Six small and four medium bottles of lotion give a combined total of 93 fluid ounces of lotion. Which of the following pieces of information could help you determine the number of fluid ounces of lotion in a small bottle and the number of fluid ounces in a medium bottle?
Please answer this question. Giving out BRAINLIEST.This is due today, please help.
Answers
b. 8 small and 4medium bottle
Answer:
B
Step-by-step explanation:
In answer choice B, there is the same number of medium bottles as the number of medium bottles that you are given in the question.
Because you know that there are 93 fluid ounces in six small bottles and four medium bottles, you know that any different amount of fluid ounces with the answer choice would be because of the increase in small bottles.
By having a consistent change with only one variable (which is the small bottle) you can find the rate of change. Once you figure out how many fluid ounces are in the small bottles, you can find the total amount of fluid ounces that are in the small bottles. The amount that remains is the total fluid ounces for medium bottles.
Related Questions
A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = 2x3 + 11x2 – 23x – 14. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = 13x2 + 11x + 16. After how many days does the retailer start making money?
1
2
5
7
Answers
After 5 days, the retailer starts making the money. The solution has been obtained by using the concept of break - even.
What is break - even?
The balance point known as "break-even" results in neither a profit nor a loss. Every value below the break-even mark represents a loss, whereas any value above it represents a gain.
We are given revenue function as R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex].
The cost function is given as C(x) = [tex]13x^2 + 11x + 16[/tex].
The retailer will start earning only when the cost will be covered. This means that he will earn after when the R(x) = C(x).
So,
⇒ R(x) = C(x)
⇒ [tex]2x^3 + 11x^2 - 23x - 14[/tex] = [tex]13x^2 + 11x + 16[/tex]
⇒ [tex]2x^3[/tex] = [tex]2x^2 + 34x + 30[/tex]
⇒ [tex]x^3[/tex] = [tex]x^2 + 17x + 15[/tex]
⇒ [tex]x^3[/tex] - [tex]x^2 - 17x - 15[/tex] = 0
⇒ (x - 5) (x + 1) (x + 3) = 0
⇒ x = 5, -1, -3
Since, the days cannot be negative so, x = 5.
Hence, after 5 days, the retailer starts making the money.
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Question:
A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex]. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = [tex]13x^2 + 11x + 16[/tex]. After how many days does the retailer start making money?
a. 1
b. 2
c. 5
d. 7
Angela just subscribe to her favorite magazine she pays $44 for a two-year subscription she gets one magazine per month how much is she paying for each magazine
Answers
Answer: The answer is 1.8 or 1.83 repeating
Step-by-step explanation: When you do 44 divided by 24 (2 years) it gives you how much she needs to pay per month.
Answer:
Angela pays $1.83 for each magazine.
Step-by-step explanation:
Considering that there are 12 months in 1 year, there would be 12 * 2 = 24 months in 2 years. If she gets one magazine per month, she would get 24 magazines.
She would be paying $44 / 24 magazines = 11/6 ≈ 1.83.
So, she is paying about $1.83 for each magazine.
Find the surface area of the equilateral triangular pyramid.
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
Answers
The surface area of a triangular pyramid is the sum of areas of all faces of a triangular pyramid. Here, the surface area of a triangular pyramid with side 12 cm, base height 10 cm is equals to the 228 cm². So, the option (b) is correct choice.
Generally, a triangular pyramid has a triangular base and is bounded by three lateral triangular faces with one vertex. The units of measured surface area are square units like cm², m², ft² or cubit². The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. Mathematically,
Surface area = 1⁄2(a × b) + 3⁄2(b × s).
Where b --> the side of a pyramid
a --> the height of a base triangle, and
s --> the slant height of a pyramid. We have a triangular pyramid as present in above figure. Here height of base, a = 8 cm
slant height , s = 10 cm
side of a pyramid, b = 12 cm
So, Area of base triangle is, A1 = 1⁄2(a × b)
= (1/2)(8×12) = 48 cm²
Area of one triangular face = 1/2( b×s)
= 1/2( 12 × 10) = 60 cm²
Area of all triangular faces of a pyramid, A2 = 3× 60 = 180 cm²
The surface area of a pyramid = A1 + A2
= 48 + 180 = 228 cm²
Hence, required area is 228 cm².
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Complete question:
Find the surface area of the equilateral triangular pyramid. See the above
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or TI-84 graphing calculator to choose the correct plot below. All plots have the following window settings: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Answers
Answer:
I can provide guidance on how to create a box and whisker plot on a TI-83, TI-83 Plus, or TI-84 graphing calculator using the given data.
To create a box and whisker plot:
Enter the data into a list on the calculator. For example, L1={90.1, 91.1, 91.5, 92.2, 92.5, 93.1, 94.0, 94.6, 96.1, 98.3}.
Press STAT, then go to Edit.
Select L1, then press STAT again and select CALC.
Choose 1-Var Stats and press Enter. This will generate a list of statistics for the data set.
Press 2nd, then Y= (STAT PLOT).
Select Plot1, then turn it on.
Choose Box Plot as the plot type.
Select L1 as the data list.
Set the X list to any unused list (e.g. Xlist: L2).
Make sure the frequency is set to 1.
Set the window settings as follows: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Press GRAPH to view the box and whisker plot.
Note: If the plot does not display properly, try adjusting the Ymax and Ymin values until the plot is visible.
Erica has 2. 2 pounds of uncooked hamburger meat. A hamburger patty weighs about 6 ounces before it is cooked. Which is the maximum number of hamburger patties that Erica can make? i need help!!
Answers
Erica can make a maximum of 5 hamburger patties with the amount of meat she has.
What role do unit conversions have in mathematical and scientific calculations?In scientific and mathematical computations, unit conversions are crucial because they guarantee that data are stated in the proper units, enabling consistency and correctness. To combine or compare numbers and to understand the findings meaningfully, values must be converted to a standard unit of measurement. Calculation mistakes and erroneous conclusions can result from improper unit conversion.
Given that, a hamburger patty weighs about 6 ounces before it is cooked.
Thus,
2.2 pounds = 35.2 ounces (1 pound = 16 ounces)
35.2 ounces / 6 ounces per patty = 5.87
Erica can make a maximum of 5 hamburger patties with the amount of meat she has.
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Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 = display floor space (square meters), X 2 = competitors' advertising expenditures (thousands of dollars), X 3 = advertised price (dollars per unit). (a) Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p -values to 4 decimal places.) (b-2) Choose the correct option. Only CompetingAds differs significantly from zero. Only FloorSpace differs significantly from zero. Only Price differs significantly from zero.
Answers
zero
Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 = display floor space (square meters), X 2 = competitors' advertising expenditures (thousands of dollars), X 3 = advertised price (dollars per unit).Part a) the table is not given with the question. Please provide the required data and we will try our best to answer your question.The null and alternative hypotheses in a hypothesis test are:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3. Since we have 3 predictors in the model so there will be three hypothesis test as well:Null and alternative hypotheses for hypothesis tests for β1, β2, and β3 are as follows:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3.Therefore, if the absolute value of the computed t-value is greater than the absolute value of the table t-value for a specified α and n – k – 1 degrees of freedom, then the null hypothesis for that predictor is rejected. Hence, we can say that the predictor variable is significant at the α level.The table for t-values and p-values will be created based on the degree of freedom (d.f), the significance level (α), and the t-distribution function. The t-value is calculated using the following formula:t= (βi- 0) / SE(βi).Part b) Only CompetingAds differs significantly from zero is the correct option.
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Answer the question faster! I only have 5 mins left!
Answers
The net of the pyramid is attached and the surface area of the triangular based prism is 54 ft²
The net of the pyramidThe shape is given as
A triangular based prism
This means that the net would have 2 triangles and 3 rectangles
See attachment for the net of the prism
How to determine the surface areaThe surface area of a triangular based prism is calculated as
Area = (Perimeter of triangle) * Length + 2 * Base area
Substitute the known values in the above equation, so, we have the following representation
Area = (3 + 2 1/2 + 2 1/2) * 6 + 2 * 0.5 * 2 * 3
Evaluate
Area = 54
Hence, the surface area is 54 ft²
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please answer i’m giving most of my points
Answers
Answer:
Aprove or deny a loan
Step-by-step explanation:
If the bank knows you can't pay them back they won't.
They choose this by checking your net worth.
(09.04 MC)
A circle has its center at (−2, 5) and a radius of 4 units. What is the equation of the circle? (1 point)
Answers
According to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]
What is circle ?
A circle is a two-dimensional geometric shape that consists of all points in a plane that are a fixed distance, called the radius, from a given point called the center. A circle can also be defined as the set of all points that are equidistant from a central point.
The equation of a circle with center (h, k) and radius r is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
In this case, the center of the circle is (-2, 5) and the radius is 4, so the equation of the circle is:
[tex](x - (-2))^2 + (y - 5)^2 = 4^2[/tex]
Simplifying this equation gives:
[tex](x + 2)^2 + (y - 5)^2 = 16[/tex]
Therefore, according to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]
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What is the volume of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Height 9 m
Radius 4 m
cubic meters
Answers
a footrace takes place among four runners. if ties are allowed (even all four runners finishing at the same time), how many ways are there for the race to finish?
Answers
The race can finish in 256 possible ways, accounting for the possibility of ties among the four runners.
There are 4 runners in the race and any of them can finish first, so there are 4 ways to choose the winner. Once the winner is chosen, there are 4 remaining runners who can finish in second place.
Therefore, there are 4 × 4 = 16 ways for the first two places to be filled.
Once the first two places are filled, there are 4 remaining runners who can finish in third place.
Therefore, there are 4 × 16 = 64 ways for the first three places to be filled.
Finally, once the first three places are filled, there are 4 remaining runners who can finish in fourth place.
Therefore, there are 4 × 64 = 256 ways for all four runners to finish the race.
Therefore, there are 256 ways for the race to finish, including ties.
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Complete the table for the quadratic function below. Type the value of y that
corresponds with each value of x.
y=2(x-3)²-2
xy=2(x-3)²-2
1
2
3
4
5
Answers
Answer: in the following order:
6
0
-2
0
6
Step-by-step explanation:
Just need to evaluate the function for each value of X
for x=1 y=2(1-3)^2-2= 6
for x=2 y=2(2-3)^2-2= 0
for x=3 y=2(3-3)^2-2= - 2
for x=4 y=2(4-3)^2-2= 0
for x=5 y=2(5-3)^2-2= 6
its me again ....
loll answer?
thankssss
Answers
Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).
What is Estimate?Estimate, a near enough approximation of the true value. To make arithmetic simpler and more understandable, many assumptions are made.
Estimate is less than actual answer :
6.35 + 3.4 = 9.75
2.3 * 4.15 = 9.545 (≈ 9.55)
Estimate is more than actual answer :
7.9 * 4.85 = 38.315
3.6 + 4.8 = 8.4
So here, Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).
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how do you find the dimensions of the parallelogram
Answers
To find the dimensions of a parallelogram, you need to know the length of its base and the perpendicular distance from the base to the opposite side, which is also called the height or altitude of the parallelogram.
What is a parallelogram?A quadrilateral (a four-sided polygon) with two pairs of parallel sides is referred to as a parallelogram. This means that the opposite sides of the parallelogram are parallel and have the same length, while the adjacent sides are unequal in length.
The properties of a parallelogram include:
The opposing sides seem to be congruent and parallel (equal in length)
Congruent opposite angles (equal in measure)
The angle adjacent to each other are supplementary (their sum is 180 degrees)
Diagonals bisect each other (the diagonals divide each other into two equal parts)
If you have the measurements of the sides and angles of the parallelogram, you can use trigonometry and geometry to find the length of the base and the height. For example, if you have the lengths of two adjacent sides and the angle between them, you can use the sine function to find the height. The base can be found by using the formula for the area of a parallelogram, which is base times height.
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Apnex, Inc. , is a biotechnology firm that is about to announce the results of its clinical trials of a potential new cancer drug. If the trials are successful, Apnex stock will be worth $ 68 per share. If the trials are unsuccessful, Apnex stock will be worth $ 18 per share. Suppose that the morning before the announcement is scheduled, Apnex shares are trading for $ 56 per share
Answers
The probability of the trials being successful is 0.625 or 62.5%. So, the expected value of Apnex stock after the announcement is $53.25 per share.
The odds of the trials being successful or failed, as well as the associated stock prices, must be taken into account in order to determine the predicted value of Apnex shares after the announcement.
we can state:
P(success) + P(failure) = 1
Let the market has already taken the probability into account and that the $56 stock price at the moment reflects the stock's anticipated value following the announcement. To put it another way, we can construct an equation based on the anticipated value formula:
Estimated Value = $68 for success and $18 for failure
Also, we are aware that the present stock price and the predicted value are equal:
Estimated Value = $56
When the second equation is substituted for the first equation, we obtain:
P(success) x $68 plus P(failure) x $18 equals $56.
For P(success), we obtain:
P(success) is equal to ($56 - $18) / ($68 - $18), or 0.625.
Thus, 0.625 or 62.5% of the trials will be successful.
We may determine the anticipated value of the shares following the announcement using this probability:
Estimated Value: 0.625 times $68 plus 0.375 times $18 equals $53.25
therefore, $53.25 per share is the anticipated value of Apnex shares following the announcement.
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.Pam wants to make a snack mixture of three parts of dried fruit to every four parts of assorted nuts. How many pounds of dried fruit will she need to make 35 pounds of the mixture?
Answers
Answer:
15 pounds
Step-by-step explanation:
for every 3 parts of dry fruit , four parts of nuts are added.
we know the total composition of the mixture is 35 pounds.
The total Composition of the mixture will be 7 parts
3/7 is dry fruit
4/7 is assorted nut
we can multiply the dry fruit composition to total
= 3/7 * 35 = 3*5 = 15
Pam needs 15 pounds of dry fruit to make the mixture.
Please help me!!!!!!!
Answers
Answer:
Below
Step-by-step explanation:
The ENTIRE CIRCLE arc length (360° circumference ) is given by pi * 2 r
= pi * 2 * 10 = 20 pi cm
We want to find 299 out of 360ths of this
299/360 * 20 pi = ~ 52.2cm
Coins are placed into a treasure chest, and each coin has a radius of 1.2 inches and a height of 0.0625 inches. if there are 250 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? round to the nearest hundredth and approximate using π = 3.14.
a. 0.28 in3
b. 70.65 in3
c. 117.75 in3
d. 282.60 in3
Answers
Answer:
i only know the answer (I guessed on but I think it's 70.65
Step-by-step explanation:
let me know if I'm right 0w0
A trapezoid has a base of 5 millimeters,
another base of 7 millimeters, and a height
of 6 millimeters. Explain how the area of the
trapezoid will change if the height and both
bases are doubled.
Answers
The area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
What is trapezoid ?Trapezoids can be defined as quadrilaterals that have two parallel sides and two non-parallel sides.
The area of a trapezoid is given by the formula:
A = (b1 + b2) * h / 2
Where
b1 and b2 are the lengths of the two basesh is the heightIf we double both bases and the height, we get:
b1' = 2 * b1 = 2 * 5 mm = 10 mm
b2' = 2 * b2 = 2 * 7 mm = 14 mm
h' = 2 * h = 2 * 6 mm = 12 mm
Now we can calculate the area of the new trapezoid:
A' = (b1' + b2') * h' / 2
A' = (10 mm + 14 mm) * 12 mm / 2
A' = 12 * 12 mm^2
A' = 144 mm^2
Therefore, the area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y=-4x²+141x−703
Answers
The maximum amοunt οf prοfit the cοmpany can make is $543
What is prοfit?Prοfit is the mοney yοu have left after paying fοr business expenses. There are three main types οf prοfit: grοss prοfit, οperating and net prοfit.
Grοss prοfit is biggest. It shοws what mοney was left after paying fοr the gοοds and services sοld. Operating prοfit is next. It shοws what's left after alsο paying οperating cοsts such as rent, electricity, phοnes and in sοme cases staff.
Net prοfit cοmes last. It shοws what yοu made after deducting all cοsts and tax. Yοu get tο hοld οntο net prοfit.
Let y represent the amοunt οf prοfit and x represent the selling price.
The relatiοnship between x and y is:
y = -4x² + 141x – 703
The maximum prοfit is at dy/dx = 0, hence:
dy/dx = -8x + 141
-8x + 141 = 0
8x = 141
x = 17.625
The maximum prοfit is:
y = -4(17.625)² + 141(17.625) – 703 = 543
The maximum amοunt οf prοfit the cοmpany can make is $543
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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. a scatter plot and line of fit were created for the data. scatter plot titled students' data, with points plotted at 1 comma 60, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 80, 3 comma 90, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 40 and 2 comma 70. find the y-intercept of the line of fit and explain its meaning in the context of the data.a. 30; for each additional hour a student studies, their grade is predicted to increase by 30% on the testb. 15; for each additional hour a student studies, their grade is predicted to increase by 15% on the test c. 70; a student who studies for 0 hours is predicted to earn 70% on the test d. 40; a student who studies for 0 hours is predicted to earn 40% on the test
Answers
Answer: The y-intercept of the line of fit can be found by looking at the point where the line crosses the y-axis. From the given information, we know that the line passes through the points (0, 40) and (2, 70). To find the equation of the line, we can use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. We can find the slope of the line by using the two points:
m = (y2 - y1) / (x2 - x1)
m = (70 - 40) / (2 - 0)
m = 30
So the equation of the line is:
y = 30x + b
To find the y-intercept, we can plug in one of the points and solve for b. Let's use the point (0, 40):
40 = 30(0) + b
b = 40
Therefore, the y-intercept of the line of fit is 40. In the context of the data, this means that a student who did not study at all (0 hours) is predicted to earn a grade of 40 on the test. However, it's important to note that this prediction is based on the data collected from the sample of 8 students and the line of fit may not accurately predict the grades of all students who did not study.
Your welcome.
high voltage, inc., a light bulb manufacturer, wants to know if there's a difference in mean life span between its product and that of a competitor. they collect paired data and calculate the difference in each pair to create one set of numbers that represents the differences within each pair. what notation should high voltage use to construct its null and alternative hypotheses?
Answers
High Voltage, Inc. should use the following notation to construct its null and alternative hypotheses: Null Hypothesis: H0: μ1 - μ2 = 0; Alternative Hypothesis: H1: μ1 - μ2 ≠ 0; where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.
The notation High Voltage should use to construct its null and alternative hypotheses is:
(i) Null Hypothesis: H0: μ1−μ2=0
where μ1 represents the mean life span of High Voltage's product and μ2 represents the mean life span of the competitor's product.
(ii) Alternative Hypothesis: Ha: μ1−μ2≠0
Where,μ1 and μ2 are the mean lifespan of the light bulbs of High Voltage and its competitor, respectively.
In this problem, paired samples t-test should be used to test the hypotheses.
Paired sample t-test: It is a statistical procedure used to compare two population means with two samples of dependent observations, where the dependent variable is the same or the same subject measured under different conditions. It is used when the observations are paired, i.e., each pair of observations consists of two measurements made on a single subject or item.
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A bag contains 30 balls, of which x are blue and the rest are red. If 5 red balls are removed, the probability of picking a blue ball at random increases by 1/30. Find the value of x.
Answers
Answer:
∴ We have 12 blue balls and 3 red balls .
A 20,000 gallon swimming pool contains 5000 gallons of water when a hose is placed in the pool and begins adding water at a rate of
1250 gallons per hour.
Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool
until the pool is full
Answers
Therefore , the solution of the given problem of unitary method comes out to be for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t .
What is an unitary method?To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.
Here,
=> V(t) = 5000 + 1250t
where V(t) represents the amount of water in the pool at moment t (in hours)
t equals time (in hours)
The pool initially has 5000 gallons of water in it, so we add that to the 1250 t of water introduced by the hose.
We can use the time period as the x-axis (horizontal axis) and the amount of water as the y-axis to graph this equation. (vertical axis).
For instance, we can select the water volume interval from 0 to 20,000 gallons and the time interval from 0 to 16 hours (when the pool is full).
Then, for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t and connect them with a line in order to get the image.
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if the actual length is 28.3m and the scale is 1cm to 2m, what is the length on drawing
Answers
The length on drawing with the given scale is 14.15 cm.
How to determine the length on drawingUsing the given scale of 1cm to 2m, we can set up the following proportion to find the length on the drawing:
1 cm : 2 m = x cm : 28.3 m
where x is the length on the drawing that we want to find.
To solve for x, we can cross-multiply and simplify:
1 cm * 28.3 m = 2 m * x cm
Evaluate the products and remove the units
28.3 = 2x
Divide both sides by 2 to solve for x
x = 28.3 / 2
Evaluate
x = 14.15
Therefore, the length on the drawing is 14.15 cm.
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Required information Note this is a multi-part problem. That means the parts must be worked in order (a first, then b, then c, and so on). Furthermore, if you check your answer on one part, it will count as a check for all parts of the problem. Therefore, work all parts of the problem (in order!), then check your answer. Rework all missed parts before using your next "check my answer". Let X=5 L 40' and Y = 20 L -30° The polar form of the quantity (X + Y)X* is Oy Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees.
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The polar form of the quantity will be 100.83 L 76.47°.
Given X = 5 L 40'andY = 20 L -30°(X + Y)X* .The expression (X + Y)X* can be simplified as: X * X + Y * X* =X² + Y * X* .Now, we need to find the polar form of the quantity (X + Y)X*.That is, we need to representX² + Y * X* in polar form. By using rectangular to polar conversion, we can convert the above expression to polar form.
Using the formula:
r² = x² + y²... Equation 1
θ = tan⁻¹(y / x)... Eq 2 (Where,x = real part of the expression)
x = X² = 5² = 25... Eq 3 (y = imaginary part of the expression)
y = Y * X*... Eq 4
Therefore, Y
Y * X* = 20 L -30° * 5 L 40'20 L -30° * 5 L 40' = 100 L 10°... Eq5
y = 100 L 10°.
Substituting the values of x and y in equations 1 and 2, we get:r² = x² + y²r² = 25² + 100²r² = 10025 + 100²r = 100.83θ = tan⁻¹(y / x)θ = tan⁻¹(100 L 10° / 25)θ = tan⁻¹(4 L 10°)θ = 76.47°
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Show that x^5-5x^3+5x2+-1=0 has 3 equal roots and find that root
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First, we can find the derivative of the polynomial:
f(x) = x^5 - 5x^3 + 5x^2 - 1
f'(x) = 5x^4 - 15x^2 + 10x
Next, we can set f(x) equal to zero and solve for x:
x^5 - 5x^3 + 5x^2 - 1 = 0
We can then substitute this value of x into the derivative f'(x):
f'(x) = 5x^4 - 15x^2 + 10x
f'(x) = 5(x^4 - 3x^2 + 2)
f'(x) = 5(x^2 - 1)(x^2 - 2)
We can see that the derivative has two roots, x = -1 and x = 1, each with multiplicity 2. This implies that the original polynomial has three equal roots, since each of these roots will be a repeated root of multiplicity 2.
To find the roots, we can use synthetic division to divide the polynomial by (x - 1)^2:
1 | 1 0 -5 5 -1
| 1 -1 4 -1
| 1 1 -6 9 -2
1 | 1 1 -6 9 -2
| 1 -5 1
| 1 2 -11 10
So, (x - 1)^2 is a factor of the polynomial, and we can factor the remaining quadratic as:
(x - 1)^2(x^2 + 2x - 10) = 0
Solving for the roots of the quadratic factor, we get:
x^2 + 2x - 10 = 0
(x + 1 + sqrt(11))(x + 1 - sqrt(11)) = 0
Therefore, the roots of the original polynomial are:
x = 1 (with multiplicity 2)
x = -1 + sqrt(11)
x = -1 - sqrt(11)
So, the three equal roots of the polynomial are 1, 1, and -1 ± sqrt(11).
An account with an initial balance of $3500 earns interest that is compounded annually. If no other deposits or withdrawals are made, the account will have a balance of $4390.40 after 2 years.
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Answer:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial balance
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:
$4390.40 = $3500(1 + r/1)^(1*2)
$4390.40/$3500 = (1 + r)^2
1.2544 = (1 + r)^2
√1.2544 = 1 + r
1.12 = 1 + r
r = 0.12 or 12%
Therefore, the annual interest rate is 12%.
What is the difference?complete the stament -2-8=
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Answer: -10
Step-by-step explanation: You're welcome <3
Evaluate the expression shown below and write your answer as a
fraction in simplest form.
1/4 - 1/10
Answers
Explanation/Work:
( If you want an explanation just tell me in the comments, and I shall provide it)
1/4 - 1/10
5/20 - 2/20
3/20