Eli was swimming upstream in a river and lost a plastic bottle at bridge A. He noticed the loss after swimming 10 minutes , so immediately started to swim downstream to catch it. He caught it at bridge B, which was 1 mile away from bridge A. What was the rate of water flow in miles per hour?
Using proportions, it is found that the rate of water flow was of 6 miles per hour.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the bottle flowed 1 mile in 10 minutes. How much does it flow in 1 hour = 60 minutes? The rule of three is given by:
1 mile - 10 minutes
x miles - 60 minutes
Applying cross multiplication:
10x = 60
x = 60/10
x = 6.
Hence, the rate of water flow was of 6 miles per hour.
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Looking for some furniture for her new apartment, Susan visits the local swap meet in search of something cheap. Knowing that most swap meet vendors will not accept credit cards and that she will not have any money until her next payday, Susan decides to take out a $200 cash advance on her credit card at an interest rate of 32%. If Susan had no previous balance on her credit card, and she manages to pay off the balance within 1 month, how much will she have to pay in interest? a. $5. 33 b. $32. 00 c. $173. 33 d. $205. 33 Please select the best answer from the choices provided. A B C D.
The amount that Susan will have to pay in interest is given by: Option A: $5.33 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we're given that:
Amonut Susan took out = $200Interest rate = 32% annually (interest rates are usually expressed in annual (yearly) terms).Amount paid off within 1 monthThe interest was 32% annually, so in monthly terms, it would be 32/12 = 2.667% approx. (as there are 12 months in each year)
Since the balance was paid within one month, the interest would be simply 1 time calculated on the main balance.
Thus, we get:
Interest amount ≈ 2.667% of $200 = [tex]\dfrac{200}{100} \times 2.667 = 5.334 \approx 5.33 \: \rm (in \: dollars)[/tex]
Thus, the amount that Susan will have to pay in interest is given by: Option A: $5.33 approx.
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Mrs. Barnett has 5 cups of sugar. A batch of cookies uses 1/3 cup of sugar.
How many batches of cookies can she make?
Answer:
15 batches of cookies
Step-by-step explanation:
We need to find out how many third cups do into 5 cups. We can do this by 5 ÷ 1/3
When dividing fractions, use KFC:
Keep the first fraction the sameFlip the second fractionChange the sign from ÷ to ×Therefore, 5 ÷ 1/3 = 5 × 3/1 which is 15 batches of cookies
Hope this helps!
Please help me with my work
Answer:
JM = 5 mm
Step-by-step explanation:
Δ JMK is the right angled triangle ⇒ JM² = JK² + KM²
JM² = 3² + 4²
JM = 5 mm
Please help me, I have no Idea how to solve this.
Answer:
19 ducks are NOT WINNERS
There is a 76% CHANCE that you will not choose a winning duck, so it is VERY LIKELY that you will choose a duck that is not a winner.
Step-by-step explanation:
Answer: 1.) 19 rubber ducks are not winners
2.) There is a 76% chance of not choosing a winning duck
1.) Step-by-step explanation: 25 times 0.24 equals 6, 25-6=19
2.) 0.24 is equal to 24% and 100-24= 76 so 76% chance of not choosing a rubber duck
the ratio of 20 paise to Rupees 1 is option 1:5, 2:1 , 20:1, 2:3
Answer:
1:5
Step-by-step explanation:
divide by 20 on both sides, 5 : 1.
2. What is the measure of angley?
(2 pts.)
52°
to
Answer: the answer is 55 degrees
Step-by-step explanation:
Cover the entire area except for today's date and year April, 1st, Monday
Answer:
It's friday for me so here u go
Step-by-step explanation:
What is the constant term in the expression 8xy + 9x2 y − 5x − 2?
−5
−2
8
9
Answer:
-2
Step-by-step explanation:
In the expression [tex]8xy + 9x^2y -5x -2[/tex]
[tex]x[/tex] and [tex]y[/tex] are the variablesThe numbers directly before the variables are the coefficientsThe number that it not attached to a variable is the constant termTherefore, the constant term is -2
Answer: -2 is the constant term in the expression 8xy + 9x2 y − 5x − 2
Step-by-step explanation:
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
the expression 8xy + 9x2 y − 5x − 2
now, we know that,
constant is the number with no variable attached to it.
-2 is the constant term in the expression 8xy + 9x2 y − 5x − 2.
please help
what is the equation for the following graph
A=1
Answer:
[tex]f(x)=\sqrt{x+5}-3[/tex]
Step-by-step explanation:
Given function for graph: [tex]f(x)=\sqrt{x-h}+k[/tex]
Therefore, the parent function is [tex]f(x)=\sqrt{x}[/tex]
[tex]f(x)=\sqrt{x-h}+k[/tex] can be obtained by translating [tex]f(x)=\sqrt{x}[/tex] to [tex]h[/tex] units to the right and [tex]k[/tex] units up
The x and y intercept of [tex]f(x)=\sqrt{x}[/tex] is the origin
Therefore, this graph has been translated 5 units to the left and 3 units down.
Therefore, [tex]h=-5[/tex] and [tex]k=-3[/tex]
Substituting these values into the given function:
[tex]\implies f(x)=\sqrt{x-(-5)}+(-3)[/tex]
[tex]\implies f(x)=\sqrt{x+5}-3[/tex]
K(-3, 0), I(0, 2), and T(3, 0) are three vertices of a kite. Which point could be the fourth vertex?
The coordinates of the fourth vertex of the kite with vertices (-3, 0), (0, 2) and (3, 0) are represented by the point E(x,y) = (0, -2).
How to determine the fourth vertex of a kiteA rhomboid is a quadrilateral with two pairs of sides of equal length and two pairs of equal angles. A kite is a rhomboid whose vertices observe the following properties: [tex]P_{1} (x, y) = (-x, 0)[/tex]. [tex]P_{2} (x,y) = (0, y)[/tex], [tex]P_{3}(x,y) = (x, 0)[/tex], [tex]P_{4}(x,y) = (0, -y)[/tex].
In this question we must determine the coordinates of the fourth vertices according to the kite characteristics. After a quick comparison in the known points, the coordinates of the fourth vertex are E(x,y) = (0, -2).
The coordinates of the fourth vertex of the kite with vertices (-3, 0), (0, 2) and (3, 0) are represented by the point E(x,y) = (0, -2). [tex]\blacksquare[/tex]
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constitutional amendment that has significantly changed the structure of congress as written in the original constitution
Which set of numbers could represent the lengths of the sides of a right triangle?
13, 21, 34
8, 14, 21
15, 18, 26
12, 16, 20
Answer:
9*9+40*40=41*41
Step-by-step explanation:
The largest length is always the hypotenuse. If we were to multiply any triple by a constant, this new triple would still represent the sides of a right triangle. Therefore, 6, 8, 10 and 15, 20, 25, among countless others, would represent the sides of a right triangle.
please help? , no decimals please,please explain to see picture.
Answer:
[tex]8x\sqrt{3xy[/tex]
Step-by-step explanation:
A teacher claims that his coffee cools to a temperature of 100 degrees Fahrenheit in 5 minutes after he brews it at home in his single-cup coffee brewer. To further investigate this claim, the teacher measures how long it takes for his coffee to cool to 100 degrees for each of the next 30 days. He would like to carry out a t-test for one mean to determine if there is convincing evidence that the true mean amount of time it takes for his coffee to cool to 100 degrees is less than 5 minutes. Are the conditions for inference met?
No, the random condition is not met.
No, the 10% condition is not met.
No, the Normal/large sample condition is not met.
Yes, all conditions for inference are met.
The answer is: No, the random condition is not met.
The ratio of the dimensions of a rectangular patio are 4:7. if the shorter
dimension is 10 feet, What are the area and perimeter of the patio?
If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:
[tex]\frac{4}{7} =\frac{10}{x}[/tex]
You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.
[tex]\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}[/tex]
This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is: [tex]w*l[/tex]
So we can plug our dimensions into the formula: [tex]10*17.5=175[/tex]
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is 175 square feet.
PERIMETER
The formula for the perimeter of a rectangle is: [tex]2(w+l)[/tex]
We can plug our dimensions into the formula: [tex]2(10+17.5)=55[/tex]
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is 55 feet.
Dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. His sample size is 7 with a mean of 93. 5. Which of the following correctly depicts the z-statistic for this data? 0. 28 0. 36 1. 98 2. 63.
The value of the z statistic for the considered data is given by: Option C: 1.98 approximately.
How to find the z score (z statistic) for the sample mean?If we're given that:
Sample mean = [tex]\overline{x}[/tex] Sample size = n Population mean = [tex]\mu[/tex] Sample standard deviation = sThen, we get:
[tex]z = \dfrac{\overline{x} - \mu}{s}[/tex]
If the sample standard deviation is not given, then we can estimate (in some cases) it by:
[tex]s = \dfrac{\sigma}{\sqrt{n}}[/tex]
where [tex]\sigma[/tex] = population standard deviation
For this case, we're specified that:
Sample mean = [tex]\overline{x}[/tex] = 93.5Sample size = n = 7Population mean = [tex]\mu[/tex] = 92Population standard deviation = [tex]\sigma[/tex] = 2Thus, the value of the z-statistic is evaluated as:
[tex]z = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}} = \dfrac{93.5 - 92}{2/\sqrt{7}} \approx 1.98[/tex]
Thus, the value of the z statistic for the considered data is given by: Option C: 1.98 approximately.
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Find area of shaded region.
area of shaded region = 1/4 of the circle area - triangle area
circle area = pi x r² = 3,14 x 2² = 12,56 m²
so 1/4 circle area = 12,56 : 4 = 3,14 cm²
and
triangle area = 1/2 x 2 x 2 = 2 m²
=> area of shaded region = 1,14 cm²
(Use distributive property)
6 (5x + 3)
Answer:
30x + 18
Step-by-step explanation:
Using distributive property, you can find the answer like so.
Multiply 6 and 5x first
6(5x + 3)
30x + 3
Now multiply 6 by 3
6(5x + 3)
30x + 18
Hope I explained this well to you. :)
Help me pls
-3^3(-8n^3-3n^2)
(PLEASE HELP ASAP!! 50 POINTS! question in the image)
SUB - Mathematics
Grade - 9th
Q.1) Visualise 3.765 on the number line , using Succescive Magnification.
Note:-
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Step-by-step explanation:
Introduction:-Successive magnification:
In this process, we use to represent real numbers and visualize them on the number line such as by the magnifying glass, due to this we refer it as successive magnification.
Solution:-Since, we're given to visualize 3.765 on the number line, we take the number line from between 3 and 4Then, in between 3 and 4, we then visualize the portion of 3.7 and 3.8Again, in between 3.7 and 3.8, we visualize the portion of 3.76 and 3.77.At last, we point out the required number for visualizing that is 3.765, in between 3.76 and 3.77.Shane went bowling with his friends. The bowling alley charges $20 for an hour of group bowling plus a fee to rent each pair of shoes. Shane's group bowled for one hour, rented 4 pairs of shoes, and paid a total of $31. Which equation can you use to find the fee, x, to rent each pair of shoes?
Answer:
4x+20=31
Step-by-step explanation:
So one hour of bowling is 20 dollars and they bowled for one hour hence the 1x20 which is equal to 20. That is the base coast we add to the variable of x that is the cost of renting one pair of shoes. And since they rented 4 pairs of shoes you multiply x by 4 to get 4x. Add the 20 dollars they paid to bowl and it is 4x+20. They paid 31 dollars in total so equal the equation to 31. 4x+20=31. Solution is $2.75 per pair of shoes. (If you want an explanation as to how to get the answer, just ask
A rugby match lasts for 80 mins. 20 mins of a match have been played. a) what Fraction of he match has been played? b) what percentage of the match is there left to play?
Answer:
a, 1/4
b, 75%
Step-by-step explanation:
a, total mins meant to be played = 80mins
mins being played = 20mins
fraction of the match being played = 20 /80 = 1/4
b, percentage of the match left to be played
= 80 - 20 = 60
then we find the fraction of the match meant to be played
60 / 80 = 3 /4
then we multiply by 100 to get the percentage
3/4 × 100 = 75 %
if this helped pls give brainliest
The expression 0.09x+(x−30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax. The tax is on the original price.
Which expression represents the amount of tax that is paid on the bicycle?
ANSWER
I believe that the amount of the instant rebate is $30. X represents the price of the bike, and 0.09 is the sales tax.
So if the bike cost $100:
0.09(100) + (100-30) = 9 + 70 = $79
Although I think I would want them to tax the bike after the instant rebate and not on the original price.
If I'm wrong about the instant rebate then it would be 1.09x-30. Hope this helps.
THIS IS MY LAST QUESTION PLEASE HELP ME
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price
Zion Sun Chairs must sell each chair for to break even if the total annual fixed costs are $17,363.50
and the variable cost per chair is $52.17.
O $57.03
O $64.50
O $81.25
O $79.65
Answer:
81.25
Step-by-step explanation:
Each glass mug below has a radius of 2 inches and a height of 3.75 inches. If the mugs are
sold in sets of 4, find the total surface area of the mugs, not including
the handles.
Total surface area includes the area of the 2 bases and the area of the curve surface area this was found to be 289.064 square inches for all four mugs
Mensuration of SolidsGiven Data
Radius r = 2 inchesHeight h = 3.75 inchesNumber of mugs = 4Total surface area of cylinder = 2πr(r + h)
TSA of 1 mug = 2*3.142*2(2+3.75)
TSA of 1 mug = 12.568(5.75)
TSA of 1 mug = 72.266 square inches
if the total surface area of one mug is 72.266 square inches
hence the total surface area of 4 mugs will be
= 72.266*4
= 289.064 square inches
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A rectangle has an area of 227.9m^2.
One of the sides is 5.3m in length.
Work out the perimeter of the rectangle.
Divide the area by the side length to find the length of the other side:
227.9/5.3 = 43 m
now calculate the perimeter:
43 + 43 + 5.3 + 5.3 = 96.6m
Answer: 96.6m
Answer:
96.6 m
Step-by-step explanation:
Let the length of the other side b x m .
Then the area = 5.3 * x
227.9 = 5.3x
x = 227.9 / 5.3
= 43 m
So the perimeter = 2 * (width + length)
= 2(5.3 + 43)
= 2 * 48.3
= 96.6 m
Solve the following equation for x to find the total number of people who downloaded songs from a music site for a certain month:
x = 0.6x + 384
How many people downloaded songs from the site that month?
Answer:
960 people.
Step-by-step explanation:
x = 0.6x + 384
x - 0.6x = 384
0.4x = 384
x = 384 / 0.4 = 960.
WHOEVER RESPONDS FIRST WILL GET MARKED BEST.
A circle has a diameter of 14.5 inches. Using 3.14 for 1, what is the circumference of the circles, rounded to the nearest hundredth of an inch?
22.77 inches
45.53 inches
91.06 inches 165.05 inches
[tex]c = 2 \pi \: r[/tex]
[tex]c = 2 \times 3.14 \times 14.5[/tex]
[tex]c = 91.06[/tex]
Answer:
2nd option - 45.53 inches
Step-by-step explanation:
Circumference of a circle when given the diameter is given by the formula :
[tex]\pi d[/tex]
Since we are given a certain value for pi we use that and multiply it by the diameter to given the cirumference:
3.14 × 14.5 in =
45.53 inches
Therefore our answer is 43.53 inches (the 2nd option)