Juan sold a bicycle at a discount of 15%. If the selling price was $340, find the usual price of the bicycle.
Answer: $400
Step-by-step explanation:
Discount = 15%
The original price/value of an item is always 100%
So selling price (%) = original price - discount = 100%-15% = 85%
We got selling price as 85%
This implies that 85% = 340
Let's find 1% first, then 100%
1% = 340÷85 = 4
100% = 4 × 100 = $400
The usual (normal/original) price is $400
Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let's represent the usual price of the bicycle by P.
Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).
We can express this relationship as an equation:
S = 0.85P
We also know that the selling price of the bicycle was $340.
Substituting S = $340 into the equation above, we get:
$340 = 0.85P
To find P, we can solve for it:
P = $340 / 0.85
P = $400
Therefore, the usual price of the bicycle was $400.
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A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
.
The maximum number of tables the restaurant can have is 37. This ensures that the total number of people seated at the tables (37 * 4 = 148) is less than the legal limit of 150 people in the restaurant at one time.
To find the maximum number of tables the restaurant can have, we need to solve the inequality 4t < 150.
Dividing both sides of the inequality by 4, we have:
t < 150/4
Simplifying the right side, we get:
t < 37.5
Since the number of tables must be a whole number, we can conclude that the maximum number of tables the restaurant can have is 37.
Let's verify this by substituting t = 37 into the original inequality:
4t < 150
4(37) < 150
148 < 150
Since 148 is less than 150, the inequality holds true. However, if we increase the number of tables to 38, we get:
4(38) < 150
152 < 150
In this case, 152 is not less than 150, so the inequality is no longer satisfied.
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What do I do?
Brief Calculus Question: Find Each limit (if it exist)
For the given function the value of limits are
\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5
\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0
\(\lim _{x\to 0}\left x^2+5\)is 5
The given function is f(x)= x²+5, when x≤0
f(x)=2x when x>0
\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)
Which is \(\lim _{x\to 0^-}\left x^2+5\)
The given limit is a left hand limit as there is minus in the limits
When we apply x as 0 we get the value 5
Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)
So \(\lim _{x\to 0^+}\left 2x\)
The given limit is a right hand limit as there is positive in the limits
When we apply x as 0 we get 0
Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)
Which is \(\lim _{x\to 0}\left x^2+5\)
We get 5
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A total of 50 randomized samples were assigned into 5 different treatment groups in a pharmaceutical science experiment. Each group includes 10 persons (subjects). In order to test if any difference is discernible among these 5 treatments, one-way ANOVA was conducted for the study. Here are data we calculated: Sum of square between group = 232. Sum of square within group = 400.Subject Treatment 1 Treatment 2 Treatment 3 Treatment 4 Treatment 51 2
---
10ANOVA Summary Table
Source Sum of Square Degree of freedom Mean Square F
Between 232
Within 400
Totala. State null hypothesis and alternative hypothesis. b. Calculate the degree of freedom between group, and the degree of freedom within group. c. Mean squares between groups. d. Mean squares within groups.e. F ratiof. If critical value of F is 2.61, should we reject or accept the null hypothesis?g. State your conclusion for this research.
The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments
How to calculate the valuesDegree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45
Mean squares between groups is calculated as follows:
Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58
Mean squares within groups is calculated as follows:
Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places
F ratio is calculated as follows:
F= Mean squares between groups/Mean squares within groups
= 58/8.89
= 6.524184477
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Round each number to the nearest hundred 124 =
2311=
48=
An Olympic diver is competing for a metal. His height in meters above the water can be modeled by the function
f (x)= -4.9x^2+9.8x+14.7f(x)=−4.9x +9.8x+14.7
where is is the time in seconds after he begins the dive.
After how many seconds does he reach the water?
What domain makes sense for this scenario?
Answer:
-4.9x²+75x=-4.9x+50x+38
75x=50x+38
25x=38
x=1.52
1.52 -4.9(1.52)²+75(1.52)=102.67904≈102.7 meters
Double check: -4.9(1.52)²+50(1.52)+38=102.67904≈102.7. Yes.
102.7 meter.
Step-by-step explanation:
Find an equation of the line that satisfies the given conditions.
Through (2, 9); parallel to the line passing through (3, 7) and (−1, 3)
9514 1404 393
Answer:
y = x +7
Step-by-step explanation:
The slope of the given line can be found as ...
m = (y2 -y1)/(x2 -x1)
m = (3 -7)/(-1 -3) = -4/-4 = 1
Then the point-slope form of the equation for the desired line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y - 9 = 1(x -2)
y = x -2 +9
y = x + 7 . . . . slope-intercept form
__
The attachment shows a graphing application that will write the equation of the line. Here, it shows the desired line has the equation ...
x -y = -7 . . . . desired line equation in standard form
Enter the equation of a circle that is congruent to circle C and is centered at point P
The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².
What is the equation of a circle?In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.Based on the information provided, we have the following parameters for the equation of this circle:
Center (h, k) of P = (1, 5)Radius (r) of P = 5 units.By substituting the given parameters, we have:
(x - h)² + (y - k)² = r²
(x - 5)² + (y - 1)² = 5²
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Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.
A) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + 2nπ)
B) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
C)(6, negative pi divided by 5 + (2n + 1)π) or (-6, negative pi divided by 5 + 2nπ)
D) (6, negative pi divided by 5 + 2nπ) or (6, pi divided by 5 + (2n + 1)π)
All polar coordinates of point P where P = ordered are given are mathematically given as
(6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
Option B is correct.
What are all polar coordinates of point P where P = ordered pair 6 commas negative pi divided by 5.?Generally, the equation for all polar coordinates is mathematically given as
\(P= 6,\frac{-pi}{5}\)
Finding the whole set of polar coordinates for An arbitrary point's polar coordinates may be written as (r, ), where (r, ) = (r, +2n) for some n and r.
If n is a positive integer and r is negative, then (r,) = (-r, +(2n+1)).
In conclusion, we may solve the problem by setting r = 6 and = -/6.
If n is an integer and r is positive, then P(6,-/6) = (6, -/6) + 2n, and if n is an integer and r is negative, then P(-6,-/6) = (-6, -/6) + (2n+1).
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\( \sqrt[3]{800} \)
between 2 and 3
between 4 and 5
between 9 and 10
Given that n is an integer and 0 < 4n <30, what is the sum of all possible integer values of n
n can be all the way upto 7 as 8 x4 = 32 which is higher than 30. The lowest possible diggit is 1.
n = 1, 2, 3, 4, 5, 6, 7
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
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What is the value of x (x+30) 2x
Answer: 30
Step-by-step explanation:
Vertical angles are congruent.
\(x+30=2x \implies x=30\)
Terrence made a scale drawing of a boarding school. The scale he used was
7 centimeters: 3 meters. If the actual length of a building at the school is 300 meters, how
on is the building in the drawing?
The building in the drawing is 700 centimeters or 7 meters.
Define the unitary method.The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What are ratios and proportions?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Given 3 meters on real is equal to 7 centimeters on drawing
i.e. 3 meters=7 centimeters
or, 1 meter = 7/3 centimeters
We need to find reading for 300 meters so,
or, 300 meters=7/3*300 centimeters
=700 centimeters or 7 meters
Therefore the building in the drawing is 700 centimeters or 7 meters.
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Write the Fractions in Simplest Form
12/16
Answer:
3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
12/4 = 3
12/4 = 4
simplest form is 3/4
Find the equation of a circle whose
center is (-3,5) and passes through
P(1,8).
The equation of the circle is \((x+3)^2 + (y-5)^2 = 5^2\)
What does the equation for a circle look like in cartesian form?
Cartesian coordinate system with the origin indicated in red and a circle with a radius of two. A circle has the equation (x a)^2 + (y b)^2 = r^2, where a and b are the center's coordinates (a, b) and r is the radius.
The equation of a circle has the following conventional Cartesian form:
\((x-h)^2 + (y-k)^2 = r^2\) ---------- 1
where (h, k) is the circle's center, (x, y) is any point on the circle, and r is its radius
Substitute the center (-3,5) into equation [1]:
\((x+3)^2 + (y-5)^2 = r^2\) --------------------- 2
Substitute the point (1,8) into equation [2] and solve for r:
\((1+3)^2 + (8-5)^2 = r^2\\(4)^2 + (3)^2 = r^2\\16 + 9 = r^2\\25 = r^2\\r = 5\)
Substitute 5 for r into equation [2]
\((x+3)^2 + (y-5)^2 = 5^2\)
Hence the equation of the circle is \((x+3)^2 + (y-5)^2 = 5^2\)
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A baker makes 51 loaves of bread in 8 1/2 hours. What is the unit rate for the number of loaves in one hour. I need a answer pleaseee
Answer:
6
Step-by-step explanation:
51 divided by 8.5
what will be the value of d when an airplane flies at 420 miles per hour for three hours?
Answer:
1260 I think
Step-by-step explanation:
because if the airplane is travelling at 420 mph for THREE hours then 420x3=1260
The main sail of a sailboat has the dimensions shown in the figure at the right. What is the height of the main sail?
Answer:
\(h = 16.1\)
Step-by-step explanation:
\(sin A /a = sin B / b = sin C/c\) where A is angle and a is side opposite of angle
\(sin (49) / h = sin(41)/ 14\) cross-multiply
\(h*sin(41) = 14 * sin(49)\)
\(h = (14*sin(49))/ sin(41)\)
\(h = 16.1\)
On a piece of paper, graph f(x) = (4x≤3. Then determine which answer
12 if x > 3
choice matches the graph you drew.
The graph of the piecewise function is the one in option D-
Which one is the graph of f(x)?First, we know that:
f(x) = 4 when x ≤ 3
So, we want to have a horizontal line in the left side of the graph, such that it ends in a closed circle at x = 3 (we need to have a closed circle because the symbol ≤ is used).
From the given graphs, the only one with that form is D.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 10,846 total votes, how many yes votes were there?
Answer:
4930
Step-by-step explanation:
Let the number of yes votes be 5x and the number of no votes be 6x.
Total votes = yes votes + no votes
= 5x + 6x
= 11x
11x = 10,846
No. of yes votes (5x) = \(\frac{5}{11}\) × 10,846
= 4930
You flip a coin 100 times and record that 48 are heads and 52 are tails. What is the relative frequency or experimental probability of landing on heads?
whats the percentage
As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.
What is probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.
The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:
Number of Heads / Total Number of Flips = Experimental Probability of Heads
The number of heads in this case is 48, and the total number of flips is 100. Therefore,
Heads Experimental Probability = 48 / 100 = 0.48
We can multiply this by 100 to get a percentage:
Heads Experimental Probability = 0.48 * 100 = 48%
As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.
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If you open a bank account with 23,000 and its annual interest is compounded quarterly. What would the interest have to be for the amount to grow to $50,000 in 7 years?
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}\)
\(50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r\)
[5-TI] 4. The layout of Joe's yard is shown below. Joe must spread out topsoil to a depth
of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and
contains 10 cubic yards of topsoil. How much will the topsoil cost to complete
this job?
75 feet
64 feet
36 feet
53 feet
19 feet
22 feet
The total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB).
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that Joe must spread out topsoil to a depth of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and contains 10 cubic yards of topsoil.
In 10 yards³ = 466,560.1 in³
Assume the length and breadth to be [L] inches and [B] inches. The height is 15 inches.
Volume of the layout will be -
V = (15 x L x B) in³
466,560.1 in³ of the topsoil costs $67.89.
1 in³ of the topsoil will cost $(67.89/466560.1)
(15 x L x B) in³ of the topsoil will cost -
$(67.89/466560.1) x (15LB)
(1.46 x 10⁻⁴)(15LB)
Therefore, the total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB)
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The first number in a pattern is 84. The pattern follows the rule divide by 2 then add 10. Find the next three terms and then describe the pattern
Answer:
84
34
27
Step-by-step explanation:
A proportion is two fractions that have an equal sign between them. True or False?
Answer:
True
Step-by-step explanation:
That is one way to write a proportion, yes, so I say this is True.
the following figure shows triangle abc with side lengths ab=10 bc=8 and ca=5 de is constructed parallel to ab and to originate at point d, the missing of ac
Answer:
Step-by-step explanation:
There are 10 girls and 8 boys at a party. A cartoonist want to sketch a picture of each boy with each girl. How many sketches are required?
Answer:
80
Step-by-step explanation:
Each boy can be sketched with all of the girls so. 8*10=80
The table shows three unique, discrete functions.
x f(x) g(x) h(x)
-1
0
3
185
15
2
3
0
-25
-10-204
2
3
2
-3
2
3
4
5
6
Which statements can be used to compare the
characteristics of the functions? Select three options.
Of(x) has the greatest maximum.
h(x) has the greatest x-intercept.
g(x) has the smallest minimum value.
All three functions share the same domain.
All three functions share the same y-intercept.
All thre functions share the same y intercept
We can analyze the characteristics of the given functions based on the information provided in the table.
We cannot determine which function has the greatest maximum based on the table alone, as we do not have the complete graph of any of the functions.
We can see from the table that h(x) has an x-intercept of 0, which is the smallest among the three functions. Therefore, we can say that h(x) has the smallest x-intercept.
We can see from the table that g(x) has a minimum value of -204, which is the smallest among the three functions. Therefore, we can say that g(x) has the smallest minimum value.
We cannot determine if all three functions share the same domain based on the table alone. We can only see that all three functions have been evaluated at the same set of input values.
We can see from the table that the y-intercept of f(x) is 2, the y-intercept of g(x) is 3, and the y-intercept of h(x) is 4. Therefore, we can say that all three functions have different y-intercepts.
Therefore, the statements that can be used to compare the characteristics of the functions are:
h(x) has the smallest x-intercept.
g(x) has the smallest minimum value.
All three functions have different y-intercepts.
Let P(x) = -50x+20,000x-1,5000,000 represent the profit function for manufacturing a particular model of recreational
vehicle (RV) and x represent the number of RVS produced monthly. Use a compound inequality to state the range of the
number of RVs that need to be sold each month for the company to make a profit.
O 0
100
200
none of the answer choices
O 0
O 100
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.
The profit function is given by P(x) = -50x + 20,000x - 1,500,000.
To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:
-50x + 20,000x - 1,500,000 > 0.
Combining like terms, we have:
19,950x - 1,500,000 > 0.
Now, let's solve this inequality for x:
19,950x > 1,500,000.
Dividing both sides by 19,950, we get:
x > 1,500,000 / 19,950.
Simplifying the right side, we have:
x > 75.
The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
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Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
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