Answer:
There Are 40 Bicycles And 23 Tricycles
Step-by-step explanation:
Let, x be bicycles and y be tricycles
Condition 1;
: x + y= 63
: x =63-y
Condition 2;
Number Of Tires=149
:2x + 3y =149 [2x=Two Tires Of Bicycle And
3y=Three Tires Of Tricycle]
:x = 149-3y/2
Combination 1 & 2;
63-y = 149-3y/2
126-2y = 149-3y
y=23
x = 63-23
=40
For the functions f(x)=2x3 and g(x)=3x3−2, find (f∘g)(1) and (g∘f)(1).
Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
What is composite function?
Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x
Main body:
according to question;
f(x) = 2x³
g(x) = 3x³ -2
we need to find composite function:
f o g (x) = 2(3x³-2)
{to find composite function , we replace one function as value of x in another}
f o g(x) = 6x³ -4
= 6x³ -4
f o g(1) = 6*1 -
= 2
g o f(x) = 3(2x³)-2
g o f(x) = 6x³ -2
= 6x -2
g o f(1) = 6*1 -2
= 5
Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
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A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items, find the probability that no item is defective
The probability of the defective items is given as 0.015.
Given that,
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items,
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Number of the item = 200
1.5% of the item is defective, = 0.015 [200]
Probability of the defective item = 0.015[200] / 200 = 0.015
Thus, the probability of the defective items is given as 0.015.
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Need help with math question
A vertex with degree 2 in a graph has an edge that loops around itself. The graph is therefore a cycle graph.
What is Euler circuit?Every edge of a graph is used precisely once in an Euler circuit. An Euler path has two distinct vertices where it begins and finishes. A vertex serves as the beginning and conclusion of an Euler circuit.In an Eulerian path, we pass over two unvisited edges with one end point, v, each time we visit a vertex. As a result, the degree of each middle vertex in the Eulerian Path must be even. Since any vertex can be the central vertex in an Eulerian cycle, all vertices must have an even degree.All of a graph G's vertices must be even if it has an Euler circuit. Or, to put it another way, G cannot have an Euler circuit if the number of odd vertices is more than 0.To learn more about Euler circuit refer :
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Use the following table to find the rate of change. Remember the below equation rise/ run
X 2 4 6 8 10
Y 4 8 12 16 20
pls help :)
The rate of change of the function that is defined by the table:
X: 2 4 6 8 10
Y: 4 8 12 16 20
is r = 2
How to find the rate of change?For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:
r = ( y₂ - y₁)/(x₂ - x₁)
Here we have the table that defines a function:
X: 2 4 6 8 10
Y: 4 8 12 16 20
Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:
(2, 4) and (10, 20)
The rate is:
r = (20 - 4)/(10 - 2) = 16/8 = 2
If we use the first two pairs (2, 4) and (4, 8) we get:
r = (8 - 4)/(4 - 2) = 4/2 = 2
So the rate of change of the function is r = 2.
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what is the solution to -3x-3<6
Answer:
x>-3
Step-by-step explanation:
1
Add
3
to both sides
-3x-3<6
-3x-3+
2
Simplify
Add the numbers
Add the numbers
-3x<9
3
Divide both sides by the same factor, and flip the relation because the factor is negative
-3x<9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
x>-3
URGENT!!!!!!!!!!
identify the conic section represented by the equation x+2=-2(y-3)^2
circle
ellipse
hyperbola
parabola
Step-by-step explanation:
[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]
[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]
A parabola with a vertex (-2,3)
A restaurant prepares 250 side salads per day and estimates that 15% of the salads will spoil. What s the spoilage amount for the side salads? (Round up to nearest whole number.) A. 38 salads B. 15 salads C. 40 salads D. 6 salads
Answer:
A
Step-by-step explanation:
15 : 100 = x : 250
x = 250 * 15 / 100
x = 2.5 * 15
x = 37.5
x = 38
Put the following values in order from greatest to least.
Justify your answer.
0.388
3/8
38.38%
0.39
Answer:
0.39, 0.388, 38.38%, 3/8
Step-by-step explanation:
Which scale factors produce a contraction under a dilation of the original image? Select each correct answer. Responses −6 , negative 6, −0.5 , negative 0.5, 0.5 0.5 6
The set of scale factors that would produce a contraction under a dilation of the original image are:
B. -0.5
C. 0.5
What is scale factor?A scale factor can be defined as the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.
In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:
A geometric figure is enlarged when the scale factor is greater than 1 (k > 1).A geometric figure is reduced or contracted when the scale factor is less than 1 (k < 1).A geometric figure will remain the same when the scale factor is equal to 1 (k = 1).For a contraction under a dilation of the original image, the scale factor (k) must either be negative or less than one (1). Therefore, the required values are -0.5 and 0.5 respectively.
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The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?
The ratio shows how many times one value is contained in another value.
The number of top dogs is 192.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of top dogs to fat cats was 24 to 19.
if they were 152 fat cats.
This means,
Number of top dogs = 24x
Number of fat cats = 19x
Now,
Number of fat cats = 152
This means,
152 = 19x
x = 8
Now,
Number of top dogs = 24x
= 24x
= 24 x 8
= 192
Thus,
The number of top dogs is 192.
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A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 14 ounces and standard
deviation 0.8 ounce. Among a sample of 1000 of those peaches, about how many could be expected to have weights of more than
11.2 ounces?
About 999 plants have weights more than 11.2 ounce.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree
Given:
Mean= 14
Standard deviation = 0.8
So, P( x > 11.2) = P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > (11.2- 14/ 0.8)
= P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > -3.5)
= 0.999767
Hence, about 999 plants have weights more than 11.2 ounce.
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PLEASEEEEE HELP MEEEEEE!
Which of the functions is represented by the graph
Answer:
a
Step-by-step explanation:
just becsue
The following figure is made of 1 triangle and 1 rectangle.
7,2,11 find the area for each part of the figure and the whole figure
The area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
What is the area?The measurement that expresses the size of a region on a plane or curved surface is called an area.
Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The area of rectangle A:
Area = l*b
Area = 9*6
Area = 54 units²
Area of rectangle C:
Area = l*b
Area = 3*7
Area = 21 units²
Area of triangle B:
Area = 1/2 * b * h
Area = 1/2 * 3 * 2
Area = 1 * 3
Area = 3 units²
Therefore, the area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
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You can play a game for $1. In the game, you roll an 8-sided die. If you roll an 8, you get $9. If
roll an odd number, you get $1. Otherwise, you gain nothing.
(a) What is the expected value of this game?
The expected value of the game, given the amounts to be made when a number is rolled, is $ 1.25
How to find the expected value ?First, find the probability of rolling an 8 :
= Number of eights / Number of sides
= 1 / 8
= 0.125
The the probability of rolling an odd number :
= Odd numbers from 1 to 8 / Number of sides
= 4 / 8
= 0.5
The expected value of the game is:
= ( Probability of getting an 8 x Amount if you get 8 ) + ( Probability of getting an odd x Amount if you get an odd ) + ( Probability of not getting an 8 or odd x Loss )
= ( 0.125 x 9 ) + ( 0.5 x 1 ) + ((1 - 0.125 - 0.5) x -1)
= $ 1.25
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write the equation of the trigonometric graph.
A trigonometric equation is an equation containing one or more trigonometric ratios of unknown angles. It is expressed as the ratio of the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.
What are examples of trigonometric equations?
Trigonometric equations are equations containing trigonometric functions with one variable. For example, sin x + 2 = 1 is an example of a trigonometric equation. The equation can be as simple as this, or as complex as sin2 x – 2 cos x – 2 = 0.
What are the 4 types of trigonometry?
Side length ratios can be found with six trigonometric functions. The six functions are sine (sin), cosine (cos), tangent (tan), cosecant(cosec), secant (sec), and cotangent (cot).
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Answer(s):
[tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2 \\ y = -3cos\:(\frac{2}{3}x \pm \pi) + 2 \\ y = 3cos\:\frac{2}{3}x + 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{3}{4}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{2}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:\frac{2}{3}x + 2,[/tex]in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{4}\pi\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{3}{4}\pi\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{3}{4}\pi} = \frac{-\frac{\pi}{2}}{\frac{2}{3}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-4\frac{1}{2}\pi, -1],[/tex]from there to [tex]\displaystyle [-1\frac{1}{2}\pi, -1],[/tex]they are obviously [tex]\displaystyle 3\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 3\pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 2,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of 12.5 beats per minute. A) If 4 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.
The probability that their mean pulse rate is less than 80 beats per minute is of:
0.7389 = 73.89%.
How to obtain a probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (80 - 76)/6.25
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
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LaShonda is buying tickets for a group of families going to a ballet. She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50. LaShonda wants to spend no more than $400. Which system of inequalities can LaShonda use to find the number of tickets she can buy?
Answer: You Like Big Black Men and You love them dancing on you
Step-by-step explanation:
I have your search history ;)
The system of inequalities can LaShonda use to find the number of tickets she can buy will be;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
Now,
Let the number of adult tickets = x
And, The number of child tickets = y
Here, She wants to have at least 25 tickets.
So, We get;
⇒ x + y ≤ 25
And, Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
So, We get;
⇒ 22.50x + 17.50y < 400
Thus, The system of inequalities can LaShonda use to find the number of tickets she can buy are;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
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Find The value of my coins. If i have p pennies, n nickels and twice as many quarters as pennies.
Translate into an algebraic expression and simplify if possible.
The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or $(51p + 5n)/100.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given that you have p number of coins of pennies, n number of coins of nickels and twice as many quarters as pennies.
Thus the number of coins of quarters is 2p.
The value of penny, nickel, and quarter are
1 penny = 1 cent
1 nickel = 5 cents
1 quarter = 25 cents
The value of p number of pennies is p cents.
The value of n number of nickels is (n×5) =5n cents.
The value of 2p number of quarter is (2p × 25) = 50p cent.
The total value is p + 5n + 50p = (51p + 5n) cents
Divide 51p + 5n by 100 to convert it into dollar:
(51p + 5n) cents = $(51p + 5n)/100
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Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.
The rate of change of the modelled equation is 3.5 and the initial value is 5.
How to find the rate of change in a slope intercept equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Equation in slope intercept form is as follows:
y = mx + b
where
m = slope = rate of changeb = y-intercept = initial valueTherefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.
The equation is modelled in slope intercept form.
Therefore,
rate of change = 3.5
initial value = 5
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Choose ALL correct answers
(1, -3)
(4, 1)
(6, 3)
(2, -2)
Answer:
(a) (1, -3)
(b) (2, -2)
Step-by-step explanation:
You want to identify two points on the line through (3, -1) that has a y-intercept of -4.
GraphGraphing the line and points is suggested. The attached shows that graph, and identifies the two points on the line as ...
(1, -3) and (2, -2)
__
Additional comment
The equation of the line is x-y=4, so you can tell if the points fall on the line by seeing if they have that difference.
Find the value of each trigonometric ratio.
Answer:
sinA = 7/25
tanX = 35/12
Step-by-step explanation:
Trigonometric ratio for:
sinA = perpendicular/hypotenuse = 14/50 = 7/25
tanX = perpendicular/base = 35/12
Simplify by combining like terms.
3a +15-2a²+5a²-7+5a
Answer:
8a + 3a^2 + 8
If a sum of $500 were shared among a group of people in the following ratios, how much would each person receive?
If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
What is ratio?
Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.a) 6:4
Let it be 6x , 4x
6x + 4x = 500
10x = 500
x = 50
Then, 6x = 300 and 4x = 200.
b) 1:4:5
Let be x, 4x, 5x
x + 4x + 5x = 500
10x = 500
x = 50.
Then x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1
x + 8x + x =500
10x = 500
x = 50
Then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1
10x + 5x + 4x + x = 500
20x = 500
x = 25
Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
Hence, If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
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2/5*6/7 multiple and write fraction or mixed number in simplest form
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
multiple the numerators together 2 x 6 = 12 and multiply the denominators togethers 5 7 = 35
The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?
Recall the formula Cube volume = s cubed.
Answer:
S=64 x S = length
Select the correct location on the expression.
Mateo uses this exponential expression to determine the balance of his savings account. Which value in the expression represents the
annual interest rate for his savings account?
100(1+0,02)
12t
Answer:
0,02
Step-by-step explanation:
i got it correct
Which property is shown in the matrix addition below?
-6
9
15 -2
0
-3
+
6
-9
-15 2
0
3
commutative property
associative property
Oinverse property
Oidentity property
0 0 0
0 0 0
For the given matrix the additive inverse property is shown.
What is additive inverse of matrix?
The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.
Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix
M = - M.
Consider the given matrix,
[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]
Here each element in first matrix is negative of the element of second matrix.
That is each element is inverse of the element in second matrix.
And the addition of elements is 0.
Hence, for the given matrix the additive inverse property is shown.
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Pls help what this is
Stem-and-leaf plots
Answer:
C is the answer
Step-by-step explanation:
Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!
Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.
2_
Look at the numbers next to it, there's 2,3, and 8.
Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.
So in the graph there is 22,23 and 28.
If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.
Select the correct answer.
Consider the graph and the equation of function f.
f(x)=2 sin (1/2x) + 1
Answer:
y = 1
Step-by-step explanation:
The middle of the equation on the graph is y = 1.