After solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.
What are equations?Equation: A statement stating the equality of two expressions containing variables or numerical values.
Equation: A formula that uses the equals sign to combine two expressions and declare their equality.
In essence, equations are questions, and the methodical pursuit of solutions to these questions has served as the driving force behind the creation of mathematics.
Sean mass = x
Lan mass = x - 2.5
Then, form the equation and solve it as follows:
x + (x - 2.5) = 121.5
x + x - 2.5 = 121.5
2x - 2.5 = 121.5
2x = 121.5 + 2.5
2x = 124
x = 124/2
x = 62
Then, x - 2.5 = 59.5.
Therefore, after solving the equation we know that the mass of Sean and Ian is 62kf and 59.5 ks respectively.
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Alice wanted to compare birthday cake prices in two supermarkets. She wrote down the daily prices for a few days and found that the difference of the two sample means is $4.01. The standard deviation of the difference of the sample means is $5.46. The 95% confidence interval of the sample mean difference is between and .
Considering a period of 10 days, the 95% confidence interval of the sample mean difference is between $0.1 and $7.9.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 10 - 1 = 9 df, is t = 2.2622.
The parameters for this problem are given as follows:
[tex]\overline{x} = 4.01, s = 5.46, n = 10[/tex]
Then the lower bound of the interval is given as follows:
4.01 - 2.2622 x 5.46/sqrt(10) = 0.1.
The upper bound of the interval is given as follows:
4.01 + 2.2622 x 5.46/sqrt(10) = 7.9.
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Use the function y= 3/4x-1 to answer parts (a) & (b) below:
a. Find the equation of the inverse function of the given function using only algebra.
b. Using the coordinate grid, show how you can find the inverse function of the given function without using algebra. Then explain in at least one complete sentence how you know you found the correct inverse function based on your graph.
The inverse function of [tex]y = (3/4)x - 1[/tex] is: [tex]y = (4/3)(x + 1)[/tex]).
What is the inverse function of the given function?An inverse function refers to the function that returns the original value for which a function has given the output.
To find the inverse function of y= 3/4x - 1, we must to interchange x and y and solve for y:
x = (3/4)y - 1
x + 1 = (3/4)y
y = (4/3)(x + 1).
b. Finding the inverse function of a given function without using algebra can be done by graphing the function and reflecting it across the line y = x which is known as the reflection property of inverse functions.
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On Monday,1 7/8 inches of rain fell. On Tuesday,it rained 1/4 inch. What was the total rainfall for the two days?
Answer:
2.125 inches
Step-by-step explanation:
We Know
On Monday, 1 7/8 inches of rain fell. On Tuesday, it rained 1/4 inch.
1 7/8 = 15/8
What was the total rainfall for the two days?
We Take
15/8 + 1/4 = 15/8 + 2/8 = 17/8 inches of rainfall
17/8 = 2.125
So, the total rainfall for the two days is 2.125 inches.
Answer:
2 1/8 inches
Step-by-step explanation:
You need to add the two amounts of rainfall together to get your answer, which is 1 7/8 + 1/4. To add these fractions, make the fractions equivalent. To find equivalent fractions, we multiply the numerator and the denominator by the same number.
Since 1/4 can be 2/8, you can now add 1 7/8 + 2/8. This equals 2 1/8.
Therefore, the total rainfall for the two days was 2 and 1/8 inches.
IM SO SORRY IF THIS DID NOT MAKE SENSE!
HELP ILL GIVE YOU EVERYTHING
Answer: 33
Step-by-step explanation: I promise its right i got you
What is the equation of a circle located (5,-3) and radius of 6?
Answer:
the answer is d
Step-by-step explanation:
55 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
(B ) joint is the answer.
invert and multiply 2/3 divide by 4
Inverting and multiplying the expression 2/3 divide by 4, we get 1/3
Inverting and multiplying the expressionsThe expression from the question is given as
2/3 divide by 4
When inverted, we have
2/3 divide by 4 = 2/3 multiplied by 1/4
Express properly
So, we have
2/3 divide by 4 = 2/3 * 1/4
Evaluate the product
So, we have
2/3 divide by 4 = 1/3
Hence, the solution is 1/3
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Question
Two people rented a car from the same agency. The first person drove 1010 miles and paid $232.30 for mileage. The
second person drove 765 miles and paid $175.95 for mileage. What is the agency's fee per mile?
The fee of agency's per mile is $0.23 or 23 cents.
Let the fee charged by agency for per mile drive be $x.
It is given that first people drove 1010 miles and charged $232.30 by agency.
So the equation for first person is,
1010x + y = 232.30........... (i), where y is fixed charge by the agency if it is there.
Also given that second person drove 765 miles and paid $175.95 to agency.
So the equation for the second person is,
765x + y = 175.95 ............. (ii)
Subtracting equation (ii) from equation (i) we get,
1010x + y - 765x - y = 232.30 - 175.95
245x = 56.35
x = 0.23
Hence the fee of agency's per mile is $0.23 or 23 cents.
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Infuse 0.8 liters for 9 hours at a drop factor of 60 gtt/ ml. how many ml will be infused per hour
the infusion rate is 88.89 ml/hr or 88.89 gtt/min.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Next, we can use the formula:
Flow rate (ml/hr) = (Volume infused ÷ Time in hours)
Flow rate (ml/hr) = (800 ml ÷ 9 hours)
Flow rate (ml/hr) = 88.89 ml/hr (rounded to two decimal places)
Finally, we can convert the flow rate from ml/hr to drops per minute (gtt/min) using the drop factor of 60 gtt/ml:
Flow rate (gtt/min) = Flow rate (ml/hr) x Drop factor (gtt/ml) ÷ 60 (min/hr)
Flow rate (gtt/min) = (88.89 ml/hr x 60 gtt/ml) ÷ 60 (min/hr)
Flow rate (gtt/min) = 88.89 gtt/min (rounded to two decimal places)
Therefore, the infusion rate is 88.89 ml/hr or 88.89 gtt/min.
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Triangle ABC ~ triangle DEF. Use the image to answer the question. a triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 4.4 Determine the measurement of EF. EF = 3.47 EF = 3.16 EF = 1.39 EF = 1.1
Answer:
FD = 3.16
Step-by-step explanation:
To determine the length of FD, we can use the property of similar triangles that corresponding sides are in proportion to each other. That is,
AB/DE = BC/EF = CA/FD
We are given the lengths of AB, CA, and BC in triangle ABC, and we know that triangle ABC is similar to triangle DEF. We can use the first two sides to find the third side of triangle DEF as follows:
AB/DE = 11/DE = 7.9/EF
=> EF = (DE * 7.9) / 11
Next, we can use the third proportionality to find FD:
CA/FD = 7.6/FD = 11/EF
=> FD = (11 * 7.6) / EF
=> FD = (11 * 7.6) / ((DE * 7.9) / 11)
=> FD = (11^2 * 7.6) / (DE * 7.9)
Now, we just need to substitute the given values and solve for FD:
FD = (11^2 * 7.6) / (4.4 * 7.9)
FD = 3.16
Therefore, the length of FD is 3.16.
Quadrilateral CDEF is a parallelogram. solve for x
Answer:
x = 25
Step-by-step explanation:
the consecutive angles in a parallelogram sum to 180° , that is
∠ C + ∠ D = 180
4x + 28 + 52 = 180
4x + 80 = 180 ( subtract 80 from both sides )
4x = 100 ( divide both sides by 4 )
x = 25
Consider a triangle like the one below. Suppose that c=57, b=15 , and C=108°. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
Answer: the sides of the triangle are a ≈ 41.5, b = 15, and c = 57, and the measures of the angles are A ≈ 42.7°, B ≈ 29.3°, and C = 108°.
Step-by-step explanation:
2x
(3x + 5)
Need a and b answered
Step-by-step explanation:
Triangle has 180 degrees in its interior angles .....90 degrees is the right angle leaving 90 degrees for 2x + 3x+ 5
2x + 3x+5 = 90
5x = 85
x = 17
smallest angle is then 2x = 34 degrees
The height of an object in motion at time "t" seconds is given by h(t)=-t^2 + 6t +10. Find the maximum height.
The height of the object at any given time t is given by the function h(t) = -t^2 + 6t + 10. To find the maximum height, we need to find the vertex of the parabola described by this function.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the y-coordinate of the vertex.
In this case, a = -1, b = 6, and c = 10, so we have:
t = -b/2a = -6/(-2) = 3
To find the maximum height, we need to evaluate h(3):
h(3) = -(3)^2 + 6(3) + 10 = 9 + 18 + 10 = 37
Therefore, the maximum height of the object is 37 units, which occurs when t = 3 seconds.
pic below
Which statement is supported by the information in the graph?
Answer B The income in Year 5 was twice the income in Year 1.
A Expenses have increased $200,000 each year over the last 5 years.
C The combined income in Years 1, 2, and 3 was equal to the combined expenses in Years 1, 2, and 3.
D The combined expenses in Years 3 and 4 were $300,000 more than the combined income in Years 3 and 4.
Correct option is D. the combined expenses are $300,000 more than the combined income.
What is the bar chart?In business, economics, statistics, and science, bar charts are frequently used to display and compare data. When dealing with data that can be divided into discrete categories, like nominal or ordinal data, they are especially helpful.
According to the Income and expenses graph;
We can verify each options one by one.
A. Expenses have increased $200,000 each year over the last 5 years:
If we see the graph for expenses in each year that is increased by $100,000 not the $200,000 over the last 5 years.
So, the option is wrong.
B. The income in Year 5 was twice the income in Year 1:
Income in year 1 = $600,000
Income in year 5 = $900,000
We can see here, income is not just double.
So, the option is wrong.
C. The sum of all expenses in Years 1, 2, and 3 was the same as the sum of all income in those years:
combined income in Years 1, 2, and 3 = $600,000 + $600,000 + $400,000 = $1600,000
combined expenses in Years 1, 2, and 3 = $400,000 + $500,000 + $600,000 = $1500,000
Both are not equal.
So, the option is wrong.
D. The total amount expenses in Years 3 and 4 were $300,000 more than the total amount income in Years 3 and 4:
combined expenses in Years 3 and 4 = $600,000 + $700,000 = $13,00,000
combined income in Years 3 and 4 = $400,000 + $600,000 = $10,00,000
We can see here the combined expenses are $300,000 more than the combined income.
So, the option is correct.
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There are 80 students in a certain class taking a test. Seventeen of the students finished the test before 1 hour. twelve more students finished the test before 1.25 hours, and twenty-two students finished the test before 1.75 hours. What percent of the students are still taking the test after 1.75 hours? Round your answer to the nearest hundredth
The percentage of students still writing the test is
23.75%
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign( %).
For example if there are 80 student in a class and 20 are boys, the percentage of boys in the class is ; 20/80 × 100 = 25%
The total number of students that finished the test before 1.75hours = 17+12+22 = 61
The number of students left in the class = 80-61
= 19
Therefore percentage of of the student still taking the test after 1.75 = 19/80 × 100
= 1900/80
= 23.75 %
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If you know the answer I will give a hundred brainist
Answer:
18.09
Step-by-step explanation:2.4x2.4, then x3.14
Answer:
answers below
Step-by-step explanation:
If you are trying to find the area the answers are:
Earth= 289.52918
Saturn=6,532.5021
The formula for area for a sphere is:
4 x pie x r2
If you are trying to find the volume the answers are:
Earth=57.90584
Saturn=46,647.01596
The formula for volume for a sphere is:
4/3 x pie x r3
Also the radius (r) is half of the diameter, so you divide the diameter by 2.
What’s the 4th term in the sequence?
The fourth term of the sequence is -18.
What is arithmetic progression? How do you respond to arithmetic progression?In arithmetic progression, the first term is denoted by "a", the last term by "l", the common difference of two terms is denoted by "d", and the number of terms by "n". To find the sum of an arithmetic progression, we must know the first term (a), the number of terms (n), and the common difference (d) between successive terms. Then substitute the values Sn = n/2[2a (n − 1) × d].
To find the 4th term of the sequence, we can simply substitute n = 4 instead of the nth term in the formula:
a(4) = -6 - 4 (4-1)
= -6 - 4 (3)
= -6 to 12
= -18
Therefore, the fourth term of the sequence is -18.
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Divide.
(4x²-24x+15)÷(x−5)
Your answer should give the quotient and the remainder.
In the problem given, the result of the polynomial long division shows that the quotient is 4x - 4 and the remainder is -5.
How to Perform the Division?To perform polynomial long division of (4x²-24x+15) by (x-5), we follow these steps:
4x - 4
--------------
x - 5 | 4x² - 24x + 15
4x² - 20x
------------
-4x + 15
-4x + 20
----------
-5
Therefore, the quotient is 4x - 4 and the remainder is -5.
We can check our answer by verifying that:
(4x - 4) * (x - 5) + (-5) = 4x² - 24x + 15
which is indeed the original polynomial.
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Question 12/18
6 Units
The volume of a pyramid is 50 cubic units. The base is a square with sides of length 5. What is the height?
(A) 2 Units
10 Units
0v
D) 4 Units
The height of the pyramid is 6 units.
What is the formula of the volume of a pyramid?
The volume of a pyramid is [tex]V = ( \frac{1}{3} ) \times B \times h[/tex], where B is the area of the base and h is the height of the pyramid.
In this case, the base is a square with sides of length 5, so the area of the base is [tex]B = 5 \times 5 = 25 \: square \: units[/tex]
We are also given that the volume of the pyramid is 50 cubic units.
So we are putting these values into the formula and solve for h,
[tex]50 = ( \frac{1}{3} ) \times 25 \times h \\ 150 = 25 \times h \\ h = 6[/tex]
Therefore, the height of the pyramid is 6 units.
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Correct question is "The volume of a pyramid is 50 cubic units. The base is a square with sides of length 5. What is the height?
(A) 2 Units
(B)10 Units
(C) 6 Units
D) 4 Units"
Which function best models the stock data shown in the scatter plot?
A. Y=0.3(2.94) +56.5
B. Y=442x+53
C. Y=0.92)+58
D. Y=7.7x+47.7
Submit
Answer:
Without a visual or additional information, it is difficult to determine the best function that models the stock data shown in the scatter plot.
However, we can make some observations based on the answer choices:
A. Y=0.3(2.94) +56.5 is not a linear function and does not seem to fit the general trend of the data.
B. Y=442x+53 is a linear function with a positive slope, but it does not seem to fit the general trend of the data.
C. Y=0.92)+58 is not a linear function and appears to be missing a variable.
D. Y=7.7x+47.7 is a linear function with a positive slope that seems to fit the general trend of the data.
Therefore, the best function that models the stock data shown in the scatter plot is likely D) Y=7.7x+47.7.
Paula’s investments increased by 87.4% in 2020. Those same investments increased by 12.9% in 2012. Calculate the absolute change in the percentage increase amounts from Paula’s investments
the absolute change in the percentage increase amounts from Paula's investments is 74.5%.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
The absolute change in the percentage increase amounts is the difference between the two percentages.
Absolute change = |87.4% - 12.9%| = |74.5%| = 74.5%
Therefore, the absolute change in the percentage increase amounts from Paula's investments is 74.5%.
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Match the word with the definition.
Question 1 options:
Rise
Run
Y Intercept
Ordered Pairs
Perpendicular Lines
Linear Equation
Y-axis
Coordinate plane
Slope
Slope-intercept form
X-axis
Origin
X Intercept
Parallel Lines
Quadrant
1.
Plane with two axes as a frame of reference.
2.
The vertical number line in a coordinate plane
3.
The horizontal number line in a coordinate plane
4.
A pair of numbers that are used to correspond to a point on a graph where the first number is the x-coordinate and the second number is the y-coordinate.
5.
Where the x and y axis meet. The point (0, 0).
6.
One of the four regions into which the x and y axis separate the coordinate plane.
7.
An equation with two variables that makes up a straight line on a coordinate plane.
8.
The vertical change in a line from one point (x1,y1) to a second point (x2, y2).
9.
The horizontal change in a line from one point (x1,y1) to a second point (x2,y2).
10.
The ratio of a line's rise over its run.
11.
The point where a graph crosses the x axis.
12.
The point where a graph crosses the y axis.
13.
A linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
14.
Lines that have the same slope and never intersect.
15.
Two lines that intersect at a 90° angle. Slopes of these lines are opposite reciprocals.
Step-by-step explanation:
1.
Plane with two axes as a frame of reference. - Coordinate plane
2.
The vertical number line in a coordinate plane - Y-axis
3.
The horizontal number line in a coordinate plane - X-axis
4.
A pair of numbers that are used to correspond to a point on a graph where the first number is the x-coordinate and the second number is the y-coordinate. - Ordered Pairs
5.
Where the x and y axis meet. The point (0, 0). - Origin
6.
One of the four regions into which the x and y axis separate the coordinate plane.- Quadrant
7.
An equation with two variables that makes up a straight line on a coordinate plane. - Linear Equation
8.
The vertical change in a line from one point (x1,y1) to a second point (x2, y2). - Rise
9.
The horizontal change in a line from one point (x1,y1) to a second point (x2,y2). - run
10.
The ratio of a line's rise over its run. - Slope
11.
The point where a graph crosses the x axis. - X Intercept
12.
The point where a graph crosses the y axis. - Y Intercept
13.
A linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. - Slope-intercept form
14.
Lines that have the same slope and never intersect. - Parallel Lines
15.
Two lines that intersect at a 90° angle. Slopes of these lines are opposite reciprocals. - Perpendicular Lines
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Weekly revenue, in dollars, at Pizza Garden can be modeled by the equation y = 1000 + 18x, whe
sold. The pizzeria's weekly expenses, in dollars, can be modeled by the equation y = 1700 + 13x.
How many pizzas must be sold at Pizza Garden in a week for the pizzeria to break even?
Note: The phrase break even refers to the value where the two functions are equivalent. When x is less than the break-even value, the pizzeria has
revenue below expenses, and so it loses money. When x is above the break-even value, the pizzeria has revenue above expenses, and so it makes a
profit.
O 140
O 540
O 3500
O 3520
Answer:
To find the break-even point, we need to set the revenue equal to the expenses and solve for x:
1000 + 18x = 1700 + 13x
5x = 700
x = 140
Therefore, Pizza Garden needs to sell 140 pizzas in a week to break even. So the answer is 140.
I heard that you might have to increase your prices by 12% if I normally pay $45 per order how much would my order be if the price increase happens the price for your next order would be what
On solving the equation, the price for next order is obtained as $50.40.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
If the price increase is 12%, we need to add 12% of the original price to the original price to get the new price.
So, the new price equation would be -
$45 + 12% of $45
= $45 + 0.12*$45
= $45 + $5.40
= $50.40
Therefore, if the price increase happens, the price for your next order would be $50.40.
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5x – 2 = 3125
Solve for x
Answer: x = 625.4
Step-by-step explanation:
5x – 2 = 3125
+2 +2
5x = 3127
/5 /5
x = 625.4
Answer: x=3127
Step-by-step explanation:5x times 2 - (3125)=0
5x times -3127=0
5x=3127
x=3127/1
x=3127
How many positive integers less than 1000 have the sum of their digits equal to 4
Answer:
15
Step-by-step explanation:
radian measure of 267.38 to the nearest tenth
How can the system of equation be represented in a matrix 3x−2y=−25, 5x−2y=−39
?
Answer:
{x,y}={7,-2}
Step-by-step explanation:
3x - 2y = 25
-5x + 2y = -39
[2] 2y = 5x - 39
[2] y = 5x/2 - 39/2
// Plug this in for variable y in equation [1]
[1] 3x - 2•(5x/2-39/2) = 25
[1] -2x = -14
// Solve equation [1] for the variable x
[1] 2x = 14
[1] x = 7
Question content area top Part 1 Consider a political discussion group consisting of 7 Democrats, 5 Republicans, and 3 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting a Republican and then an Independent.
The probability of selecting a Republican and then an Independent is 1/15
Finding the probability of selecting a Republican and then an Independent.From the question, we have the following parameters that can be used in our computation:
Political discussion group consisting of
7 Democrats5 Republicans3 Independents.If the people are replaced, then we have
P(Republicans) = 5/15
P(Independents) = 3/15
So, we have
The probability of selecting a Republican and then an Independent
P = 5/15 * 3/15
Evaluate
P = 1/15
Hence, the probability of selecting a Republican and then an Independent is 1/15
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