem be applied?
Therefore, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 0.9251.
To apply the central limit theorem, we need to check if the sample size is sufficiently large. According to the theorem, if the sample size is greater than or equal to 30, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution.
In this case, the sample size is 55, which is greater than 30, so we can assume that the distribution of sample means will be approximately normal.
Now, we can find the z-scores for the given values of the sample mean:
z1 = (17 - 17.2) / (2.5 / sqrt(55)) = -1.87
z2 = (18 - 17.2) / (2.5 / sqrt(55)) = 1.87
Using a standard normal distribution table or calculator, we can find that the probability of a z-score being between -1.87 and 1.87 is approximately 0.9251.
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Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?
1.6.89 + t = 8.00
2.6.89 - t = 8.00
3.6.89t = 8.00
4.6.89 = 8.00 Divided by t
Answer:
1 6.89+t=8
Step-by-step explanation:
Because she left 6.89 to pay for her food and a tip. So whatever the tip was plus the 6.89 she owed equaled $8.
Solve for the number of days that
skier must go to the mountain in order
to justify buying a season pass. A season pass is $450 plus a $10 fee for each day the pass is used. A one day ticket is $100.
Step-by-step explanation:
Let x be the number of days the skier goes to the mountain.
The total cost for using a season pass is:
Cost_season_pass = 450 (initial cost) + 10x (daily fee)
The total cost for using one day tickets is:
Cost_one_day_tickets = 100x (daily cost)
In order to justify buying a season pass, the total cost of the season pass must be less than the total cost of using one day tickets:
450 + 10x < 100x
Subtract 10x from both sides:
450 < 90x
Now, divide both sides by 90:
x > 5
So the skier must go to the mountain for more than 5 days to justify buying a season pass. The minimum number of days to justify the pass would be 6 days.
In the figure below, S is the center of the circle. Suppose that JK= 13, LM = +3x1, SN = 6, and SP = 6. Find the following.
Answer:
x=4
Step-by-step explanation:
LM=JK
3x+1=13
3x=12
x=4
a sector of a circle is created from a central angle with a measure of 60 . if the diameter of the circle is 6 inches, what is the area of the sector?
The area of the sector created by a central angle of 60° in a circle with a diameter of 6 inches is approximately 4.7124 square inches.
To find the area of a sector of a circle, we need to know the central angle and the radius of the circle. In this case, we are given the central angle of 60° and the diameter of the circle, which we can use to find the radius.
The diameter is given as 6 inches, so the radius is half of that, which is 3 inches.
To calculate the area of the sector, we can use the formula:
Area of Sector = (θ/360°) * π * r²
where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius.
Plugging in the values:
Area of Sector = (60°/360°) * π * (3)²
Area of Sector = (1/6) * 3.14159 * 9
Area of Sector ≈ 4.7124 square inches
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Please help you guys, the AP calc an exam coming soon and I need to know how to do this, much appreciated.
To be continuous at x=0, you need three things:
1. f(0) must be defined
2. limit as x –> 0 must exist
3. f(0) = limit as x –> 0
f(0) in this case is the following:
[tex]f(0) = k + 2 \ln(0+e^{0+1}) = k + 2 \ln(e) = k + 2[/tex]
We have to pause on this, since this by itself cannot give us the value of k.
For the limit, you need to make sure the limit from the left matches the limit from the right.
[tex]\lim\limits_{x\to 0^+} k+2\ln(x+e^{x+1}) = k+2[/tex]
[tex]\lim\limits_{x\to 0^-} \frac{\sin(7x)}{2x} =\frac{7}{2}[/tex]
The only way this limit can exist is if [tex]k+2 = \dfrac{7}{2}[/tex], which means [tex]k = \dfrac{3}{2}[/tex].
Using that k-value also allows f(0) = 7/2, which makes your function continuous.
If you need to know how to make that second limit work out to 7/2, there are two steps to take.
The first is to bring the 1/2 out front, since it's a constant factor inside the limit.
[tex]\lim\limits_{x\to 0^-} \frac{\sin(7x)}{2x} =\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{x}[/tex]
The second is to manipulate the what you're taking the limit of to turn it into a "sin(u)/u" situation. To do this, we'll multiply by 7/7 inside the limit:
[tex]\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{x}=\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{{\boldsymbol7\cdot{}}\sin(7x)}{{\boldsymbol7\cdot{}}x}[/tex]
We'll then factor out the 7 in the numerator like we did with the 1/2:
[tex]=\frac{7}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{7x}[/tex]
And now with a quick u-substitution, we'll let u = 7x and x->0 is the same as u->0, we have
[tex]=\frac{7}{2}\cdot\lim\limits_{u\to 0^-} \frac{\sin(u)}{u}[/tex]
This is useful because a good limit to know in calculus is that [tex]\lim\limits_{u\to 0} \frac{\sin(u)}{u}=1[/tex].
Explain step-by-step
Answer:
$ 528000
Step-by-step explanation:
buying price = $ 600000
100% = 600000
loss = 12%
selling price = 88%
= 88% × 600000
= $ 528000
How much would Little Squeezer's pay for a shift if 11 pizzas are delivered?
The amount of money that Little Squeezer will pay Tony if he delivers 11 pizzas would be =$81
How to calculate the amount of money Tony will receive for 11 pizzas?From the table given, without the delivery of pizza, the salary of Tony = $48
For every additional two pizza, $6 is being added. That is;
2 pizzas = $54
4 pizzas = 54+6 = $60
Therefore for every 1 pizza is = $3 to his salary.
That is, 11 pizzas = 78+3 = $81
Therefore,the amount of money that Little Squeezer will pay Tony when a total of 11 pizzas are delivered would be = $81.
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my peabrain don't know
The base of the rhombus would be = 10.2m.
How to calculate the base of the given rhombus?To calculate the base of the given Rhombus, the the formula for the area of the Rhombus should be used. That is;
Area of Rhombus = b²/2
But area = 52cm²
That is:
52 = b²/2
make ab the subject of formula;
b² = 52×2 = 104
b =√104
= 10.2m
Therefore the base of the Rhombus whose area is given should be = 10.2m.
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NEED HELP ASAP Ahab drove 46 miles. Given that 1 kilometer is approximately 0.6
miles, how far did Ahab drive?
Round your answer to the nearest tenth.
The distance covered by Ahab 100 km.
Given that Ahab drove 46 miles we need to calculate his distance in Km.
So, since 1 km = 0.46 miles
1 mile = 100/46
Therefore,
46 miles = 100/46 x 46
46 miles = 100 km
Hence the distance covered by Ahab 100 km.
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