Answer:
31/8 or 5 1/8
Step-by-step explanation:
[tex]4-\dfrac{1}{8} = \dfrac{4(8) -1}{8} = \dfrac{32 -1}{8} = \bf \dfrac{31}{8} \\[/tex]
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 10 inches and height of 7 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 5 squared times 7
V equals 355 over 113 times 7 squared times 5
V equals 355 over 113 times 7 squared times 10
V equals 355 over 113 times 10 squared times 7
The correct method to calculate the number of cubic units(volume) of cake batter needed to fill the mold is option (a) , i.e V equals 355 over 113 times 5 squared times 7.
What is mensuration?Mensuration is the branch of mathematics concerned with the study of various geometric shapes, their areas and volumes. In a broad sense, it is about the process of measurement. Measurement is a branch of mathematics. That is measurement.
Solution:
Given, Diameter = 10 inches
Radius = 5 inches
Height = 7 inches
Volume of cylinder = πr²h
= (355/113)×5²×7
= 3.14×25×7
= 549.77 inches³
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You are trying to get back in shape. In the first week, you swim 15 laps every day.
Then, each week, you increase your distance by 5 laps. Which recursive formula
models this situation?
The recursive formula model to represent this situation is L(n) = L(n-1) + 5 where you can swim 15 laps every day.
What is recursive formula?A recursive formula is a formula that defines a sequence in terms of one or more of its preceding terms. In other words, it is a way to generate the terms of a sequence using the previous terms of the same sequence.
According to question:The given situation describes a sequence of numbers where each term is obtained by adding a fixed constant to the previous term. This is called an arithmetic sequence.In this case, we start with 15 laps swum in the first week, and then increase the distance by 5 laps each subsequent week. Let L(n) denote the number of laps swum in week n.To find the number of laps swum in week n, we can add 5 laps to the number of laps swum in week n-1, since the distance increases by 5 laps every week. This can be represented mathematically as:L(n) = L(n-1) + 5
where
L(n-1) represents the number of laps swum in the previous week.
The recursive formula above defines the arithmetic sequence that models the situation described in the problem. We know that L(1) = 15, since in the first week, 15 laps were swum, and we can use the formula recursively to find the number of laps swum in any subsequent week.To know more about recursive visit:
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'Paraphrasing'
Original: Scientists are quick to state that the presence of these organic molecules is not sufficient evidence for ancient life on Mars, as the molecules could have been formed by non-living processes.
A- Scientists cannot agree whether the discovery of organic material on Mars is proof that creatures lived on Mars or not in the past.
B- Scientists quickly say that the existence of these organic materials is not sufficient proof for ancient life on Mars, as the molecules could have been formed by other non-living methods.
C- Scientists claim life on Mars was not possible, and that natural processes are responsible for discovering any organic molecules.
D- Science experts are not strongly convinced that the discovery of organic materials on Mars is proof that living creatures existed before on Mars. It is possible the organic matter was created naturally due to different natural causes.
The presence of these organic elements, according to scientists, is insufficient evidence for the existence of ancient life on Mars since the molecules been created via other non-living processes. This assertion true.
What kinds of things are organic materials?Everything that includes carbon compounds produced by living things is considered to be organic matter. Lawn trimmings, leaves, twigs, branches, moss, algae, lichens, any animal parts, sewage, dust, insects, earthworms, and bacteria are just a few examples of what it includes.
Which three categories best describe organic materials?Carbohydrates, lipids, protein, and nucleic acids are the four main kinds of organic substances that are found in all living organisms.
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Which of these areas is getting the least precipitation?
Answer:
A. Lancaster
Lancaster is on the edge of the yellow area.
MTH 115 Lesson 8 Practice Problems
Answer Key
1. A credit card charges 23% APR and a minimum of 2.5%. If you pay the minimum on a balance of $450 what would the decrease in your balance be? Round to the nearest cent $2.63.
2. A month has 30 days in it. You post a payment of $600 on the 15th of the month. The Balance was $2000 before the payment. What is the interest on the average daily balance if the APR is 23%? $32.58
3. The monthly payment on a house loan is $876. The purchase price of the house was $125,000. If you pay this for 30 years how much interest did you pay? $190,360
4. A house costs $275,000. The rate is 7.3% with monthly payments for 30 years. What is the payment? Round to the nearest dollar. $1885
1. The decrease in the balance would be $11.25 2. The interest on the average daily balance would be $28.77. 3. The total interest paid would be $214,960. 4. The payment would be $1,978.
Describe Interest?Interest refers to the amount of money that is charged or earned for the use of borrowed money. It is a fee paid by a borrower to a lender for the use of funds, or a payment received by a depositor from a bank for the use of their money.
Interest rates are typically expressed as a percentage of the principal amount and can be fixed or variable, depending on the terms of the loan or investment. The interest rate charged on a loan is determined by a number of factors, including the creditworthiness of the borrower, the length of the loan, and prevailing market conditions.
1. The decrease in the balance would be $11.25.
Calculation:
Minimum payment = 2.5% of $450 = $11.25
New balance after paying the minimum = $450 - $11.25 = $438.75
The decrease in the balance would be $450 - $438.75 = $11.25.
2. The interest on the average daily balance would be $28.77.
Calculation:
The balance for the first 14 days of the month = $2000
The balance for the last 16 days of the month = $1400
Average daily balance = (14 * 2000 + 16 * 1400) / 30 = $1666.67
Interest for the month = 0.23 / 12 * $1666.67 = $28.77
3. The total interest paid would be $214,960.
Calculation:
No. of payments = 30 * 12 = 360
Total amount paid = $876 * 360 = $315,360
Total interest paid = $315,360 - $125,000 = $190,360
4. The payment would be $1,978.
Calculation:
Monthly interest rate = 7.3% / 12 = 0.6083%
Number of payments = 30 * 12 = 360
Payment = $275,000 * 0.006083 / (1 - (1 + 0.006083)^-360) = $1,977.54 (rounded to nearest dollar: $1,978)
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A square with side s has area s to the 2nd power. Brandon uses a square mat when he practices karate. The mat is 11 feet on each side.
Answer:
Step-by-step explanation:
i assume you mean that the mat is 11 feet on each side so
area = s*s(or S^2)
so 11*11=121feet sq
Calculate the lengt line x
Answer:
90
Step-by-step explanation:
The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. What is the best predicted value for y given x=41? Assume that the variables x and y have a significant correlation.
X= 38 41 45 48 51 53 57 61 65
Y= 116 120 123 131 142 145 148 150 152
The solution is : the predicted blood pressure for a person aged 64 will be : 156.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x ; ax^2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.
here, we have,
Given the data:
Age (X) :
38
41
45
48
51
53
57
61
65
Pressure(Y) :
116
120
123
131
142
145
148
150
152
From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :
The regression equation obtained is :
y = 1.48769X + 60.46103
Using the model, the predicted blood pressure for a person aged 64 will be :
y = 1.48769(64) + 60.46103
y = 95.21216 + 60.46103
y = 155.67319
y = 156 (nearest whole number)
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The best predicted value of y for the given x=41 is 121.45.
What is the correlation coefficient?The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.
Given that,
X= 38 41 45 48 51 53 57 61 65
Y= 116 120 123 131 142 145 148 150 152
∑x= 459
∑y= 1227
∑x²= 24059
∑y²= 168843
∑xy= 63544
Sxx= ∑x²-∑x²/n
= 24059-459²/9
= 650
Sxy = ∑xy-(∑x·∑y)/n
= 63544-(459×1227)/9
= 63544-62577
= 967
Now, slope =967/650= 1.488
Mean of x=459/9 =51
Mean of y=1227/9 = 136.33
Now, intercept is b=136.33-(1.488×51)
= 60.442
Here, the equation of a line is y=1.488x+60.442
When x=41, we get
y=1.488×41+60.442
y= 121.45
Therefore, the best predicted value of y is 121.45.
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Which statement best describes discretionary government spending?
Back
A. A fixed amount of money spent on the same categories every year
B. The money used to pay for Social Security and Medicare
C. A changing amount of money spent on different categories each year
D. Money that you determine how it is spent by the government when you submit your taxes
Select an answer
C. A changing amount of money spent on different categories each year
What is amount?Amount is a term used to describe a quantity of something, typically money. It is often used to refer to the total value of a financial transaction or the sum of multiple payments. Amount can also refer to any other quantifiable measure, such as a number of items, units of time, or a volume or quantity of something.
Discretionary government spending is a type of government spending that is determined each year by the Congress, and typically includes funds for defense, education, infrastructure, and other government programs. The amount of money spent on each category can vary from year to year, making it a type of changing, or discretionary, spending.
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Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each
section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40
students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college
$29,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $298,000
in revenues, how many sections of each course should it offer?
Finite Math
Applied Calculus
Computer Methods
Need Help?
Read It
section(s)
section(s)
section(s)
Watch It
Answer:
Step-by-step explanation:
Let's use the following variables:
Let F be the number of sections of Finite Math
Let A be the number of sections of Applied Calculus
Let C be the number of sections of Computer Methods
We can create a system of equations based on the given information:
F + A + C = 7 (the college wishes to offer a total of seven sections)
40F + 60A + 290C = 298000 (the college wishes to bring in $298,000 in revenues)
40F + 40A + 10C = 220 (the college wishes to accommodate 220 students)
We can solve this system of equations using any method we prefer. Here's one possible way:
Multiply the third equation by 10 to get:
400F + 400A + 100C = 2200
Subtract the third equation from the second equation to eliminate C:
20A + 280C = 76000
Multiply the first equation by 40 and subtract it from the previous equation to eliminate A:
240C = 76000 - 1600
Solve for C:
C = 290
Substitute C = 290 into the third equation to solve for F:
40F + 40A + 10(290) = 220
40F + 40A = -2680
F + A = -67
Substitute C = 290 and F + A = -67 into the first equation to solve for A:
A = 10
Substitute A = 10 and C = 290 into the first equation to solve for F:
F = -3
We have a problem here: we obtained a negative number of sections for Finite Math, which is impossible. This means that the original system of equations is inconsistent, and there is no solution that satisfies all the requirements.
Therefore, the college cannot offer the desired number of sections while accommodating the desired number of students and revenue. Some adjustments need to be made, such as changing the number of students per section or the tuition fees.
Write the equation of the circle in standard form
X^2+y^2-8x-6y+16=0
Show work
The equation of the circle x² + y² - 8x - 6y + 16 = 0 in standard form is (x - 4)² + (y - 3)² = 3².
What is the equation of the circle in standard form?Given the equation of the circle ;
x² + y² - 8x - 6y + 16 = 0
To write the equation of a circle in standard form, we need to express it as:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
To do this, we need to complete the square for both x and y terms in the given equation.
Starting with the x terms:
x² - 8x = x² - 8x + 16 - 16
= (x - 4)² - 16
Similarly, for the y terms:
y² - 6y = y² - 6y + 9 - 9
= (y - 3)² - 9
Substituting these results into the original equation, we get:
x² + y² - 8x - 6y + 16 = 0
(x - 4)² - 16 + (y - 3)² - 9 + 16 = 0
Simplifying, we get:
(x - 4)² + (y - 3)² - 9 = 0
(x - 4)² + (y - 3)² = 9
So the equation of the circle in standard form is:
(x - 4)² + (y - 3)² = 3²
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Can somone help me with this I lost all my brain cells Lol
I NEED HELP WITH MY MATH IXL OR ELSE MY MOM TAKES ME OUT THE SCHOOL
Answer: $75
Step-by-step explanation:
In △STU , t = 1.3 inches, u = 3.5 inches and ∠S=159° . Find the length of s, to the nearest tenth of an inch. Responses 2.7
simplify (6k +5)(5k +5)
Answer:
30k^2+55k+25
Step-by-step explanation:
30k^2+30k+25k+25
=30k^2+55k+25
[tex]30k { }^{2} + 30k + 25k + 25[/tex]
[tex]30k ^{2} + 55k + 25[/tex]
Write each amount as rate
500 words in one minute
Answer:
500 words per minute.
Step-by-step explanation:
You write 6 3/10 pages of a report in 2 1/3 hours. What is the average number of pages you write per hour?
the answer is 2 5/14
Answer:
Step-by-step explanation:
To find the average number of pages written per hour, we need to divide the total number of pages written by the total time taken:
Total pages written = 6 3/10 = 63/10
Total time taken = 2 1/3 = 7/3
Average pages written per hour = Total pages written / Total time taken
= (63/10) / (7/3)
= (63/10) x (3/7)
= 9/2
Therefore, the average number of pages written per hour is 9/2, which is equal to 4.5 pages per hour.
O Which point has the coordinates (-3.5, 4)? Point W Point Y Point X Point Z
The point which has the coordinates (-3.5, 4) is point Z.
What are Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given coordinate is (-3.5, 4).
This means that the point is at a distance of 3.5 to the left of the origin and at a distance of 4 units above the origin.
So in order to find the point, mark the point -3.5 in the exact middle of -3 and -4 on the X axis.
Mark the point 4 on the Y axis.
Draw perpendicular lines from both.
Intersecting point is the given point.
Here point Z indicates this.
Hence point Z indicates the coordinates (-3.5, 4).
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Your question lacks the graph showing the points and coordinates. The graph is given below.
Can someone answer this just read the picture? Right answers only please!
The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
What is temperature?Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.
Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
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if the size of the angles of a triangle are (x-35) ( x-25) and (1/2 x - 10) find value of x
Answer: x = 100
Step-by-step explanation:
The angles of a triangle add up to 180, meaning that (x-35)+(x-25)+(1/2 x - 10) = 180. Now you can solve for x
What is the area of the drawing of the sailboat in square centimeters??
Answer:
Step-by-step explanation:
triangle-
b+h/2=a
5x6/2=30
rectangle-
2.5x12=30
area of drawing-
30+30=60
answer:60cm^2
Austin pays $2 per day for high speed internet. The equation y = 2x relates his internet charges (y) to the number of days (x) he has internet. Identify the unit rate in the equation.
Answer:
The unit rate in the equation y = 2x is 2.
This means that the cost per day for Austin's high-speed internet is $2.
Which of these correctly expresses the system of equations in standard form
Equations that correctly expresses the system of equations in standard form are x + y = 22 and 3x + 4y = 76.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given,
Cost of blue sea shells = $3
Cost of pink sea shells = $4
Cost of 22 sea shells = $76
Let number of blue sea shells is x and number of pink sea shells is y
then number of total shells
x + y = 22
Cost of shells
3x + 4y = 76
Hence, x + y = 22 and 3x + 4y = 76 are the equations that correctly expresses the system of equations in standard form
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Calculate the value 4-2(-5) =
answer is 14.
4-(2*-5)
4-(-10)
=4+10
=14.
Answer:
[tex]\bf 14[/tex]Step-by-step explanation:
[tex]\tt 4-2(-5)[/tex]
Follow the PEMDAS order of operations:-
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
1) Multiply and/ or divide:-
[tex]\tt 2\left(-5\right)[/tex][tex]\tt -10[/tex][tex]\tt 4 -\left(-10\right)[/tex]
2) Addition/Subtraction:-
[tex]\tt 4-\left(-10\right)[/tex][tex]\tt 4+10[/tex][tex]\tt 14[/tex]_____________________
Hope this helps! :)
Graph the image of the given triangle, reflected across the y = x line.
Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides. To close the triangle, select the first point again.
The image reflected by the line of the triangle is attached below.
What is an image?
A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The coordinates of the vertices of the triangle are (1, -2), (8,1), (4,-9).
The rule of reflection across the y = x line is (x,y) → (y,x).
The reflection of (1, -2) across the y = x line is (-2,1).
The reflection of (8,1) across the y = x line is (1,8).
The reflection of (4,-9) across the y = x line is (-9,4).
The coordinates of the vertices of the reflected triangle are (-2,1), (1,8), and (-9,4).
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A streaming service wants to measure the popularity of a new television show. Which quantity provides the best measure of the television show’s popularity?
the number of episodes per season
the number of minutes per episode
the number of minutes per season
the number of streams per episode
The quantity provides the best measure of the television show’s popularity is the number of streams per episode.
What is Independent and Dependent Variable?We anticipate that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependant variable.
The dependant variable is what changes as a result of the independent variable, which is what you modify.
The most accurate indicator of a television show's popularity on a streaming service is the number of streams each episode.
This is because, rather than just the length of the episodes or the number of episodes every season, the number of streams directly represents the number of viewers who are actively choosing to watch the show.
The number of streams also considers re-watchability and binge-watching, which are further indicators of how popular a show is.
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A vending machine has 6 different colors of gumballs (red, blue, pink, yellow, green, purple) and an equal chance of dispensing each. Martin buys 6 gumballs. What is the probability of Martin getting exactly 3 pink gumballs?
The prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is expressed as a number between 0 and 1, with 0 indicating an impοssible event and 1 indicating a certain event. The prοbability οf an event can be calculated by dividing the number οf favοrable οutcοmes by the tοtal number οf pοssible οutcοmes.
In the given scenariο, there are 6 different cοlοrs οf gumballs, and each has an equal chance οf being dispensed. Therefοre, the prοbability οf getting any particular cοlοr is 1/6.
Tο find the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6, we need tο use the binοmial prοbability fοrmula:
[tex]\mathrm{P(X=k) = C(n,k) \times p^k \times (1-p)^{(n-k)}}[/tex]
where:
P(X=k) is the prοbability οf getting exactly k successes
n is the tοtal number οf trials (in this case, 6)
k is the number οf successes we want (in this case, 3)
p is the prοbability οf success (in this case, the prοbability οf getting a pink gumball, which is 1/6)
C(n, k) is the number οf cοmbinatiοns οf n things taken k at a time, which can be calculated as n! / (k! × (n-k)!).
Plugging in the values, we get:
P(X=3) = C(6,3) × (1/6)³ × (5/6)³
= (6! / (3! × 3!)) × (1/6)³ × (5/6)³
= 20 × (1/216) × (125/216)
= 0.1608
Therefοre, the prοbability οf Martin getting exactly 3 pink gumballs οut οf 6 is apprοximately 0.1608 οr 16.08%.
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Use synthetic division to evaluate for the indicated x value.
--x³-2; f (5)
f (5)
=
We can write the function f(x) = (- x³ - 2) at {x} = 5 as -
f(5) = - 127.
What is expression?An expression is a term made up of both constants and variables.
Given is the function as -
f(x) = - x³ - 2
We can write f(5) as -
f(5) = - (5)³ - 2
f(5) = - 125 - 2
f(5) = - 127
Therefore, we can write the function f(x) = (- x³ - 2) at {x} = 5 as -
f(5) = - 127.
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At a restaurant, the bill comes to $76. If you decide to leave a 20% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:
Tip amount = 0.20 x $76 = $15.20
To find the total amount to pay, we add the bill amount and the tip amount:
Total amount = $76 + $15.20 = $91.20
Rounding this to the nearest dollar gives:
Total amount = $91
Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.
Step-by-step explanation:
Help plssss Quickkkk!!!!!
1. Patrick makes more per hour by $6.
2. Betthany makes more per hour by $5.25
3. Tommy makes more per hour by $ 1.25.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
The rate of Change of Critters and Co
Slope= Rise/ Run
= 15/2
= 7.5
So, the equation is y = 7.5x
and, rate of Change of Little Paws
= (52.50-35) / (6-4)
= 17.5 / 2
= 8.75
So, the equation is y = 8.5x + 5
and, rate of Change of The Waging Tail
= 8.25
1. Patrick makes more per hour by $6.
2. Betthany makes more per hour by $5.25
3. Tommy makes more per hour by $ 1.25.
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