Answer:
14.1
Step-by-step explanation:
To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.
d=l2+w2+h2−−−−−−−−−−√
Substitute 8 for l, 19 for w, and 25 for d
Then solve for h
25=82+192+h2−−−−√
Simplify.
25=64+361+h2−−−−√
Square both sides.
625=425+h2
Subtract 425 from both sides.
200=h2
Take the positive square root of both sides.
200−−−√=h
Round to the nearest tenth.
14.1≈h
Therefore, the height of the rectangular prism is about 14.1ft
a tree casts a 25 foot shadow. At the same time, a 6 foot stick csts a 4.5 foot shadow. how tall is the tree
Amber is solving the inequality |x+6| - 12 < 13 by graphing. Which equations should Amber graph? a. y1 = |x+6|, y2 = 25 b. y1 = x+6, y2 = 25 c. y1 = |x+6|, y2 = 13 d. y1 = x+6, y2 = 13
Option(a) is the correct answer.
The inequality is:
|X+6|- 12 < 13
Here we can add 12 to both sides:
|X+6| <13 + 12
⇒|X+6| <25
⇒|X+6| < 25
We can separate it into two equations:
if x > -6, then |X+6| = x + 6
⇒ (x + 6) < 25
⇒x < 25 - 6
⇒ x < 19
if x < -6, then |X+6| = -(x + 6)
⇒-(x + 6) < 25
⇒ -x < 31
⇒ x > -31 (changing the sign)
And with those two equations, we get the:
-31 < x < 19
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c=1/30x^2-2x+1530 what is the minimum cost
The minimum cost is $1500.
What is Vertex form?
The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants of the parabola is at (h, k).
Given:
y =1/30 x²-2x+1530
y= 1/30 x² - 2x + 1530
comparing the above equation with y ax²+ bx +c we get
a = 1/30
b = -2
c = 1530
Now, the the x coordinate of the vertex
h = -b/(2a)
h = -(-2)/(2x(1/30))
h = 2/(2/30)
h = (2/1) x (30/2)
h = (2 x 30)/(1 x 2)
h = 60/2
h = 30
So, The x coordinate of the vertex is 30.
Now, we plug in x = 30 to find the y coordinate of the vertex.
y =1/30 x²-2x+1530
y =1/30 (30)²-2(30)+1530
y =1/30 (900)-60+1530
y= 1500
Thus, the minimum cost is $1500
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80 figs are kept in a container. Each fig weighs 0.02 kg. What is the
total weight of the figs?
the Total weight of the container that kept figs is 1.6 kg.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, 80 figs are kept in a container. Each fig weighs 0.02 kg.
Since,
One fig is weighing = 0.02 kg
So,
80 figs will weigh = 0.02 * 80
80 figs will weigh = 1.6 kg
Therefore, the Total weight of the container that kept figs is 1.6 kg.
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a box of candy hearts contains 52 hearts, of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange, and 6 are green. if you select nine pieces20 chapter 1 probability of candy randomly from the box, without replacement, give the probability that (a) three of the hearts are white. (b) three are white, two are tan, one is pink, one is yellow, and two are green.
(a) Probability(3 white) = (19/52) * (18/51) * (17/50) = 0.027
(b) P(3 white, 2 tan, 1 pink, 1 yellow, 2 green) = (19/52) * (18/51) * (17/50) * (10/49) * (9/48) * (7/47) * (5/46) * (6/45) * (6/44) = 0.00004
(a) The probability of selecting three white hearts is calculated by multiplying the probability of selecting each heart. The probability of selecting one white heart is 19/52. The probability of selecting two white hearts is 18/51, and the probability of selecting three white hearts is 17/50. When multiplied together, the overall probability is 0.027.
(b) The probability of selecting three white hearts, two tan hearts, one pink heart, one yellow heart, and two green hearts is calculated by multiplying the individual probabilities for each heart. The probability of selecting one white heart is 19/52, the probability of selecting two tan hearts is 10/49, the probability of selecting one pink heart is 7/47, the probability of selecting one yellow heart is 5/46, and the probability of selecting two green hearts is 6/45. When multiplied together, the overall probability is 0.00004.
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Nate's weekly pay, in dollars, when he works x hours is represented by this expression.
16. 50 x
24.75 (a
How much is Nate paid for each hour he works over 40?
0≤x≤ 40
40) + 660 x > 40
Nate is paid 16.50 dollars for each hour he works over 40.
How to calculate?We have that Nate's weekly pay is represented by the expression 16.50x + 24.75(a),
where x is the number of hours worked and a is a value such that 0 <= x <= 40.
We know that a mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
If x > 40, the pay for each additional hour worked is given by the rate of change of the expression, which has it at 16.50 dollars per hour.
We therefor ca conclude that Nate is paid 16.50 dollars for each hour he works over 40.
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find the volume of the solid formed by rotating the function about the x-axis. round to four decimal places.
The volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to the integral of the area of the cross-section of the solid from x=0 to x=1. The area of the cross-section is equal to the area of a circle with radius x, which is equal to πx. Thus, the volume of the solid is equal to the integral of πx from x=0 to x=1.
This integral can be solved using the formula for the area of a circle, which is equal to πr. Thus, the volume of the solid is equal to π∫x dx from x=0 to x=1. After solving the integral, the volume of the solid is equal to π/3. Thus, the volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to 0.3333.
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What kind of angle is this
The triangles are similar by SSS.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
The sides of first triangle are, 6, 9.6, 12.3
And, The sides of second triangle are, 2, 3.2, 4.1
Now, The ratio of corresponding sides of triangle are,
⇒ 6 / 2 = 3
⇒ 9.6 / 3.2 = 3
⇒ 12.3 / 4.1 = 3
Thus, The triangles are similar by SSS.
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y+1=2(x-1) in standard form
Answer: 2x-y=3
Step-by-step explanation: Search math w ay on the internet
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,440 ft Determine the flag's width and length if the length is 340 ft greater than the width
The flag's width is ft. Its length is ft.
Answer:
width of the flag is 440 feet and the length is 780 feet
Step-by-step explanation:
Let's call the width of the flag "w". Then the length of the flag can be represented as "w + 340".
The perimeter of the flag is the sum of all four sides, so we can write the following equation:
2w + 2(w + 340) = 2,440
Expanding the second term on the left side and simplifying:
2w + 2w + 680 = 2,440
4w + 680 = 2,440
Subtracting 680 from both sides:
4w = 1,760
Dividing both sides by 4:
w = 440
So the width of the flag is 440 feet and the length is 780 feet (440 + 340).
You have 2 different savings accounts. For Account A, the simple interest earned after 6 months is $3.30. For Account B, the simple interest earned after 30 months is $37.50. If the interest rate is 3.3% for Account A and 2.5% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer
Principal amount in each account is $200 for Account A and $600 for Account B. Simple interest is most earned for Account B.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Simple interest is calculated by the formula,
SI = P × r × t,
where P is the principal amount, r is the interest rate and t is the time in years.
Account A :
t = 6 months = 0.5 year
S.I = $3.30
r = 3.3% = 0.033
Substituting in the formula,
3.30 = P × 0.033 × 0.5
P = 200
Principal amount in Account A is $200.
Simple interest earned in the first month = 200 × 0.033 × (1/12) = $0.55
Account B :
t = 30 months = 2.5 years
S.I = $37.50
r = 2.5% = 0.025
Substituting in the formula,
37.50 = P × 0.025 × 2.5
P = 600
Principal amount in Account B is $600.
Simple interest earned in the first month = 600 × 0.025 × (1/12) = $1.25
Account B earned more interest in the first month.
Hence Account B earned most interest in the first month with am amount of $1.25.
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The width of a rectangle is 8 units less than the length. The area of the rectangle is 9 square units. What is the length, in units, of the rectangle?
The length, in units, of the rectangle is 9 units.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Length = x
Width = x - 8
Area = 9 square units
Now,
The area of the rectangle = length x width
9 = x (x - 8)
9 = x² - 8x
x² - 8x - 9 = 0
Solve for x.
x² - 8x - 9 = 0
x² - (9 - 1)x - 9 = 0
x² - 9x + x - 9 = 0
x(x - 9) + 1(x - 9) = 0
(x - 9) (x + 1) = 0
x - 9 =0 and x + 1 = 0
x = 9 and x = -1 (rejected)
Now,
Length = 9
Width = 9 - 8 = 1
Thus,
Length is 9.
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Can you help please
Answer: No, it is not proportional.
Step-by-step explanation: X will be the mystery number here. So first, we want to find a common denominator. 5 times x equals 20. We want to divide 20 by 5. 20/5 equals 4. X = 4. So now we want to multiply the 4 from 4/5 by 4. 4 times 4 equals 16.
4/5 = 16/20
Evaluate
a*b= a+b -2ab
(2*3)*5
The solution to the algebraic expression (2*3)*5 using a*b= a+b -2ab is; 68
How to solve Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without truly specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c etc. These letters are usually referred to as variables.
We are given the format for the algebraic expression as;
a*b = a + b - 2ab
Thus, we can solve the expression (2*3)*5 as;
(2*3) = 2 + 3 - 2(2*3)
= -7
(-7 * 5) = -7 + 5 - 2(-7 * 5)
= -2 + 70
= 68
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Suppose if f(x) = 2x+ 1, x more than or equal to 0 ; -2x+ 1, x less than 0
Then f(0)=
f(1) =
f(-1)=
The value of the functions are;
f(0) = 1
f(1) = 3
f(-1) = 4
What is a function?A function can be described as a rule, law or expression explaining the relationship between two variables.
These variables are called;
The dependent variableThe independent variablesFrom the information given, we have that;
F(x) = 2x + 1 when x is greater than or equal to zero
Also,
f(x) = -2x - 1 when x is less than zero
Then for f(0)
f(0) = 2(0) + 1
expand the bracket
f(0) = 1
For f(1) = 2(1) + 1
expand the bracket
f(1) = 3
f(-1) = -2(-1) + 1
expand the bracket
f(-1) = 4
Hence, the values are 1, 3 and 4
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Write a formula for the function g(x) obtained when the graph of f(x) = 1/x
is shifted down 7 units and to the right 5 units.
A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.
In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent a function.By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:
g(x) = f(x - 5) - 7
g(x) = 1/(x - 5) - 7
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8 piglets are evenly sharing 5 liters of milk.
How much milk should each piglet get?
Each piglet will receive 0.625 L of milk.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
We have 8 piglets that only have 5 liters of milk to share in between them. We need to split the milk between the 8 piglets.
We can divide the amount of milk we have already by the amount of piglets total:
5 liters of milk ÷ 8 piglets
Evaluating this, we should get 0.625 L of milk per piglet, assuming we don't lose a single drop while splitting the milk.
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Please help me!!!! I would appreciate it!!! Ty!!! Find the volume and add explanations..
Answer:
523.3
Step-by-step explanation:
memorize this formula:
V = 4/3 π r³, where V = volume and r = radius.
so v=4/3π *5³ =125*4/3π =523.3
to make sure you understand the derivation based on the five assumptions (a-e), select the correct order in which the assumptions were used in the derivation above.
The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.
The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.
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for a numerical variable, instead of categories, we construct a series of intervals (sometimes called classes). we must make certain decisions about the number of intervals, as well as the width of each interval. which of the following is a guideline for developing the intervals?
The guidelines for developing the intervals are
Interval limits are easy to recognize and interpret.The total number of intervals in a frequency distribution normally ranges from 5 to 20. Intervals are exhaustive.An interval in math is calculated in terms of numbers. An interval comprises all the numbers that come between two particular numbers. This range includes all the real numbers between two numbers.
A closed interval is an interval that includes all its limit points and is denoted with square brackets. For example, [0, 1] means that greater than or equal to 0 and less than or equal to 1.
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0.23 as a whole,percent, fraction, and decimal
0.23 as:
a whole number: 0a percent: 23%a fraction: 23/100 or 0.23/1a decimal: 0.23How The answer was obtained0.23 as a whole number: 00.23 as a percent:23% (0.23 * 100 = 23)
0.23 as a fraction: 23/100 (0.23 can be expressed as 23 hundredths)0.23 as a decimal: 0.23A decimal is a number that expresses fractional values with a base of 10. It uses the place value system where the position of a digit determines its value relative to other digits. Decimals are written using a decimal point to separate the whole number part from the fractional part. For example, 3.14 is a decimal representation of the fractional value pi.
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An airline ticket costs $260 without the tax if the tax raise 8% what's the total bill for the ticket
using a scale of 1 inch = 2 feet and wing of airplane is 24 feet how long is the wing
The length of the wing is, 12 inches.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The scale is,
⇒ 1 inch = 2 feet
And, Wing of airplane is 24 feet.
Now, We have;
The scale is,
⇒ 1 inch = 2 feet
Hence, The length of wing is,
⇒ 24 / 2 inches
⇒ 12 inches
Thus, The length of the wing is, 12 inches.
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(50 POINTS AND BRAINLYEST GURANTEE)
Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing
formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total
area answer)
Answer:
53.137 (sq.units).
Step-by-step explanation:
1. to draw red line in order to divide the given shape by two figures;
2. the required area consists of two: green - area of semicircle with radius r= 3 and blue - area of trapezoid with bases 8 and 5 and height 6. Then
3. the required area is
A=A(semicircle)+A(trapezoid);
A≈0.5*3.1415*3²+0.5*(8+5)*6=0.5*(28,274+78)=53.137
Answer:
53.137 sq.units also its a explanation for this answer
Step-by-step explanation:
the sq.untits would be a 53.137 hope this helps!
Camille is making cupcakes for her mom's birthday! She wants to find the total amount of sugar in the recipe so she can calculate the amount of sugar in each cupcake. The recipe calls for 2 1/4 cups of brown sugar and ¾ cup of white sugar. What is the total amount of sugar in this recipe?
Answer: 3
Step-by-step explanation:
2 1/4 cups of brown sugar + ¾ cup of white sugar.=the total amount of sugar in this recipe
2 1/4 + 3/4 =3
or
2 1/4=2.25 and 3/4=.75
2.25+.75=3
2. a) b) 5 3 c) d) a What is 258 plus 329? What is 258 plus-319? What is 1 023 minus 648? What is 648 minus 1 023? 3
Answer:
A=587
B=-61
C=375
D=-375
Step-by-step explanation:
Indefinite integral of cos(x) sin(x) dx
The solution of the indefinite integral ∫ sin x cos x dx is (1 / 2) · sin² x + C.
How to determine the indefinite integral by algebraic substitution
There are integrals that can be solved by means of algebraic substitutions, which simplifies the expression and allow a quicker solution. Now we proceed to find the solution. First, define algebraic subtitution:
u = sin x
du = cos x dx
Second, simplify the integral by formulae defined in the previous step:
∫ sin x cos x dx
∫ u du
Third, integrate the resulting expression:
(1 / 2) · u² + C, where C is the integration constant.
Fourth, reverse the algebraic substitution:
(1 / 2) · sin² x + C
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1. which of the following initializes an 8 x 10 matrix with integer values that are perfect squares? (0 is a perfect square.) int[][] mat
B. II only. This initializes an 8 X 10 matrix with integer values that are perfect squares by looping through the rows and columns of the matrix and setting each element equal to the row number multiplied by itself.
II initializes an 8 X 10 matrix with integer values that are perfect squares. The initialization starts by declaring the matrix with the line int [][] mat = new int [8][10]; which creates the 8 X 10 matrix. The next step is to use a nested for loop to loop through the rows and columns of the matrix. The first loop, for(int r=0; r<mat.length; r++), begins by setting an integer variable r to 0 and looping through all of the rows in the matrix. The second loop, for(int c=0; c<mat[r].length; c++), begins by setting an integer variable c to 0 and looping through all of the columns in the matrix. Finally, the last line, mat[r][c] = r*r;, sets each element of the matrix equal to the row number multiplied by itself. This ensures that the values in the matrix are all perfect squares.
The complete question : Which of the following initializes an 8 X 10 matrix with integer values that are perfect squares? (0 is a perfect square.)
I. int [][] mat = new int [8][10];
II. int [][] mat = new int [8][10];
for (int r=0; r<mat.length; r++){
for(int c=0; c<mat[r].length; c++){
mat[r][c] = r*r; }}
III. int [][] mat = new int [8][10];
for (int c=0; c<mat[r].length; c++){
for(int r=0; r<mat.length; r++){
mat[r][c] = c*c; }}
A. I only
B. II only
C. III only
D. I and II
E. I, II, and III
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Determine the matrix equation for:
x1 + 2x₂ = 11
3x1 + 4x2 = 25
A. [ 1 2 3 4 ] = [11 25] [x1 x2]
B. [ 1 2 3 4 ] [x1 x2] = [11 25]
The matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.
What is matrix?A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that is used to represent a mathematical object or a characteristic of one.
Matrix representations of linear mappings without additional details enable explicit computations in linear algebra. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.
The given equation is:
x1 + 2x₂ = 11
3x1 + 4x2 = 25
The equation is represented in matrix form as follows:
[tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex]
Hence, the matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.
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Find the length of the three missing sides in the rhombus below.
x=
y=
z=
The length of the three missing sides in the rhombus are x=75,y=75,z=75
What is rhombus and some of its properties?Rhombus is a parallelogram whose all sides are of equal lengths.
Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).
Its vertex angles are bisected by its diagonals.
The triangles on either side of the diagonals are isosceles and congruent.
Given;
One side of rhombus= 75
Now, as we know that all sides of rhombus are equal
x=y=z=75
Therefore, the sides of rhombus will be x=75,y=75,z=75.
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