x = -3
[tex]6( {2x}^{2} - 5) \\ \\ 6(2 \times { (- 3)}^{2} - 5) \\ \\ 6(2 \times ( 9) - 5) \\ \\ 6( 18 - 5) \\ \\ 6 \times ( 13) \\ \\ 78.[/tex]
A new building is formed by a square prism with a square pyramid on top. The base has an edge length of 60 feet, and the height of the prism is 150 feet. The height of the pyramid is one-sixth the height of the prism. What is the surface area of the exterior of the building rounded to the nearest hundred square feet?
The surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².
What is surface area ?Surface area is the amount of space covering the outside of a three-dimensional shape.
Given, base of prism = 60 feet, height of the prism h₁= 150 feet, and height of the pyramid h₂ = 1/6 (150)
= 25 feet.
The surface area of the exterior of the building = lateral surface area of prism + pyramid.
SA = ( 4ah₁ ) +(a√(a² + 4h₂²) )
SA = ( 4(60)150 ) + ( 60(√60² + 4(25)² )
= ( 240* 150 ) + 60(√3600 +2500 )
= 36000 + 60(√6100)
= 36000 + 60(78.1024)
= 36000 + 4686.15
= 40686.15
≈ 40700 feet².
Therefore, the surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².
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Answer:
The surface area of the exterior of the building is approximately 40700 feet
HELP PLSSS I NEED THIS ASAP
Four students are simplifying the expression 5x(-3-7x).
Which student's work is correct?
O5x(-3-7x)
(5x)(-3) - 7x
-15x-7x
O 5x(-3-7x)
(5x)(-3) - (5x)(7x)
-15-35x
O5x(-3-7x)
-3 + 5x-7x
-3-2x
O5x(-3-7x)
(5x)(-3)+(5x)(-7x)
-15x-35x²
Multiplying the linear expressions, the correct sequence is given as follows:
5x(-3 -7x)(5x)(-3) + (5x)(-7x)-15x - 35x²How are linear expressions multiplied?They are multiplied applying the distributive property, in which all the terms are multiplied and the like terms are combined.
Hence:
5x(-3 -7x)
(5x)(-3) + (5x)(-7x)
-15x - 35x²
Hence the last option is correct.
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Round to the nearest ten thousandths 15.76548908 *
how to find the side length of x
Which of the following statements best describes the relationship between the point (3, 0) and the system
of inequalities below?
3x +2y ≤4
(-x+ 5y > 6
A. The point does not satisfy either the top or the bottom inequalities. Therefore, it is not a
solution to the system.
B. The point satisfies the top inequality but not the bottom. Therefore, it is not a solution to the
system.
C. The point satisfies the bottom inequality but not the top. Therefore, it is not a solution to the
system.
D. The point satisfies both the top and the bottom inequalities. Therefore, it is a solution to the
system
Answer:
d because the point satisfied both
Answer:
D
Step-by-step explanation:
Suppose f(x)=x²+4 and g(x)=2x+1.
Find the value of f(-2)g(-2).
Answer: -24
Step-by-step explanation:
I am assuming you want the value of (f × g)(-2)
[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]
[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]
8 × -3 = -24
In 2005 , a study at Blinn College was conducted to determine whether a relationship exists between a student who eats breakfast and his or her Biology grade. The study examined 1259 college students on a specific biology test. The accompanying tables show the relative frequency, by grade, of the 825 students who did eat breakfast and the 434 who did not eat breakfast on the morning of the test.
Students who did not eat breakfast
Grade Relative frequency
A 0.10
B 0.19
C 0.22
D 0.17
F 0.32
Students who ate breakfast
Grade Relative frequency
A 0.18
B 0.38
C 0.17
D 0.14
F 0.14
Select the statements that are accurate regarding the given data sets.
Eating breakfast ensures that a student will pass an exam.
The data show that skipping breakfast is associated with earning lower exam grades.
There is an increase in B's for those who do eat breakfast before the exam.
The data shows that skipping breakfast is not associated with earning lower grades.
Students are more likely to earn an A on an exam if they do not eat breakfast.
Answer:
1. The data show that skipping breakfast is associated with earning lower exam grades.
2. There is an increase in B's for those who do eat breakfast before the exam.
Which of the following are square roots of the number below? Check all that
apply.
4
A. 41/2
B. 8
C. -41/2
D. 2
E. -2
F. 16
Answer:
D. 2
E. -2
Step-by-step explanation:
Write an equation for the transformed logarithm shown below, that passes through (-2,0) and (0,-3)
Using translation concepts, the equation for the transformed logarithm is given by:
[tex]f(x) = \log{(x + 3)} - 3.48[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The logarithm function is given by:
[tex]f(x) = \log{x}[/tex].
We have that:
It passes through (1,0), and in this problem it passes through (-2,0), that is, it was shifted left 3 units, hence x -> x + 3.Hence:
[tex]f(x) = \log{x + 3} + b[/tex]
To find the shift up/down, we consider that f(0) = -3, hence:
[tex]-3 = \log{0 + 3} + b[/tex]
[tex]b = -3 - \log{3}[/tex]
b = -3.48.
Hence the function is given by:
[tex]f(x) = \log{x + 3} - 3.48[/tex]
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Rewrite the following expression
X 9/7
Answer:
X1 2/7
Step-by-step explanation:
Step-by-step explanation:
We can write it in radical form, and the denominator of the exponent became the power of the radical. That is
And
We can also write it as
And that's the simplified form of the given exponential form .
there are 20nstudents in a math class who have brown hair this represent 80 percent of the students in the class with equation can be used to find the total os student in the math
Answer:
Equation is 20 = 0.8 time x
x=25
Step-by-step explanation:
80% = 0.8
So to find x we 20/8
and we get 25 as the final answer
Suppose the derivative of a function is ′()=(−7)^7(−2)^2(+13)^10. Then the function is increasing on the interval _____.
Suppose that A ∩ C = B ∩ C. Is it true that A=B? Justify your answer.
Answer:
No
Step-by-step explanation:
If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.
Write 9.7 to one significant figure
9.7 to one significant figure is 10
How to approximate the number?We have:
9.7
To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.
When 9.7 is approximated, we have:
10
Hence, 9.7 to one significant figure is 10
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An administrator is asked to file papers in a box which has the following dimensions height 15cm width 30cm and depth 20cm. Calculate the volume of the box.
The volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width 30cm and depth of 20cm
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have:
An administrator is asked to file papers in a box that has the following dimensions height of 15 cm width of 30 cm and depth of 20 cm.
Let L be the length
W be the width
H be the height of the box:
Given:
L = 20 cm
W = 30 cm
H = 15 cm
The volume of the box
= 15×30×20
9000 square cm
Thus, the volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width of 30cm, and depth of 20cm
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Pandas: There is a well-studied panda population in Wuyipeng. In 1981 there were 25 pandas and the researchers determined that they had an annual population grows by 6.6% each year. Which of the following models correctly represents this data?
The equation that models the data on pandas is FV = 25(1.066)^t.
What models the data?The formula for calculating future value of the pandas is:
FV = P (1 + r) ^n
FV = Future value P = Present value R = annual population growthN = number of yearsFV = 25(1.066)^t
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little melinda has nickels and quarters in her bank she has 8 fewer than nickels she has 5.60 in the bank how many coins of each type does she have
Answer:
She has 20 coins in her bank, where she has 12 nickels and 8 quarters
Step-by-step explanation:
A quarter is 25 centsA nickel is 5 centsSince she has 8 fewer than nickels, we add 8 to the number of nickelsQ = N + 8, 25Q + 5N = 560
25(N + 8) + 5N = 560
25N + 200 + 5N = 560
25N + 200 - 200 + 5N = 560 - 200
30N = 360
30N / 30 = 360 / 30
N = 12 nickels
Finding amount of Quarters:
Q = N + 8 → Q = 12 + 8
Q = 20 quarters
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Let’s say you bought a car for $16,500. The car is expected to last 8 years and then it can be sold for scrap for $500. The value at the end of the life of the car is sometimes called the “salvage value” or “residual value.” Part A: If we assume that the relationship between the value of the car and the year is linear, how much will the value of the car depreciate each year? Explain your strategy. Part B: Complete the table of values. Years of Ownership Value of the Car 0 1 2 Part C: Create a sketch of the data points on your paper. Be sure to label the graph thoroughly. Would it make sense to connect the points? 3) Consider all of the information you have collected in Question 2. Part A: Write an equation for the value of the car in terms of the year. Part B: What is the slope of the line? Explain what the slope means in this context. 4) Are the value of the car and the number of years since the car was purchased proportional? Justify your response. 5) Look at the changes in the value of the car and the corresponding changes in the years of ownership. Are the changes proportional? How do you know? 6) Examine the proportionality of these two equations: � = 2� + 3 � = 2� Which is an example of a linear equation that is also proportional? Justify your
Answer:
value of car depreciate each year = $2000
y + 2000x = 16,500
slope of line = -2000
No, not proportional
Step-by-step explanation:
Value of depreciation of an object is given by :-
Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]
according to question ;
total cost = $16500
scrap value = $500
estimated life = 8 years
therefore,
depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000
now,
let the value of car after 'x' years be 'y'
therefore linear equation showing the relation of x and y is
y + 2000x = 16500
The graph of a linear equation is a line.
If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.
If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.
here equation is of type,
y = mx +c, thus it is not linear.
also in the equation y = mx +c,
'm' is the slope of line
therefore by comparing the equation,
y +2000x = 16500
y = -2000x + 16500
slope is - 2000
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can you please help me
The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.
The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.
All parabolas can be obtained from the basic parabola by a combination of:
translationreflectionstretchingrotation.Thus, all parabolas are similar.
Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
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Which of the following terms describes the measure indicated by the black
arrow below?
4
A. Median
B. Range
C. Mean
D. Minimum
Answer:
the answer is A
Step-by-step explanation:
The line is the middle point of the graph/ the middle number of all therefore it's the median.
Help please asap I’m desperate!
Answer:
f(x)=x-2x+3; f(x)=-bx
x-2x=3=-bx
x+4x+3=0
(x+3) (x+1) = 0
x=-3 or x=-1
when x+-3. f(x)=b x(-3)=18
x=-1. f(x) = - b x (-1) = b
so system of equations : ( -3, -18)
; (-),b
Step-by-step explanation:
hope it helps
Given that a is rational and √2 is irrational and a is not equal to 2, show that. √2-1 is irrational
Answer:
Let us assume that √2 is a rational number.
So it can be expressed in the form p/q where p, q are co-prime integers and q≠0
√2 = p/q
Here p and q are coprime numbers and q ≠ 0
Step-by-step explanation:
√2 = p/q
On squaring both the sides we get,
=>2 = (p/q)2
=> 2q2 = p2……………………………..(1)
p2/2 = q2
So 2 divides p and p is a multiple of 2.
⇒ p = 2m
⇒ p² = 4m² ………………………………..(2)
From equations (1) and (2), we get,
2q² = 4m²
⇒ q² = 2m²
⇒ q² is a multiple of 2
⇒ q is a multiple of 2
Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√2 is an irrational number.
Find the linear regression equation for the transformed data. x=1,2,3,4,5 y=13,19,37,91,253 log y=1.114,1.279,1.568,1.959,2,403
A. log(y)=-0.687x+0.326
B. log(y)=0.687x+0.326
C. log(y)=-0.326x+0.687
D. log(y)=0.326x+0.687
Answer:
The answer is OPTION (D)log(y)=0.326x+0.687
Linear regression:
It is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y)
The Linear regression equation for the transformed data:
We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.
(1, 13) 1.114
(2, 19) 1.279
(3, 37) 1.568
(4, 91) 1.959
(5, 253) 2.403
X Y Log(y)
1 13 1.114
2 19 1.740
3 37 2.543
4 91 3.381
5 253 4.226
Sum of X = 15
Sum of Y = 8.323
Mean X = 3
Mean Y = 1.6646
Sum of squares (SSX) = 10
Sum of products (SP) = 3.258
Regression Equation = ŷ = bX + a
b = SP/SSX = 3.26/10 = 0.3258
a = MY - bMX = 1.66 - (0.33*3) = 0.6872
ŷ = 0.3258X + 0.6872
The graph is plotted below:
The linear regression equation is log(y)=0.326x+0.687
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what is 2 plus two.
please answer quickly
Answer:
2 + 2: 4
or 2 + 2: 5 from the dystopian novel 1984.
Identify each of the following as rational or irrational
√23
104.42
√64
49.396
10.97846727460
Answer:
1-irrational 2-rational 3-rational 4-rational 5-irrational
Step-by-step explanation:
Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.
Answer: The data cannot be modeled by an exponential function because the data is for a linear function (as there is a constant increase in f(x) each time x increases by 1)
Which expression simplifies to 2 divided 15 ?
Answer: 4/30
Step-by-step explanation:
it does
Patrisse and Makayla began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Patrisse took a test in English and earned a 81.4, and Makayla took a test in Art History and earned a 60.6. Use the fact that all the students' test grades in the English class had a mean of 72.8 and a standard deviation of 11.8, and all the students' test grades in Art History had a mean of 67 and a standard deviation of 8.6 to answer the following questions. a) Calculate the z-score for Patrisse's test grade. z = [Round your answer to two decimal places.] b) Calculate the z-score for Makayla's test grade. z = [Round your answer to two decimal places.] c) Which person did relatively better? Patrisse Makayla They did equally well.
a) Z-score for Patrisse test grade is 0.7288
b) z-score for Makayla test grade is -0.7441
c) Patrisse did better.
What is z- score?
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Z-score for Patrisse test grade.
X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 81.4 - 72.8/ 11.8
Z= 0.7288
Now, z-score for Makayla test grade.
X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 60.6 - 67/ 8.6
Z= -0.7441
Hence, Patrisse did better as she had better z- score.
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21 less than or equal to -3(x-4) less than 30
Answer:
-3(-4-4) would work giving you 24
Step-by-step explanation:
im sorry that qustion doesnt make sense, if you mean higher then 21, less than 30 than -3(-4-4) would work giving you 24
Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither.
f(x)=x³ - 2x
Answer: The function is odd and symmetric with respect to the origin.
Step-by-step explanation:
A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.
[tex]f(x)=x^{3}-2x\\\\f(-x)=(-x)^{3}-2(-x)=-x^{3}+2x=-f(x)[/tex]
Therefore, the function is odd, and thus the function is symmetric about the origin
