When we factor the expression, we are going to obtain the result;
9a(9a + 4) + 4
How do you factor an expression?Factoring an expression involves breaking it down into simpler parts that can be multiplied together to obtain the original expression. The specific method used to factor an expression depends on the type of expression.
It's important to note that factoring can sometimes be a challenging process, and not all expressions can be factored using real numbers.
We can carry out this factorization by the use of the nesting method, Hence;
81a^2 + 36a + 4
(81a^2 + 36a ) + 4
9a(9a + 4) + 4
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PLEASE PLEASE PLEASE HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!
The femur length for someone with a height of 187 cm is; 55 cm
How to find interpret the scatter plot?The formula for the equation of a line formed by 2 coordinates is;
(y2 - y1)/(x2 - x1) = (y - y1)/(x - x1)
Using the coordinates (30, 127) and (35, 139), we have;
(139 - 127)/(35 - 30) = (y - 127)/(x - 30)
12/5 = (y - 127)/(x - 30)
12(x - 30) = 5(y - 127)
12x - 360 = 5y - 635
5y = 12x + 275
Thus, when the height is y = 187 cm, we have;
5(187) = 12x + 275
935 = 12x + 275
12x = 935 - 275
12x = 660
x = 660/12
x = 55 cm
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calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9. round your answer to the nearest tenth.
The z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.
The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the data value, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (80 - 52) / 9 = 3.11 (rounded to two decimal places)
Therefore, the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.
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The z-score for a data value of 80 in this data set is approximately 3.1.
Calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9.
To find the z-score, follow these steps:
Identify the data value (x), mean (µ), and standard deviation (σ).
In this case, x = 80, µ = 52, and σ = 9.
Use the z-score formula:
z = (x - µ) / σ
Plug in the values:
z = (80 - 52) / 9
Perform the calculations:
z = 28 / 9
Round the answer to the nearest tenth: z ≈ 3.1
So, the z-score for a data value of 80 in this data set is approximately 3.1.
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Simplify the radical
[tex]\sqrt{x} 245[/tex]
The radical expression √45 when simplified has a value of 3√5
Simplifying the radical expressionFrom the question, we have the following parameters that can be used in our computation:
The radical expression √45
Express 45 as the product of 9 and 5
So, we have the following representation
√45 = √(9 * 5)
Expand the expression
This gives
√45 = √9 * √5
Take teh square roots of 9
This gives
√45 = 3 * √5
Lastly, we have
√45 = 3√5
Hence, the radical expression when simplified is 3√5
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Complete question
Simplify the radical √45
if the series 3 3z 6z^2 9z^3 is geometric, give the initial term, and the ratio between successive terms
The series is not geometric.
What is geometric series?
In mathematics, the geometric series means the sum of the terms that have a common ratio between every adjacent two terms of them. There can be two types of geometric series: finite and infinite.
The given series is
3 , 3z, 6z², 9z³
The given series is either geometric or not.
The initial term or the first term is 3 which also can be written as 3z⁰
Ratio between successive terms can be determined by
second term/ first term
Here second term is 3z and first term is 3
So the ratio is 3z/3
= z
If the series is geometric then
it must be equal to 6z²/ 3z= 2z and 9z³/ 6z² = (3/2)z
The ratios are not equal to each other.
Hence, the series is not geometric.
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Quick question need help
Answer:
18.8651
Step-by-step explanation:
(im not the best at explaining, so sorry if i dont explain it well, but ill try!)
so rounding a number to a certain amount of sig figs is a pretty easy concept to grasp, in my opinion.
ex: lets say you need to round 231.45 to 3 sif figs.
basically what you have to do in this situation is count the digits up to you get to the 3rd digit.
check if the digit that follows it is smaller or bigger than 5 to see if the 3rd number will stay the same or has to go up a number.
for this problem the third digit is 1, and the digit that follows it is 4. but 1 is less than 4, so that means that it will stay as 1.
thus the answer would be 231.
if that didnt make sense, comment on my answer and ill try to give you more examples
On what interval is the function positive?
f(x) = 2(6)^(x+1) -3
Enter your answer, in interval notation. Round any necessary values to the nearest tenth.
The function f(x) is positive on the interval (-0.744, infinity).
In interval notation: (−0.744, ∞).
What is a function?A function is a relationship between inputs in which each input corresponds to exactly one output.
When [tex]f(x) = 2(6)^{X+1} -3[/tex] is greater than zero, it is positive.
[tex]2(6)^{(x+1) } - 3 > 02(6)^{(x+1)} > 3(6)^{ (x+1) } > 3/2[/tex]
Now taking logs on both sides gives
[tex]log(6)^{ (x+1) } > log3/2[/tex]
(x+1) * log6 > log3/2
(x+1) > [tex]\frac{log3/2}{log6}[/tex]
(x+1) > [tex]\frac{0.17609}{ 0.77815}[/tex]
(x +1) > 0.2265
x > 0.2265 - 1
x > -0.7735
Thus, the function f(x) is positive on the interval (-0.744, infinity).
In interval notation: (−0.744, ∞).
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In this diagram, AT = 2x + 3, CT = 3x - 1, BT = x + 5,
DT = 4x + 1, and mLATD = 41x + 8. If x = 2,
which segment is the perpendicular bisector of the other? Explain your reasoning.
Answer:
CT is the perpendicular bisector of AB
Step-by-step explanation:
calculate the segments using x = 2
AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7
BT = x + 5 = 2 + 5 = 7
thus AT = BT
CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9
thus CT ≠ DT
∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°
Thus CT is the perpendicular bisector of AB
a term used to describe the case when the independent variables in a multiple regression model are correlated is . a. correlation b. multicollinearity c. linearity d. regression
Multicollinearity refers to a situation in multiple regression where the independent variables, or predictors, in a statistical model are correlated with each other. Option B multicollinearity is correct.
Multicollinearity can result in several problems, including:
Difficulty in interpreting regression coefficients: When predictor variables are highly correlated, it becomes challenging to interpret the individual effect of each predictor on the dependent variable, as the effects may be confounded or mixed up.Unstable estimates of regression coefficients: Multicollinearity can lead to unstable or unreliable estimates of regression coefficients, as small changes in the data or the model can result in large changes in the estimated coefficients.Reduced statistical power: Multicollinearity can reduce the statistical power of a multiple regression model, making it harder to detect significant relationships between the predictors and the dependent variable.Increased standard errors: Multicollinearity can lead to increased standard errors of the regression coefficients, which can result in wider confidence intervals and decreased precision in estimating the true coefficients.It is important to identify and address multicollinearity in a multiple regression model to ensure accurate and reliable interpretation of the results. This can be done through techniques such as variance inflation factor (VIF) analysis, principal component analysis (PCA), or using a subset of predictors with low intercorrelation.
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The term used to describe the case when the independent variables in a multiple regression model are correlated is
b. multicollinearity is correct.
Multiple regression is a typical method in statistical modelling for determining the association between a dependent variable and two or more independent variables.
The fundamental tenet of multiple regression is that there is no correlation between the independent variables. Multicollinearity is the outcome when this assumption is broken, which can happen in real life.
When two or more independent variables in a multiple regression model have a high correlation with one another, multicollinearity arises.
Due to these issues, the model's coefficients may not be correctly interpreted, producing estimates that are inaccurate and unstable.
It is challenging to separate the distinct impacts of each independent variable on the dependent variable when multicollinearity is present because these effects are entangled and difficult to separate.
b. multicollinearity is correct option.
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Read each question carefully. Choose the answer that best completes the sentence.
Debt is usually expected in any of the following cases EXCEPT
O A. purchase of house
OB. credit card purchases
OC. purchase of car
O D. educational loans
nswered
The correct answer is,
Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''
We have to given that;
Debt is usually expected in any of the following cases EXCEPT ....
Now, We know that;
it's important to note that there may be individual situations where debt is expected when buying a car.
Hence, The correct answer is,
Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''
Thus, Option C is true.
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Please help me please help me please help me please help, please help
A cone has a height of 13 yards and a radius of 12 yards. What is its volume? Use л ~ 3.14 and round your answer to the nearest hundredth.
Please help me
The volume of the cone is 1960.64 cubic yards.
We have,
The formula for the volume of a cone is:
V = (1/3)πr²h
where π is approximately 3.14, r is the radius, and h is the height.
Substituting the given values, we get:
V = (1/3) x 3.14 x 12² x 13
V = (1/3) x 3.14 x 144 x 13
V = 1/3 x 3.14 x 1872
V = 1960.64
Rounding to the nearest hundredth, we get:
V = 1960.64
Therefore,
The volume of the cone is 1960.64 cubic yards.
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not rushing anyone, but if someone can help w all or most of the questions, i'll give u all my points
Answer:
Example of the distributive property: a(b + c) = ab + ac
Question #1:
a) 6(3a + 2) = 18a + 12
b) 2(7 - 5y) = 14 - 10y
c) 3(r + 1/3) = 3r + 1
d) 8(2m - 3/8) = 16m - 3
e) 5(x/5 + 4) = x + 20
Question #2:
a) 3y + 1/4 = 4
4 (3y + 1/4) = 4 (4)
12y + 1 = 16
b) x/6 + 7 = 10
6 (x/6 + 7) = 6 (10)
x + 42 = 60
c) 11/3 - 4c/3 = 2
3 (11/3 - 4c/3) = (3) 2
11 - 4c = 6
d) 2n - 1 = 1/2
2 (2n - 1) = 2 (1/2)
4n - 2 = 1
e) r/2 + 8 = 1/2
2 (r/2 + 8) = 2(1/2)
r + 16 = 1
Hope this helped!
3-5 If we project the are of a hip roof onto a horizontal plane, it will appear as two triangles and two trapezoids. (True or False)
Given statement "If we project the area of a hip roof onto a horizontal plane, it will appear as two triangles and two trapezoids"
Given statement is True.
Because, A hip roof has four sloping sides that meet at the top ridge, forming a pyramid-like shape. When projected onto a horizontal plane, the following shapes will appear:
Two triangles:
These are formed by the two ends of the roof, where the sloping sides meet the ridge.
Two trapezoids:
These are formed by the two sides of the roof, where the eave edges meet the ridge.
So, when projecting the area of a hip roof onto a horizontal plane, it will indeed appear as two triangles and two trapezoids.
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Martin is building a wire-screen chicken coop in the shape of a rectangular prism. The coop has a height of 42 inches, a width of 36 inches, and a length of 48 inches. Martin wants to determine the total surface area of the coop in order to purchase the correct amount of wire screening.
Which of the following expressions represents the total surface area of the right rectangular prism with the dimensions given above?
The total surface area of the wire-screen chicken coop is 10512 square inches.
What is surface area?The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area
According to the given information:the total surface area of the right rectangular prism, we use the formula:
2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
We are given the height, width, and length of the wire-screen chicken coop, which are 42 inches, 36 inches, and 48 inches, respectively.
Substituting these values in the formula, we get:
2(36)(48) + 2(36)(42) + 2(48)(42)
Multiplying out, we get:
= 3456 + 3024 + 4032
Adding these terms, we get the total surface area:
= 10512
Therefore, the total surface area of the wire-screen chicken coop is 10512 square inches.
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Prove that ST^2=TU*TV
Hence proved,[tex](ST)^2=(TU*TV)[/tex]for given figure.
What is the right triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
What is the Pythagoras theorem?In mathematics, the Pythagoras theorem or Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Use Pythagoras theorem , in given figure
than we get ,
in ΔTSU,
[tex](TU)^2=(ST)^2+(SU)^2[/tex]......(I)
inΔTVS,
[tex](ST)^2=(TV)^2+(SV)^2[/tex]......(II)
inΔSVU,
[tex](SU)^2=(VU)^2+(VS)^2[/tex].....(III)
from (I),
[tex](TU)^2-(ST)^2=(SU)^2=(VU)^2+(VS)^2[/tex]....(IV) {by (III)
according to figure,TU=TV +VU
∴ [tex](TV+VU)^2=(VU)^2+(VS)^2+(ST)^2=(VU)^2+(VS)^2+(TV)^2+(SV)^2[/tex]{by (II)
use the identity,is
[tex](a+b)^2=a^2+2ab+b^2\\(TV)^2+2(TV)*(VU)+(VU)^2=(VU)^2+2(SV)^2+(TV)^2[/tex]
after simplification,
⇒[tex](TV)*(VU)=(SV)^2[/tex]
according to figure,TU=TV +VU ⇒VU=TU-TV
[tex](TV)*(TU-TV)=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(TV*TU)-(TV)^2=(SV)^2\\(SV)^2+(TV)^2=(TV*TU)\\(ST)^2=(TV*TU) {by(II)\\ OR (ST)^2=(TU*TV)[/tex]
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below you are given a partial excel output based on a sample of 16 observations. anova df ss ms f regression 4,853 2,426.5 residual 485.3 coefficients standard error intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 the t value obtained from the table that is used to test an individual parameter at the 1% level is . a. 2.921 b. 2.977 c. 2.65 d. 3.012
To discover the t-value for testing a person parameter at the 1% level, we ought to isolate the coefficient appraise by its standard deviation and compare it to the t-distribution with suitable degrees of flexibility.
For case, to test the parameter gauge for x1, we would calculate the t-value as: t = (-3.682) / 2.630 ≈ -1.4
At that point compare this t-value to the t-distribution with 485 degrees of flexibility (which compares to the leftover degrees of opportunity), and decide on the off chance that it surpasses the basic esteem at the 1% level (which is around 2.977).
In any case, the given yield does not demonstrate which parameter appraise is being tried, so we cannot decide the comparing t-value. Hence, none of the reply choices are rectified.
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Solve each equation for x. X2+ax-3ab-3bx=0
The solutions of equation for x are (3b + √(9b² + 12ab(a - b))) / 2a and (3b - √(9b² + 12ab(a - b))) / 2a
To solve the equation x² + ax - 3ab - 3bx = 0 for x, we can use the quadratic formula, which is given by:
x = (-b ± √(b² - 4ac)) / 2a
In this situation, the quadratic equation's coefficients are:
a = a
b = -3b
c = -3ab
x = (3b ± √(9b² + 12ab(a - b))) / 2a
Therefore, the solutions for x are:
x = (3b + √(9b² + 12ab(a - b))) / 2a
x = (3b - √(9b² + 12ab(a - b))) / 2a
Therefore, the solutions of equation for x are (3b + √(9b² + 12ab(a - b))) / 2a and (3b - √(9b² + 12ab(a - b))) / 2a
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Answer:
Step-by-step explanation:
bro its just -14/a
that simple
to be honest if ur here ur not looking for "how to solve the question ur just looking for the answers
its just -14/a
The graph of g(x)=(x – 2)2+10 is a translation of the graph of the parent function units right and units up.
The graph of g(x)=(x – 2)²+10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up.
What is the linear function?A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
According to the given information:The graph of the function g(x) = (x-2)² +10 is a transformation of the parent function f(x) = x² that has been shifted 2 units to the right and 10 units up.
To see this, consider the vertex of the graph of g(x), which occurs at the point (2, 10). This vertex represents the minimum value of the function and is located 2 units to the right and 10 units up from the vertex of the parent function f(x), which is at the origin (0, 0). Therefore, we can say that the graph of g(x) is a translation of the graph of f(x) by a vector (2, 10).
Therefore, The graph of g(x) = (x-2)² +10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up. The vertex of g(x) is located at (2, 10), which is 2 units to the right and 10 units up from the vertex of f(x) at (0, 0).
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Which of the following people would you expect to have the best
employee benefits?
O new hire at a large company
O part-time at a small company
O full-time employee at a large company who has been there for years
O new hire at a small company
Answer:
A full-time employee at a large company who has been there for years would typically have the best employee benefits.
Large companies often have more resources to provide extensive employee benefits packages, including health insurance, retirement plans, paid time off, and other perks. Full-time employees who have been with the company for years may be eligible for additional benefits, such as higher matching contributions to retirement plans and increased vacation time.
New hires at both small and large companies may not have access to as many benefits initially, as they may need to work for a certain period before becoming eligible. Part-time employees may also have limited access to benefits, depending on the company's policies.
Overall, the length of time an employee has been with the company and the size of the company are two important factors in determining the quality and quantity of employee benefits.
a cycloid is the plane curve traced out by a point on the circumference of a circle as it rolls without slipping along a straight line. (a) assume that the line is the x-axis, and the circle has radius 1. find a parametriza- tion of the cycloid. (b) what is the arclength of one period of the cycloid?
Answer: (a) Let the circle roll along the x-axis with the center at the origin. Then, the parametric equations of the cycloid are given by:
x = t - sin(t)
y = 1 - cos(t)
where t is the angle in radians that the circle has rotated from its initial position.
(b) The arclength of one period of the cycloid is given by the integral:
L = ∫(0,2π) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the parametric equations from part (a), we get:
dx/dt = 1 - cos(t)
dy/dt = sin(t)
Therefore,
[dx/dt]^2 + [dy/dt]^2 = 2 - 2cos(t)
Substituting back into the arclength integral, we get:
L = ∫(0,2π) √(2 - 2cos(t)) dt
This integral can be evaluated using the half-angle formula:
cos(t) = 1 - 2sin^2(t/2)
Substituting this into the integral and simplifying, we get:
L = 8∫(0,π/2) √(sin^3(t/2)) dt
This integral can be evaluated using a substitution u = cos(t/2), du = -sin(t/2)dt:
L = 16∫(0,1) √[(1-u^2)^3] du
This integral can be further simplified by making the substitution u = sin(θ):
L = 16∫(0,π/2) cos^4(θ) dθ
This integral can be evaluated using integration by parts and trigonometric identities. After some algebraic manipulations, we get:
L = 8π
Step-by-step explanation:
How do you find the equation?
The equation of the line CD obtained from the slope of the line AB, and the coordinates of the point C is; 7·y - 3·x = 2
What is the slope of a line?The slope of a line is the ratio of the rise to the run of the line.
The specified information indicates;
AB ║ CD
The coordinates of the point A is (-3, 2), the coordinates of the point B is (4, 5)
The slope of the segment AB is therefore; (5 - 2)/(4 - (-3)) = 3/7
The coordinates of the point C is; (4 , 5 - 3) = (4, 2)
The equation of the line CD is therefore; y - 2 = (3/7)·(x - 4)
7·y - 14 = 3·x - 12
7·y - 3·x = 14 - 12 = 2
The equation of the segment CD is; 7·y - 3·x = 2
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Cathy & Gina sold baked goods at the festival, they were able to sell 18 items. The pies were $8 and loaves
of bread were $4. They made $112. How many loaves of bread did they sell?
Answer:
Step-by-step explanation:
They sold 34 loafs of bread
20 POINTS!!!!!!!
For what value of x must the quadrilateral be a parallelogram?
5x
X =
28
(3x+28)
work:
APR
12
!!!
tv
SA
C
. A middle school teacher conducted a survey of the 8th grade class and found that 43 students were athletes and 19 of those students drink soda. There were 33 students that were not athletes, but drank soda. Last, they found that 22 students were not athletes and did not drink soda. Given this information, how many students don't drink soda
There are 46 students don't drink soda.
Let's use a Venn diagram to represent the information given in the problem:
Athletes
/ \
/ \
Soda / \ No Soda
/ \
/ \
/ \
----------------------------------------------
| |
| |
| |
Drink No Drink
| |
| |
| |
----------------------------------------------
| |
| |
| |
19 24
| |
| |
|
----------------------------------------------
| |
| |
| |
33 10
| |
| |
| |
----------------------------------------------
| |
| |
| |
24 22
| |
| |
| |
----------------------------------------------
The diagram, we can see that there are 24 students who drink soda and are athletes, 19 who drink soda but are not athletes, 33 who are not athletes but drink soda, and 22 who are neither athletes nor soda drinkers.
The number of students do not drink soda, we need to add the number of students who are athletes but do not drink soda to the number of students who are neither athletes nor soda drinkers:
Number of students who don't drink soda
= Number of athletes who don't drink soda + Number of students who are neither athletes nor soda drinkers
Number of athletes who don't drink soda = Total number of athletes - Number of athletes who drink soda = 43 - 19 = 24
Number of students who are neither athletes nor soda drinkers = 22
The number of students who don't drink soda is:
Number of students who don't drink soda = 24 + 22 = 46.
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find the surface area of a rectangular prism if the width is 4 cm, the length is 4 cm, and the height is 15 cm
Hence, the rectangular prism has a surface area of 272 square centimetres.
what is surface area ?For instance, by multiplying the length and breadth of a rectangle, the area of the shape can be determined. Pi (roughly 3.14), multiplied by the square root of the radius, can be used to get a circle's area. Calculating the size of numerous forms and figures, including triangles, circles, squares, and polygons, involves the usage of area, a key topic in geometry. The size of a piece of land, a building's floor area, or the surface of such an object are just a few examples of the many real-world uses for it.
given
We must add up the areas of all six faces of a rectangular prism in order to determine its surface area.
In this instance, the dimensions are as follows: width (w), length (l), and height (h), all in centimetres.
You can compute the surface area (A) as follows:
A = lw + lh + lw
Inputting the values provided yields:
A is equal to 2 (4 x 4 cm) + 2 (4 x 15 cm) + 2. (4 cm x 15 cm)
[tex]A=32 cm^2 + 120 cm^2 + 120 cm^2[/tex]
A = 272 cm²
Hence, the rectangular prism has a surface area of 272 square centimetres.
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URGENT PLEASE ANSWER!!! I INCLUDED THE GRAPH!
Graph the line y = 4/3x + 1.
Use the line tool and select two points on the line.
We have (0, 1) and (3, 5) as two points on the line y = 4/3x + 1.
Selecting two points on the line.The equation y = 4/3x + 1 represents a line in slope-intercept form, where the coefficient of x (4/3) represents the slope of the line and the constant term (1) represents the y-intercept.
To select two points on the line, we can choose any values for x and use the equation to find the corresponding values of y.
For example, let's choose x = 0:
y = 4/3x + 1
y = 4/3(0) + 1
y = 1
So one point on the line is (0, 1).
Now let's choose x = 3:
y = 4/3x + 1
y = 4/3(3) + 1
y = 5
So another point on the line is (3, 5).
Since both equations hold true, we can conclude that (0, 1) and (3, 5) are two points on the line y = 4/3x + 1.
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Page 1:
1
A
1=1.5 m
75°
0
B
wiper
1) What is the radius?
2) What is the angle measure?
3) What formula can you use to find the area?
4) What is the area of the space swept by the wiper?
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1. The radius (r) of the space swept is 1.5 m; 2. The angle measure is 75°.
3. The formula to use is Area = ∅/360 * πr²; 4. Area of the space is approximately 1.47 m².
What is the Area of a Sector?The formula to use to find the area of a sector is given as:
Area = ∅/360 * πr², where:
r is the radius; and ∅ is the angle measure.
From the image given, we will solve the problem as follows:
1. The radius (r) = 1.5 m
2. The angle measure (∅) = 75°
3. The formula is:
Area = ∅/360 * πr²
4. Plug in the values:
Area = 75/360 * π * 1.5²
Area ≈ 1.47 m²
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The speed of a stream is 4 mph. A boat travels 3 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in Stillwater?
Let the speed in still water be [tex]x[/tex] miles per hour.
The speed upstream will be slower than the speed downstream.
Speed upstream [tex]= x-4[/tex] miles per hour and speed downstream will be [tex]x+4[/tex] miles per hour.
[tex]\text{Time Taken}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]
The time taken for the trip upstream and the trip downstream are the same:
[tex]\text{time}_{\text{up}}=\dfrac{3}{x-4}[/tex]
[tex]\text{time}_{\text{down}}=\dfrac{11}{x+4}[/tex]
[tex]\dfrac{11}{x+4} =\dfrac{3}{x-4} \ \ \ \ \ \ \ \leftarrow \ \text{cross multiply}[/tex]
[tex]11(x-4)=3(x+4)[/tex]
[tex]11x-44=3x+12[/tex]
[tex]11x-3x=12+44[/tex]
[tex]8x=56[/tex]
[tex]\bold{x=7}[/tex] miles per hour
PLEASE ANSWER ASAP
IT WOULD BE HELPFUL
The answer of the given question based on the cylinder is , the volume of the solid = 929.44 inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.
What is Volume?
Volume is amount of three-dimensional space occupied by object or substance. It is physical quantity that is measured in cubic units, like cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of object can be calculated by measuring its dimensions and using mathematical formula specific to its shape.
To find volume of solid, we need to subtract volume of inner cylinder from volume of outer cylinder.
Volume of the outer cylinder = πr²h
where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)
h = height of the outer cylinder = 23 inches
Volume of the outer cylinder = π(4)²(23) = 368π in³
Volume of the inner cylinder = πr²h
where r = radius of the inner cylinder = 2 inches
h = height of the inner cylinder = 18 inches
Volume of the inner cylinder = π(2)²(18) = 72π in³
So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder
= 368π - 72π
= 296π
= 929.44 inch³
The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.
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Use your shapes to create a new shape with an area of 4 square units. Trace your shape.
We can construct a shape of area 4 square meters using the four shapes square, rectangle, triangle and parallelogram.
What are your knowledge of area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The amount of units in a figure determines its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
Area of a square = side² (a²)
Area of a triangle = 1/2 × base length × height (1/2×b×h)
Area of a rectangle = length × breadth ( l×b )
Area of a parallelogram = base length × height ( b×h)
Consider the square of side 1 m
Area = 1 × 1 = 1 m²
Now consider the triangle of base length , b = 1/2 m and height, h = 2 m
∴ Area = 1/2×1/2×2 = 1/2 m²
Once more , area of the parallelogram of side 1 m and height 2 m is given by
Area = 1×2= 2 m²
For the rectangle of length 1/2 m and breadth 1 m
Area = l × b = 1/2 × 1 = 1/2 m²
∴ Total area = 1 + 1/2 + 2 + 1/2 = 4 square meter.
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Martiza's car has 16 gallons of gas in the tank. She uses 3/4 of the gas. How many gallons of gas does Martiza use?
Answer:
12
Step-by-step explanation:
4 x 4= 16 so 4 x 3=12 and 3/4 = 4 x 3