Answer:
.92367 I think. I'm I'm wrong I'm sorry
Find the surface area of the cylinder. Round your number to the nearest tenth if necessary
3ft 2ft
94.2 square feet is the surface area of the cylinder
The given cylinder has a height of 2 ft and radius of 3 ft
We have to find the surface area of cylinder
Surface area =2πrh+2πr²
Substitute the values of radius and height
=2πr(r+h)
=2×3.14×3(3+2)
=18.84(5)
=18.84×5
Surface area=94.2 square feet
Hence, the surface area of the cylinder is 94.2 square feet
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The value of side TS is,
⇒ TS = 28
First, we are going to divide the figure and named new points X and Y as:
Now, we know that TS is the sum of TX and XS.
TS = TX + XS
Additionally, TX has the same length of HJ, so:
TX = HJ = 14
Now, we want to know the length of YK, and we can calculate it using the following equation:
LK = LY + YK
LY = HJ,
so, LY = 14
And, 42 = 14 + YK
42 - 14 = YK
28 = YK
Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:
XS = YK/2
XS = 28/2
XS = 14
Therefore, TS is equal to:
TS = TX + XS
TS = 14 + 14
TS = 28
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Which equation choice could represent the graph shown below?
1) F(x) = (x - 4)(x + 1)(x - 6)
2) F(x) = (x - 4)(x - 1)(x - 6)
3) F(x) = (x - 4)(x - 1)(x + 6)
4) F (x) = (x + 4(x - 1)(x - 6)
The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)
What equation does represent a cubic function?
In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:
f(x) = (x + 6) · (x - 1) · (x - 4)
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Answer:
3) f(x) = (x - 4)(x - 1)(x + 6)
Step-by-step explanation:
The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.
From inspection of the given graph, the curve crosses the x-axis at:
x = -6x = 1x = 4According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 4)(x - 1)(x + 6)1.1 Convert 500 cm to m
Answer:
5 m
Step-by-step explanation:
To convert 500 cm to m, you simply divide by 100 since there are 100 centimeters in 1 meter.
So, 500 cm ÷ 100 = 5 m
x+3 is a factor of p(x)=x^3-7x^2+15x-9
true or false
The statement "x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex]" is false.
To determine whether x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex], we can use the factor theorem.
According to the factor theorem, if a polynomial p(x) has a factor (x - a), then p(a) = 0.
In this case, we have x + 3 as a possible factor. To check if it is indeed a factor, we substitute -3 for x in the polynomial p(x):
[tex]p(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9[/tex]
= -27 - 63 - 45 - 9
= -144
Since p(-3) is not equal to zero, we conclude that x + 3 is not a factor of p(x).
Therefore, the statement "x + 3 is a factor of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]" is false.
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Please help me find the function that explains how to get the output from the input
Answer:
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
Step-by-step explanation:
For this, first search for the Slope of the funtion
THe slope can be found by calculating this :
(y2-y1)/(x2-x1) or in this case (output2 - output1)/ (input2 - input1)
IT continues as follows:
( -48.5 - 24) / (-413 - (-703) ) =
= (-72.5) / (290)
= -0.25
The slope is -0.25. If the function is a line then the equation is
-0.25*input + B = output
with any of the choices we can determine B.
-0.25 * (-703) + B = 24
175.75 + B = 24
175.75 +B - 175.75 = 24 - 175.75
B = - 151.75
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
Tommy looks around at an assembly. He notices his younger sister to his right and his older brother 4 meters ahead of him. If Tommy's brother and sister are 5 meters apart, how far apart are Tommy and his younger sister?
Answer: Tommy's sister is four meters away from him.
Step-by-step explanation:
If Tommy's older brother is 4 meters ahead and he is 5 meters from his sister,subtract 1 from that since it is described she is right next to him,and you get four.
This is my first time answering anyone so I hope it helps.
Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000 use the 68 9599.7 route to find the percentage of buyers who paid between 150,000 and 153,300 if the standard deviation is 1100
The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.
To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.
According to the empirical rule, given a normal distribution:
approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the three standard deviations of the mean, the data are contained.
In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:
z1 = (150,000 - 150,000) / 1100 = 0
z2 = (153,300 - 150,000) / 1100 = 3
Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.
Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:
Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).
Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).
Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.
So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.
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Raj purchases a new home for $150,000. The value of the home increases by 9% every 3 years.
Determine the value of the home after 5 years.
The value of the home after 5 years would be $194,415.
How to calculate the value of the home after 5 years
First, let's calculate the increase in value for each 3-year period:
After the first 3 years:
Increase = 9% of $150,000 = 0.09 * $150,000 = $13,500
After the second 3 years:
Increase = 9% of ($150,000 + $13,500) = 0.09 * ($150,000 + $13,500) = $14,850
After the third 3 years:
Increase = 9% of ($150,000 + $13,500 + $14,850) = 0.09 * ($150,000 + $13,500 + $14,850) = $16,065
Now, let's add these increases to the initial value of the home to find the value after 5 years:
Value after 5 years = $150,000 + $13,500 + $14,850 + $16,065 = $194,415
Therefore, the value of the home after 5 years would be $194,415.
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The photo is kinda blurry but please help me with it
The perimeter of rectangle M'N'O'P' is given as follows:
54 cm.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The ratio between the areas is given as follows:
126/14 = 9.
The area is measure in square units, while the perimeter is measured in units, hence the ratio of the perimeters is the square root of the ratio of the areas, that is:
3.
Hence the perimeter of rectangle M'N'O'P' is given as follows:
3 x 18 = 54 cm.
Missing InformationThe complete problem is:
Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?
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ill mark brainliest !
Answer:
Since the line is vertical and passes through the point (3, -5), it is a vertical line with undefined slope.
Step-by-step explanation:
Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?
We have that Linda's net and expression incorrect.
Now, With the Expression of the surface area of attic
45 (40 + 25 + 25) + 1/2 (40 x 15)
Hence, Surface area is,
X = 4050 + 600
X = 4650 feet²
Hence, The answer is No, Because Her expression for the triangles are incorrect;
1/2(40 x 15)
Instead of,
1/2 x 40 x 15
Hence, Linda's net and expression incorrect,
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Complete question is,
Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes the expression below to represent the surface area of the attic. Are Linda's net and expression correct?
879 dived by 8 with remainder ad fraction
Answer: 109.875
Step-by-step explanation: 879 / 8 = 109.875 because if you divide 8 by 9 you get 1 so after you would divide 79 by 8 = 9.875 so then you put 109 then after but the decimals 109.875.
A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
A coordinate plane.
What is the value of a?
–2
–1
1
2The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The value of a is given as follows:
a = 2.
The rate of change is given as follows:
2.4 inches per hour.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope, which is the rate of change of the output variable y relative to the input variable x.b is the intercept, which is the value of y when x = 0.The line passes through the points (–1, –5) and (4, 5), hence the slope m is obtained as follows:
m = (5 - (-5))/(4 - (-1))
m = 2.
Hence:
y = 2x + b.
When x = -1, y = -5, hence the intercept b is obtained as follows:
-5 = -2 + b
b = -3.
Hence:
y = 2x - 3.
Then the value of a is obtained as the value of x when y = 1, hence:
2x - 3 = 1
2x = 4
x = 2.
The rate of change in the snowfall is given as follows:
m = (8.1 - 2.3)/2
m = 2.4 inches per hour.
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Alfred says that the line shown on the scatter plot is a good line of fit because the line goes through the middle of all the data points. Do you agree? Explain your reasoning
No, I disagree because a good line of fit has to minimize the sum of the squared distance between all the points in the data.
Line of fitA line of fit is used to mathematically model the relationship between variables in a data. A line of fit is drawn such that the best line would minimize the sum of the squared distances between the plotted points.
This means that, the line of fit should not aim to go through the middle of the data points but minimize the sum of the squared distances between them.
Hence, Alfred's reasoning is Incorrect .
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
The graph below displays a fire department's
response time, which measures the time from when
the alarm is sounded at the firehouse to the time the
first fire engine leaves the station.
Fire Department Response Times
0.4
Relative Frequency
10
02
0
10
20 30 40 50 60 70 80 90
Response Time (Seconds)
Which of the following correctly describes the shape of
the distribution?
uniform
skewed left
skewed right
roughly symmetric
The correct description of the shape of the distribution is D. Roughly Symmetric.
What is a symmetric distribution ?Symmetric distribution is an often-referenced term in statistics, representing a type of probability with data segments evenly dispersed around the mean. This denotes the perfect mirror image of the right and left halves when the distribution is split; arriving at an equal size and shape on either side when drawn at the midpoint of the line.
Looking at the distribution of a fire department's response time, we can see that the distribution is roughly symmetric because the values on the left seem to match those on the right.
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The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale. What is the difference of the medians? 0 2 4 7
The difference of medians is given as follows:
2.
What does a box and whisker plot shows?A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:
The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.The median for each day is given as follows:
Day 1: 6.Day 2: 8.Hence the difference is given as follows:
8 - 6 = 2.
Missing InformationThe box plot is given by the image presented at the end of the answer.
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Which is true about the solution to the system of inequalities shown? y > 3x + 1 y < 3x – 3 On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded. Only values that satisfy y > 3x + 1 are solutions. Only values that satisfy y < 3x – 3 are solutions. Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions. There are no solutions.
There are no solutions to the system of inequalities Option (d)
Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.
A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is
y > 3x + 1
y < 3x - 3
The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.
The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.
Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.
To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.
When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.
There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.
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Complete Question :
Which is true about the solution to the system of inequalities shown?
y > 3x + 1
y < 3x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Options:
a)Only values that satisfy y > 3x + 1 are solutions.
b)Only values that satisfy y < 3x – 3 are solutions.
c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
d)There are no solutions.
Answer:
D
Step-by-step explanation:
Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 4.7% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.
The initial deposit needed for the account is given as follows:
$19,257.37.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
[tex]A = 22000, t = 3, r = 0.0447, n = 4[/tex]
Hence the initial deposit P is obtained as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]22000 = P\left(1 + \frac{0.0447}{4}\right)^{4 \times 3}[/tex]
1.142657P = 22000
P = 22000/1.142657
P = $19,257.37.
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Which uppercase letters among W, X, Y, and Z have both
reflective and rotational symmetry?
Answer:
X
Step-by-step explanation:
Reflective symmetry, also known as mirror symmetry, exists when a figure can be reflected across a line and appear the same. Rotational symmetry exists when a figure can be rotated about a point by a certain degree less than 360 and still appear the same.
Among the uppercase letters W, X, Y, and Z:
The letter W has no reflective or rotational symmetry.
The letter X has both reflective and rotational symmetry. It's symmetrical on both the vertical and horizontal axes and has a rotational symmetry of 180 degrees.
The letter Y only has reflective symmetry on the vertical axis, but it does not have rotational symmetry.
The letter Z also has reflective symmetry on the horizontal axis, but it does not have rotational symmetry.
So among these letters, only X has both reflective and rotational symmetry.
One of the authors received a credit card bill for $2,559, but it included a charge of $1,825 th
values of the absolute and relative errors.
The value of the absolute error is $
The value of the relative error is%. (Round to the nearest integer as needed)
The absolute error is $1825, the relative error is 2
What is an absolute and relative error?An absolute error is a determinant of how large an error is. A relative error defines how good or bad an error is.
The formula for determining an absolute error is;
Absolute error = measured value - actual valueThe formula for determining a relative error is:
Relative error = absolute error ÷ actual valueFrom the parameters given:
The absolute error can be computed as:
Absolute error = 2559 - (2559 - 1825)
Absolute error = 2559 - 734
Absolute error = $1825
The relative error = 1825 ÷ 734
The relative error = 2.4
The relative error ≅ 2 (as an integer)
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Help me with this question pls. And do it fast I have to submit it soon in 3 minutes
The perimeter of the dilated rectangle M'N'O'P' is 54 centimeters.
If the area of the original rectangle is A, and the area of the dilated rectangle is A', then the relationship between their areas is:
A' = k² × A
Similarly, the relationship between their perimeters is:
P' = k × P
The original rectangle has an area of 14 square centimeters.
The dilated rectangle has an area of 126 square centimeters.
We need to find the perimeter of the dilated rectangle.
Let's denote the scale factor as "k."
126 = k² × 14
Dividing both sides by 14, we get:
9 = k²
k = 3
Now, we can find the perimeter of the dilated rectangle using the perimeter relationship:
P' = k × P
The original rectangle has a perimeter of 18 centimeters, so:
P' = 3 × 18
P' = 54 centimeters
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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?
The expected value of the car 7 years after it was purchased is $47,029.12.
To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:
Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)
In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:
Value after 7 years = 54792 - (54792 × (19/100)×7)
Value after 7 years = 54792 - (54792 × 0.19×7)
Value after 7 years = 54792 - 7762.88
Value after 7 years = $47,029.12
Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.
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The question is :
Which expression is a factor of both
x^2-9 and x^2+8x+15
Can you please explain this to me like you are talking to an elementary schooler, i kinda get it but im honestly so confused.
The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).
What is the common factor between the given polynomials?Given the polynomials in the question:
x² - 9
x² + 8x + 15
To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.
First, factorize x² - 9:
Using the difference of sqaure formula
a² - b² = ( a + b )( a - b )
x² - 9
x² - 3² = (x - 3)(x + 3)
Next, factorize x² + 8x + 15:
Using AC method
( x + 3 )( x + 5 )
From the factorizations, we can see that both expressions have a common factor of (x + 3).
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(Worth 100 Brainly points help fast)Solve the following system of equations and show all work.
y = 2x²
y = -3x -1
The solutions are : solution of the following system of equations are:
(- 1/2, 1/2)
(- 1, 2)
Here, we have,
The given system of equations is expressed as
y = 2x²- - - - - - - - - - - - - - -1
y = - 3x - 1- - - - - - - - - -- - - -2
We would apply the method of substitution by substituting equation 1 into equation 2. It becomes
2x² = - 3x - 1
2x² + 3x + 1 = 0
We would find two numbers such that their sum or difference is 3x and their product is 2x².
The two numbers are 2x and x. Therefore,
2x² + 2x + x + 1 = 0
2x(x + 1) + 1(x + 1) = 0
2x + 1 = 0 or x + 1 = 0
x = - 1/2 or x = - 1
Substituting x = - 1/2 into equation 1, it becomes
y = 2(-1/2)² = 1/2
Substituting x = - 1 into equation 1, it becomes
y = 2(-1)² = 2
Hence, The solutions are : solution of the following system of equations are:
(- 1/2, 1/2)
(- 1, 2)
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Please help. Is the answer even there?
The critical values t₀ for a two-sample t-test is ± 2.0.6
To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:
t₀ = ± t_(α/2, df)
where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.
The degrees of freedom are calculated as:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8
α = 0.05 (two-tailed)
First, we need to calculate the degrees of freedom:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]
= 24.27
Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.
From a t-distribution table, we find:
t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)
Finally, we can calculate the critical values t₀:
t₀ = ± t_(α/2, df) = ± 2.0639
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Mary goes walking everyday she walks 14ft every 4 seconds which is equation models the relationship between the time Mary walks x and the distance she walks y
Answer:
y=3.5x
Step-by-step explanation:
to find the the feet mary walks per second, divide 14 by 4
14/4=3.5 feet/second
the total distance mary walks can be represented by multiplying the number of feet she walks per second by the number of seconds she walks
y= 3.5x
in this model, x is seconds
find the volume of each figure. round to the nearest tenth as needed. please show the work, will mark the brainliest.
Answer:
4. 4155.3cm³
5. 783m³
6. 1962.44821094mm³
#4 Explanation:
First, you would separate the 2 shapes it consists of, a cylinder and a cone.
For the cone, you would use the equation (1/3)πr²h. Fill in the appropriate variables with the numbers from the formula. Pi, π, is a number itself so you leave it as it is.
r = radius = 8cm
h = height = 14cm
(1/3)(π)(8)²(14)
Put this equation into a calculator, it's important to include the parentheses or it might give you the incorrect answer, this is so that it separates the different values while multiplying. After inputting it, it should give you:
v = 938.289005872cm³
Then, you would have to find the volume of the cylinder, using the equation; πr²h.
The radius would be the same as the cone, and the height is as the problem states, 16cm.
Solve the problem after inputting the values:
π(8)²(16)= 3216.99087728cm³
Then, add the values to get the total volume.
938.289005872cm³ + 3216.99087728cm³ =
4155.27988315cm³
Round to nearest tenth: 4155.3cm³
#5 Explanation:
Again, you would separate the shapes into 2 separate ones.
The top one is a triangular prism and uses the equation (1/2)bh.
b = base = 9m
h = 12m
(1/2)(9)(12) = 54m³
The bottom shape is a rectangular prism, where we use the equation L×W×H.
Length = 9m
Width = 9m
Height = 9m
Substitute the numbers into the equation.
9×9×9 = 729m³
Add both of them together to get the total volume:
54m³ + 729m³ = 783m³
#6 Equation:
In this figure, we are looking for the outer shape, so we will have to subtract the smaller cone.
First, we find the total volume, and we will use the same equation, (1/3)πr²h.
radius = half of diameter = 20/2 = 10mm
h = 20mm
(1/3)π(10)²(20) = 2094.39510239mm³
Second, we find the volume of the smaller cone, using the same equation, (1/3)πr²h.
In order to find the diameter, we will have to subtract the 7 mm that are on either side of the cone, so 20 - 14 = 6, then divide it by 2 so we can get the necessary radius. 6/2 = 3
r = 3mm
h = 14mm
Substitute values into equation and use calculator to solve.
(1/3)π(3)²(14) = 131.946891451mm³
Subtract the value of the smaller cone from total volume in order to get the volume for this figure.
2094.39510239mm³ - 131.946891451mm³ =
1962.44821094mm³
Can someone help me with this please?
Applying linear functions, we have: a. Bakery B charges a higher delivery fee b. Bakery A charges a higher price per cookie
c. Bakery B is cheaper.
How to Solve Linear Functions?In order to solve this problem, we will need to write the linear function for bakery A and bakery B.
Where:
b = the initial delivery fee which is the y-intercept
m = price per cookie
x = number of cookies
y = total cost
For Bakery A:
b = 5 (initial delivery fee)
m = price per cookie = change in y/change in x = 10 - 5 / 2 - 0
m = 5/2 = $2.5.
The linear function for bakery A is: y = 2.5x + 5.
For Bakery B:
b = 7 (initial delivery fee)
m = price per cookie = change in y/change in x = 16 - 7 / 4 - 0
m = 9/4 = $2.25.
The linear function for bakery A is: y = 2.25x + 7.
Therefore, we have:
a. The bakery that charges a higher delivery fee is Bakery B.
b. The bakery that charges a higher price per cookie is Bakery A.
c. Substitute x = 12 into both linear functions:
Bakery A: y = 2.5(12) + 5 = $35
Bakery B: y = 2.25(12) + 7 = $34
The bakery that is cheaper is: Bakery B.
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