Answer: 99,999
Step-by-step explanation:
The volume of a cylinder closed at one end is 1056cm^2 with height 21cm, find the total surface area
Answer: ≈578 cm²
Step-by-step explanation:
[tex]V_{cyl}=1056\ cm^3\ \ \ \ H=21\ cm\\V_{cyl}=\pi R^2H\\1056=\pi *R^2*21\\1056=21\pi *R^2\\[/tex]
Divide both parts of the equation by 21π:
16=R²
4²=R²
4=R
[tex]S{tot\ sur}=\pi R^2+2\pi RH\\S{tot\ sur}=\pi R*(R+2H)\\S{tot\ sur}=\pi *4*(4+2*21)\\S{tot\ sur}=4\pi *(4+42)\\S{tot\ sur}=4\pi *46\\S{tot\ sur}=184\pi \\S{tot\ sur}\approx578\ cm^2[/tex]
Please help me!
1. Simplify 5 to the 5th over 5 to the 8th. (4 points)
1 over 5 to the 3rd power
53
1 over 25
1 over 5 to the negative 3rd
2. Simplify 5 to the negative 4th power over 5 to the 3rd. (4 points)
57
5−1
1 over 5
1 over 5 to the 7th power
3. Simplify 4 to the 7th over 5 squared all raised to the 3rd power. (4 points)
4 to the 10th over 5 to the 5th
4 to the 4th over 5
4 to the 21st over 5 to the 6th
12 to the 7th over 15 squared
4. In which expression should the exponents be multiplied? (4 points)
one fifth to the 2nd times one fifth to the 6th
9 to the 3rd over 9 to the 4th
73 ⋅ 78
(26)−5
5. Which expression is equivalent to (53)−2? (4 points)
1 over 5 to the 3rd
negative 1 over 5 times 5 times 5 times 5 times 5 times 5 times
53
1 over 5 times 5 times 5 times 5 times 5 times 5 times
Answer:
[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]
[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]
[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]
[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]
[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]
--------------------------------------------------------------
Question 2
[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]
--------------------------------------------------------------
Question 3
[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]
--------------------------------------------------------------
Question 4
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]
Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.
--------------------------------------------------------------
Question 5
[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have what property?
When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
What are equal intervals?Equal intervals denote that the variations between numbers (units) are the same anywhere on the scale (e.g., the difference between 4 and 5 is the same as the difference between 76 and 77). The difference between two successive categories is equal in an equal interval. Temperature measured in Fahrenheit, for example, has equal intervals; that is, the difference between 30 and 31 degrees is one degree, and the difference between 100 and 101 degrees is one degree.When the relationship between a scale's unit of measurement (strength) and a consequence (pounds lifted) can be described by the linear equation y = a bx, the scale is said to possess an equal intervals property.Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.
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Explain the difference between solving an equation with the variables all on one side compared to equations with variables on both sides.
An equation having variables on both sides can be solved by bringing all variables to one side.
An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,
5x = 6 + 2x;
3x = 6;
x = 2.
For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,
5y - 3 - 3y = 3y + 5 - 3y;
5y - 3y - 3y + 3y = 5 + 3;
2y = 8;
y = 4;
Thus, methods for solving both kinds of equations is similar.
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An equation having variables on both sides can be solved by bringing all variables to one side.
An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,
5x = 6 + 2x;
3x = 6;
x = 2.
For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,
5y - 3 - 3y = 3y + 5 - 3y;
5y - 3y - 3y + 3y = 5 + 3;
2y = 8;
y = 4;
Thus, methods for solving both kinds of equations is similar.
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Raíz cuadrada de 864
Raíz cuadrada de 864
Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:
The general equation of ellipse is given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , where, a is length of semi-major axis and b is length of semi-minor axis.
centro: (0,0)
focus : (0, -√28) , (0, √28)
eje conjugado = 2√3
por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:
de los focos podemos obtener que: √28
y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:
b = √3
podemos utilizar la siguiente fórmula para obtener a:
si despejamos a en la ecuación obtenemos lo siguiente:
ahora podemos sustituir los valores:
a=5
así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:
si graficamos la hipérbola, queda como en el documento adjunto.
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During the school year, each student planted
1.2 x 10^2 flowers as part of a community
service project. If there are 1.5 x 10³
students in the school, how many flowers did
they plant in total?
Answer:
18000
Step-by-step explanation:
We can multiply the number of students by the number of flowers per student.
[tex](1.2 \times 10^2)(1.5 \times 10^3) \\ \\ =(1.2)(1.5)(10^5) \\ \\ =1.8 \times 10^5 \\ \\ =18000[/tex]
Graph the equation y= -2x+250
Answer:
Graph in the picture
Suppose that f(1) = 1, f(4) = 5, f '(1) = 3, f '(4) = 3, and f '' is continuous. find the value of 4 1 xf ''(x) dx.
Answer: b
Step-by-step explanation:
I think
Which of the following options are examples of how you can name the angle?
Answer:
∠T and ∠STP
Step-by-step explanation:
You can name an angle by their middle vertex letter which, in this case, is T.
And you can name an angle using the three letters provided. P, T, and S are the three letters provided. However, the vertex letter always has to be in the middle. So, it could be ∠STP or even ∠PTS.
Let me know if you don't understand or need more explanation.
Ed’s class went on a class picnic. Ed’s teacher packed 20 sports drinks in a cooler for Ed and his classmates. Eight of the sports drinks were orange-flavored. What is the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler? Choose from the numbers listed below to create the correct ratio.
The ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.
What is Ratio?
In mathematics, Ratio is a term that is used to compare two or more numbers.
Given that their are 20 sports drinks in a cooler out of which 8 are orange flavored. Therefore, we can write that -
Number of orange flavored bottles = n[O] = 8
Total number of bottles = n[T] = 20
We can calculate the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler as follows -
Total number of non - orange flavored bottles will be -
n[C] = n[T] - n[O]
Now, the ration of non - orange bottles to the total number of bottle's can be written as -
n[C] / n[T]
(n[T] - n[O]) / n[T]
(20 - 8) / 20
12 / 20
3 / 5
Assume that the ratio is denoted by R. Therefore -
R = 3 : 5
Hence, the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.
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here were 34 bales of hay in the barn. Dan stacked more bales in the bar
today. There are now 64 bales of hay in the barn. How many bales did he store in the barn?
Solve for x.
(2x-2)°
-(x+5)°
Answer: 29°
Step-by-step explanation:
(2x-2)° + (x+5)° + 90° = 180°
(2x-2)° + (x+5)° = 90°
(2x + x)° = 87°
(3x)° = 87°
x° = 29°
I need help on this.
For the functions in this problem, we have that:
a) The function is exponential, and the table is completed as follows.
x = 0: y = 1.x = 1: y = 5.x = 2: y = 25.x = 3: y = 125.x = 4: y = 625.x = 5: y = 3125.b) The function is linear, and the table is completed as follows.
x = 0: y = 0.x = 1: y = 5.x = 2: y = 10.x = 3: y = 15.x = 4: y = 20.x = 5: y = 25.c) The function is exponential and given by:
[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.A function with initial value 1 and where the y-value is computed by multiplied the previous y-value by 5, as in item a, is an exponential function with parameters a = 1 and b = 5, hence the rule is:
[tex]y = 5^x[/tex]
Then:
x = 0: y = 1.x = 1: y = 5.x = 2: y = 25.x = 3: y = 125.x = 4: y = 625.x = 5: y = 3125.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
A proportional relationship is also classified as linear with a intercept of 0. For item b, since each y-value is the x-value multiplied by 5, the rule is:
y = 5x.
Hence the table is:
x = 0: y = 0.x = 1: y = 5.x = 2: y = 10.x = 3: y = 15.x = 4: y = 20.x = 5: y = 25.For item c, when x changes by 1, y is always multiplied by 1/2, and due to the multiplication, the function is exponential and given by:
[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]
The -16 is because when x = 0, y = -16.
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I need help with this asap, I don’t know how to solve it
I just think this way if it is wrong sry but at least I try
1. Determine whether each relation is a function.
((3, 2), (1,2), (4,3), (6, -2)}
domain = { 3,1,4,6} and range = { 2, 2 , 3 ,-2} are each relation is a function.
Describe domain.
The term "domain," which is specific to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of knowledge or a governing region.Describe Range?
Range is the difference between the largest and lowest values in a dataset in statistics and mathematics. One indicator of data dispersion is the range.
function = ((3, 2), (1,2), (4,3), (6, -2)}
domain = { 3,1,4,6}
range = { 2, 2 , 3 ,-2}
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What’s the answer pls I need help
Answer:
C= [tex]\frac{AD}{B}[/tex]
Step-by-step explanation:
the answer is c because I said it c and the way you get the answer is by dividing the equality of the fraction
- x≤-2 or x > 1 needs to be put on a number line pls help
Answer:
Step-by-step explanation:
Answer: closed circle on -2 with the arrow to the left
open circle on 1 with the arrow to the right
area of a parallelogram find the areas of the parallelograms whose vertices are given in exercises 35–40.
The area of parallelogram ABCD is found to be 2√3 square units.
What is parallelogram?A quadrilateral is known as a parallelogram in geometry. The opposite sides of a parallelogram are parallel & equal in length. Rhombus, rectangle, & square are a few examples of parallelograms.
We know that diagonal of such a parallelogram divides it into two equal triangles.
So, parallelogram area,
ABCD = 2× area of ΔABC (equation 1)
The area pf the triangle is found through the vertices are (x₁,y₁), (x₂,y₂), (x₃,y₃) is;
Area = (1/2)×[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
The vertices of the triangles are given as;
A(2,4), B(2+ √3 ,5) and C(2,6)
Area = (1/2)×[2(5−6) + (2+√3)(6−4) + 2(4−5)]
Area = (1/2)×[−2+2(2+ √3)−2]
Area = √3
When we plug this value into equation (1),
Parallelogram area,
ABCD = 2×the area of ABC
ABCD = 2×√3
ABCD = 2√3
Thus, the area of the parallelogram ABCD id estimated as 2√3 square units.
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The correct question is -
Find the area of a parallelogram ABCD if three of its vertices are A(2,4), B(2+ √3 ,5) and C(2,6)
Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for 1000 that paid 2% interest per year and purchased 3000 in corporate bonds paying 7% interest per year.
The total interest earned at the end of first year is $250 and the percentage of interest for his total investment is 6.25%.
Given, Chau invested his money by purchasing the following:
a certificate of deposit for $1000 at the rate of 2% per year, and
corporate bonds for $3000 at the rate of 7% per year.
we know that simple interest is calculated by multiplying the amount invested P by the interest rate r times the number of years invested t.
therefore, I = P × r × t
a. The first investment has a principal of P = $1,000, r = 2% = 0.02, t = 1 yr
I₁ = 2000 × 0.04 × 1
I₁ = 40
The second investment has a principal P = $3,000, interest rate r = 7% = 0.07 and time t = 1yr
I₂ = 3000 × 0.07 × 1
I₂ = 210
Therefore, total interest = I₁ ₊ I₂
= 40 ₊ 210
= $250
b. The overall rate of interest can be found by dividing:
Total interest/Total amount invested × 100
= 250/(1000 ₊ 3000) × 100
= 250/4000 × 100
= 25/4
= 6.25%
Hence we get the total interest earned at the end of first year as $250 and its overall rate of interest as 6.25%
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Your question was incomplete. Please find the missing content here.
Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for $1000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 7% interest per year.
(a) What was the total investment earned at the end of 1 year?
(b) What was the percentage interest for her total investment?
How many square feet are there in a rectangular-shaped building that is 34 feet wide and 72 feet long?
The area of the rectangular-shaped building is 2448 square feet.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-
Area of rectangle = Length x width
Area of rectangle = 34 x 72
Area of rectangle = 2448 square feet
Therefore, the area of the rectangular-shaped building is 2448 square feet.
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To calculate the average of 56,78,90,32,45
Answer:
60.2 is the average
Step-by-step explanation:
add all numbers together to get: 301
divide 301 by 5 because there are 5 numbers total to get: 60.2
Please help me answer all these 4 math questions! It is 8th-grade beginner level.
I will give Brainliest to the 1st one to answer ALL 4 questions and will give 100 points in this problem, giving people 50 points when they answer.
Answer:
Simplify the expression, Your answer would be :
1. [tex]\frac{9d}{e^{6} }[/tex]2. [tex]6d^{3}e[/tex]3.[tex]12de^{6}[/tex]Step-by-step explanation:
And to find the Value of the following expression, Your answer would be :
[tex]\frac{36}{11}[/tex]hopefully this helps you ! ~
What is 4x4....................................................
Answer:
16
Step-by-step explanation:
Miranda simplified the expression 5x+9y-4. She says the answer is 10xy.
What error did Miranda make while combining like terms?
What should her answer be?
Miranda made error by combining unlike terms, She added 5x and 9y then subtracted 4 from the answer. Answer is already in simplified form, it cannot be simplified further.
What are like and unlike terms?Like terms are ones whose exponent power and variables are the same. These variables' coefficients could differ. Terms that are comparable to one another are known as algebraic terms. As an illustration, consider the algebraic statement 8y + 2y, where y is the same variable as in the expression but has different coefficients.
Terms that have variables and exponents that differ from one another are said to be unlike terms. In contrast to terms, an expression is known to obtain when the coefficient, variables (in this case, two variables), and exponent powers (if any) are all distinct. Contrary to algebraic terms, the algebraic formula 3x + 9y is known as, where x and y are two separate variables with different coefficients.
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Need help on this question ASAP please
The equations ordered from the least to greatest is
y = (-3/4)x + 2
y - 3 = 1/2(x - 4)
3x - 4y = 7
y = 12(x - 19) + 5
Order of equationsFrom the question, we are to order the equations from least to greatest by the value of the slope
The given equations are
y = (-3/4)x + 2
3x - 4y = 7
y = 12(x - 19) + 5
y - 3 = 1/2(x - 4)
To determine the slopes of the line, we will compare the equations to the general form of the equation of a line
The general form of the equation of a line is
y = mx + b
Where m is the slope
and b is the y-intercept
y = (-3/4)x + 2By comparison,
m = -3/4
∴ Slope = -3/4
3x - 4y = 7First, rearrange
3x - 7 = 4y
4y = 3x - 7
y = (3/4)x - 7/4
By comparison,
m = 3/4
∴ Slope = 3/4
y = 12(x - 19) + 5First, simplify
y = 12x - 228 + 5
y = 12x - 223
By comparison,
m = 12
∴ Slope = 12
y - 3 = 1/2(x - 4)
First, simplify
y - 3= (1/2)x - 2
y = (1/2)x -2 + 3
y = (1/2)x + 1
By comparison,
m = 1/2
∴ Slope = 1/2
Now,
The slopes ordered from the least to greatest is
-3/4 < 1/2 < 3/4 < 12
Thus,
The equations ordered from the least to greatest is
y = (-3/4)x + 2
y - 3 = 1/2(x - 4)
3x - 4y = 7
y = 12(x - 19) + 5
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The last four weekly values of sales were 80, 100, 105, and 90 units. the last four forecasts were 60, 80, 95, and 75 units. these forecasts illustrate:_________
These forecasts illustrate bias.
What is bias?Bias is defined as a disproportionate weight in favor of or against an idea or thing, usually in a closed-minded, prejudicial, or unfair manner. Biases can be inherited or acquired. Biases for or against an individual, a group, or a belief can develop. A bias is a systematic error in science and engineering. Statistical bias occurs when a population is unfairly sampled or when an estimation process produces inaccurate results on average. As an example, the previous four weekly sales values were 80, 100, 105, and 90 units. The last four forecasts were for 60, 80, 95, and 75 units, respectively. These forecasts show bias.Therefore, these forecasts illustrate bias.
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What is the value of the expression?
40÷[20−4⋅(7−4)]
Please help im giving brainiest
Answer:5
Step-by-step explanation:
the length l cm of a sheet of paper is 29.7 cm,corredt to the nearest millimetre complete this statement about the value of l
297 mm is nearest millimetre complete this statement .
The definition of convert units?
The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.An expression of how many of one unit are equal to another is known as a conversion factor. There are 12 inches in a foot, 1609 meters in a mile, 100 centimeters in a meter, 60 seconds in a minute, and so on.1 cm = 10mm
the length of a sheet of paper = 29.7 cm
the nearest millimetre = 29.7 * 10 = 297 mm
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Question 7 of 25
Does this graph show
a function? Explain how you know.
O A. Yes; the graph passes the vertical line test.
• B. Yes; there are no y values that have more than one x-value.
O C. No; the graph fails the vertical line test.
O D. No; there are y values that have more than one x-value.
PLEASE HURRY
The answer is option C, No; the graph fails the vertical line test.
The graph given doesn't show a function.
The method that is used to determine whether a given graph is a function or not is called the vertical line test. In this test, a vertical line is drawn at an arbitrary point x. If this line touches the given graph at more than 2-points, then the given graph is not a function.
In the given graph, if we draw a vertical line for any x > -1, then this vertical line touches the graph at more than two points.
In other words, for any value x > -1, the corresponding value of y is not unique.
So, the answer is option C, No; the graph fails the vertical line test.
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The sides of a rectangle are x and 3 - 2x. Express the rectangle's area as a function of x. Express the rectangle's perimeter as a function of x. Explain why x cannot equal 2.
Answer: It is 3.5
Step-by-step explanation:
I think this because 2/2x=3/2=1.5 but you have 2 left to add which=3.5
