The radius of the cylinder with a combined volume of 1000 cubic inches is 2.4 inch
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let r represent the radius of the cylinder/cone.
For the cylinder:
Volume = π * radius² * height
but height is twice the radius, height = 2r, hence:
Volume = π * r² * 2r = 2πr³
For the cube:
Volume = side³
but side is four times the radius, side = 4r, hence:
Volume = (4r)³ = 64r³
The combined volume of a cube and a cylinder is 1000 cubic inches, hence:
1000 = 2πr³ + 64r³
r³(2π + 64) = 1000
r³ = 1000/(2π + 64)
r³ = 14.228
r = 2.4 inch
The radius is 2.4 inch
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NO LINKS!!!!
1. A savings account starts with $720 and earns an annual rate of 4.8%. Write an equation and find the amount of money in the account for 12 years.
Equation:
Solution
2. Bacteria can multiply at an alarming rate when each bacteria splits into two new cells , thus doubling. If we start with only one bacteria, which can double, how many bacteria will we have be the end of 3 days?
Equation:
Solution:
Answer:
[tex]\textsf{1.\;\;Equation:\quad$A=720(1.048)^{t}$}[/tex]
[tex]\textsf{Solution:\quad$\$1263.77$}[/tex]
[tex]\textsf{2.\;\;Equation:\quad$y=2^x$}[/tex]
[tex]\textsf{Solution:\quad$8$}[/tex]
Step-by-step explanation:
Question 1Assuming the account earns annual compound interest.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
P = $720r = 4.8% = 0.048Substitute the given values or P and r into the annual compound interest formula to create an equation for the amount of money in the account after t years:
[tex]\implies A=720(1+0.048)^{t}[/tex]
[tex]\implies A=720(1.048)^{t}[/tex]
To find the amount of money in the account after 12 years, substitute t = 12 into the equation:
[tex]\implies A=720(1.75523549...)[/tex]
[tex]\implies A=1263.76955...[/tex]
[tex]\implies A=1263.77[/tex]
---------------------------------------------------------------------------------
Question 2[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given values:
a = 1 (initial number of bacteria)b = 2 (as the bacteria doubles)Substitute the given values or a and b into the exponential function formula to create an equation for the number of bacteria after x days:
[tex]\implies y=1(2)^x[/tex]
[tex]\implies y=2^x[/tex]
To find the number of bacteria after 3 days, substitute x = 3 into the equation:
[tex]\implies y=2^3[/tex]
[tex]\implies y=8[/tex]
BRAINLIEST EASY PROBLEM!!!!!!!!!!! 7th grade) find x and y.
Answer:
x = 20
y = 20
Step-by-step explanation:
In the given triangle, we can deduce that angle x is congruent to angle y using the Isosceles Triangle Theorem. Hence, we can construct the equation xº = yº.
We also know that the measures of the interior angles of a triangle add to 180º. Hence, we can construct the equation xº + yº + 140º = 180º.
We now have a system of equations, and since we already have an identity for xº (and also for yº), we can solve the system using the substitution method.
xº + yº + 140º = 180º
↓ substituting xº for yº
xº + xº + 140º = 180º
↓ subtraction 140º from both sides
2xº = 40º
↓ dividing both sides by 2
xº = 20º
↓ removing degree sign from both sides
x = 20
Now that we have solved for x, we have also essentially solved for y, as plugging this x-value into the equation xº = yº will just yield:
20 = y
y = 20
Use the appropriate formula to find the value of the annuity . Find the interest Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years
The value of the $110 annuity given annual compounding is $9983.338.
What is the value of the annuity?The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years
r = interest rate
here, we have,
Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years
now,
r=4.5%/2
=0.0225
n= 25*2 = 50
using the formula, we get,
the value of the annuity =$9983.338
hence, The value of the $110 annuity given annual compounding is $9983.338.
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Which unit of length would a microscope best help to see?
Answer:
The unit of length that a microscope best helps to see is 1 millimeter.
Step-by-step explanation:
Microscopes are instruments used for viewing objects that cannot be seen with eyes. The unit length of an object that a microscope can view should be a length that is very small
if the speed of a boat in still water is 13 mph
A what is the speed going against a current with a rate of x mph ?
B what is it’s speed going with a current with a rate of x mph?
Answer:
A. The speed of the boat going against a current with a rate of x mph is (13 - x) mph.
B. The speed of the boat going with a current with a rate of x mph is (13 + x) mph.
Step-by-step explanation:
How much of a 14% ethanol fuel mixture should be mixed with 8 gal of 3% ethanol fuel mixture to get a mixture that is 12% ethanol?
(blank) gal of 14% ethanol solution is needed to produce a 12% ethanol solution.
Answer:
Step-by-step explanation:
A = x 14%=.14x
B=8 (4%)=.04(8)
=8x 12%= .12*8x
.14x+.04(8)=.12(8x)
.14x+.32=96x-.14x
.32=.82x/x
.32/.82=.39
The amount of 14 % of ethanol that needs to mixed is A = 36 gallons
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
14% ethanol fuel mixture should be mixed with 8 gal of 3% ethanol fuel mixture to get a mixture that is 12% ethanol
So , the equation is
A ( 14 % ) + ( 8 ) ( 3 % ) = ( A + 8 ) ( 12 % )
On simplifying , we get
14A + 24 = 12A + 96
Subtracting 12A on both sides , we get
2A + 24 = 96
Subtracting 24 on both sides , we get
2A = 72
Divide by 2 on both sides , we get
A = 36 gallons
Therefore , the value of A is 36 gallons
Hence , the equation is A = 36 gallons
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Given the following system of equations, type the target variable matrix for y.
5x-y=6
2x+7y=9
The solution of the simultaneous equations using target matrix are; x = 51/37 and y = 33/37
How to use matrix to solve simultaneous equations?The target variable is defined as the variable whose values are modeled and predicted by other variables.
We are given the simultaneous equations as;
5x - y = 6
2x + 7y = 9
In matrix form, it is expressed as;
5 -1 6
2 7 9
row 2 = row 2 + row 1 * 7
This gives us;
37 0 51
Thus;
x = 51/37
Plugging in 51/37 for x in eq 1 gives;
5(51/37) - y = 6
Multiply through by 37 to get;
5*51 - 37y = 37*6
255 - 37y = 222
-37y = 222 - 255
y = 33/37
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The coordinates of the vertices of ADOG are D (2,3,), O(2,-2), and G(-3, -2). Determine whether ACAT is a
right triangle and support your decision with evidence. Show all work.
Answer:
Consolidation
Step-by-step explanation:
Maths is a great way to get a job and then you can give it a try for a few days and then again you can give it a try for a few days and then again you can give it a try for a few days
What shape results from a plane passing through a cone that is perpendicular to the base?
Isosceles Triangle
Circle
Parabola
Ellipse
The shape that results from a plane passing through a cone that is perpendicular to the base is option B: Circle.
What is the Circle about?When a plane passes through a cone perpendicular to the base, it intersects the cone at a circle. This is because the plane is cutting the cone at a 90-degree angle to the base, and so it is cutting through the circular cross-section of the cone.
Therefore, If the plane were to be tilted or angled, the shape of the intersection would be an ellipse, which is a flattened circle. This is because an ellipse is the shape that results when a plane intersects a cone at an angle that is not perpendicular to the base.
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what is the value of the exponential expression below?
36 1/2
2) For which values of S and T does the following equation have infinitely many solutions?
Sx+81-24x+ T
a) S=24 and T=81
b) S = -24 and T = -81.
(c) S = -24 and T=81
d) S=24 and T=-81
The evaluation of the equation in the question for the number of solutions is as follows;
2) The values of S and T for which the equation Sx + 81 = -24x + T have infinitely many solutions is S = 24 and T = -81
c. S = 24 and T = -81
What is an equation?An equation is a statement of equivalence of two expressions.
The specified equation is presented as follows;
S·x + 81 = -24·x + T
The equation will have infinitely many solutions when both sides of the equation refer to the the sam line
The power of x on both sides of the equation is one, therefore, both expressions on the left and right side of the equation refer to linear relationships
The graph of two lines are the same if they have the same slope and the same y-intercept.
The slope of the expression on the left = S
The y-intercept of the expression on the left = 81
The slope of the expression on the right = -24
The y-intercept of the expression on the right = T
When both sides refer to the same line, we get;
S = -24, and T = 81
Therefore, both sides of the equation refers to the same line and therefore have infinitely many solutions when S = -24 and T = 81.
The correct option is option c
(c) S = -24 and T = 81
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Solve this you won't.
The linear equation that is represented in the table is:
y = 3*x + 2
How to write the linear equation?A general linear equation can be written in the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
First, notice that on the table we can see the point (0, 2), then the y-intercept of the linaer function is b = 2
Then we can write:
y = m*x + 2
Now we can use any other point on the table to find the value of the slope m.
Using the second point (1, 5),replacing the values we will get:
5 = m*1 + 2
Solving for m, we will get:
5 = m + 2
5 - 2 = m
3 = m
Then the linear equation is:
y = 3*x + 2
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At Dubble High School, 42% of the students play sports, 34% of the
students play a musical instrument, and 24% do both. What is the
probability that a randomly selected student at Dubble High School
plays a sport or a musical instrument?
carly walks 20 ft./s at this rate how many minutes will take Carly to walk a mile if there are 5280 feet in 1 mile
Carly can walk 1 mile in 264 seconds.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Unit rate of Carly is given.
Unit rate of an object in terms of distance covered and time taken is actually the speed of the object.
The formula for speed is,
Speed = Distance / Time
Speed = 20 feet per second
Distance = 1 mile = 5280 feet
Time taken be t.
20 = 5280 / t
t = 5280 / 20
t = 264 seconds
Hence it will take 264 seconds for Carly to walk a mile.
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The following scatter plot shows how the cumulative sea level has changed from
1880 to 2015. Which correlation coefficient best represents the scatter plot?
A. r=-0.98
B. r=-0.5
C. r=0.5
D.r=0.98
Based on the scatter plot shown, the correlation coefficient that best represents the scatter plot is r = 0.98.
What is a scatter plot?Several dots are placed on a horizontal and vertical axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences called variables.
The scatter plot shown shows a highly positive correlation between the data. Hence, the value of the correlation coefficient is very nearly 1.
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What is one way a market economy affects the lives of private citizens?Citizens can change jobs relatively easily.Citizens cannot choose their own careers.Citizens do not have to pay for their housing.Citizens have little freedom and independence.
Citizens have the freedom and independence to choose their own career paths, as well as the ability to change jobs relatively easily if they desire.
uhh can sb help it’s already over due.
The complete statement is ∠M = 40°
Similar triangles:If the only difference between two triangles is their size (and perhaps the need to rotate or flip one), but not their shape, then they are similar.
In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"
If ΔABC and ΔXYZ are similar triangles then
∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z
Here we have
ΔXYZ and ΔLMN are similar triangles
=> ∠X = ∠L, ∠Y = ∠M, and ∠Z = ∠N
From the given figure,
=> ∠X = ∠L = 25°
=> ∠Y = ∠N = 115°
=> ∠Z = ∠M
From ΔLMN
=> ∠L + ∠M + ∠N = 180°
=> 25° + ∠M +115° = 180°
=> ∠M = 180°- 115° - 25°
=> ∠M = 40°
Therefore,
The complete statement is ∠M = 40°
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1. 14 m find the area of each circle
Ran ordered 3 large pizzas for a party. At the end of
Answer:
Step-by-step explanation: At the end of what? I need the rest of the question in order to help you.
Reduce the answer to lowest terms 3/8÷ 1/7
Answer:
21/8
Step-by-step explanation:
When you are dividing fractions, use Keep-Change-Flip. See image.
Keep-Change-Flip changes the problem to a multiplication.
To multiply fractions, multiply straight across:
top × top and bottom×bottom see image.
We get 21/8 is already in lowest terms.
What two numbers multiply to 5 and add to -10
How do you use the distributive property to remove the parentheses. From 5(10+w)
1000
Step-by-step explanation:
5000
In the Introduction, we saw Janet and Patrick discussing their favorite season of the year. They asked random ninth and tenth grade students to answer the following questions: Are you in ninth grade or tenth grade? What is your favorite season of the year: spring, summer, winter, or fall? Janet and Patrick surveyed a total of 219 students. Out of the 137 ninth graders who were surveyed, 28 said summer was their favorite season, and 12 said that winter was their favorite. The results showed 22 tenth graders said that spring was their favorite season, and 8 tenth graders said winter was their favorite season. A total of 45 students said that summer was their favorite season, and a total of 74 students said that fall was their favorite season. In this activity, you will construct two-way frequency tables to help Janet and Patrick analyze the data they gathered from their survey.
A frequency table is a list of objects with the frequency of each item given in the table. The frequency table is attached below.
What is a frequency table?The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.
The steps are lengthy to explain in words, but the process is fairly straightforward. So Start with figure 1 in the diagram below. The letters A through O represent the steps you'll take to replace them. we'll replace A with 219 since that's the grand total.
Then B is replaced with 137 since we're given that 137 girls were surveyed. Then C gets replaced with 219-137 = 82, and so on.
Using arithmetic (adding and subtracting) to gradually replace each letter with the proper number as figure 2 shows.
The alphabetical order directly corresponds to the order in which the values are given by teacher.
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JTHF monitors offices for tax preparation fee averages, and considers averages greater than $625.00 to be excessive. Offices that consistently charge excessive fees may be subject to which of the following corrective actions? Select one: a. The office will immediately be terminated from the Program. b. The office will be fee capped, which will result in all Financial Product Applications with fees greater than $625.00 to be rejected. c. The office will be fee capped from charging any tax preparation fees. d. None of the above – the office can charge whatever tax preparation fees it wants. Incorrect
The corrective action that offices that consistently charged excessive fees would be subject to by JTFH is a. The office will immediately be terminated from the Program.
What is JTFH ?JTH Financial, LLC (JTHF) is a company that was formed in 2010 in Virginia and their goal and mode of operation is to help customers with tax settlement products that can help them get the best amount to pay for taxes.
JTH Financial, LLC has affiliate offices that engage in tax preparation for clients around the United States but they monitor these offices to ensure that their tax preparation fee averages is not excessive. If an office consistently has excessive fees charged to its customers, then JTH Financial terminates them from the program to protect its customers.
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Find the value of $10,000 in 10 years. The investment earns 8% for four years and then earns 4% for the remaining six years
Answer: After investing for 10 years at 8% interest
Step-by-step explanation: your $10,000 investment will have grown to $21,589 This calculator determines the future value of $10k invested for 10 years at a constant yield of 8.00% compounded annually
Help me I need to finish this by tmr
the vertical spread of the data points about the regression line is measured by the y-intercept.
The standard error of the estimate measures the vertical spread of the data points around the regression line.
The standard error of the estimate, a measurement of the average deviation of errors, is the difference between the y-values predicted by the multiple regression model and the y-values in the sample. This illustrates the precision of the regression model as well as the range of variation surrounding the estimated regression line.
The standard error of the estimate can be used to produce a confidence interval for the actual regression coefficient. The standard error is calculated by multiplying the standard deviation by the square root of the sample size. The standard deviation of the errors/residuals is the standard error of the estimate for the regression model.
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Find the angle between a diagonal of a cube and one of its faces ?
Answer:
35.26°
Step-by-step explanation:
You have to visualize this or draw a diagram
If a cube has side a, the face diagonal of the cube is √2a . The diagonal of the cube is √3a
One side of length a, another side of length √2a (face diagonal) and the third of √3a form a right triangle with the angle opposite √3a being the 90° angle
Therefore we can find the angle [tex]\theta[/tex] which the cube diagonal makes with the face diagonal using the fact
[tex]\dfrac{a}{\sqrt{2}a} = \tan\theta[/tex]
[tex]\theta = tan^{-1}\left(\dfrac{1}{\sqrt{2}\right)} \\= 35.26^\circ[/tex]
Find the mode for the Following sets of numbers 83,97,85,84,96,80,87,91,80
Answer:
80
Step-by-step explanation:
80,80,83,84,85,87,91,96,97
in this numbers there is one mode which is 80 . it is mono.
what is the greatest commen factor of 15 and 64
Answer: The greatest common factor for 15 and 64 is 1.