The ascending order for the given values will be 22%<1/4<3/8<38%<21/10<3 5/10 as the definition of ascending order will be "When numbers are arranged in ascending order, they are done so from smallest to largest."
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Ascending order, also known as increasing order of importance, is the exact opposite of descending order. The order of the items is lowest to highest value. The smallest value is placed first in the order, and the biggest value is placed last. As a result, if you were to put the numbers from the previous section in ascending order, they would be as follows: 11, 20, 49, 80, 56, and so on. The first number is always the smallest, in this case 11. The last number is always the largest, in this case 80.
Here,
22%=0.22
38%=0.38
1/4=0.25
21/10=2.1
3 5/10=3.5
3/8=0.375
22%<1/4<3/8<38%<21/10<3 5/10
According to the definition of ascending order, the given values will be in ascending order as follows: 22%<1/4<3/8<38%<21/10<3 5/10 "Numbers are arranged from smallest to largest when they are arranged in ascending order."
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Given the card is a club, what is the probability a card drawn at random will be a(n)…12.8?13.10 or ace?
A standard deck has 52 cards, there are four suits in the deck, "clubs", "diamonds", "hearts", and "spades". There are 13 ranks in each suit.
You know that the card drawn at random is a club. This means that there are 13 possible outcomes: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K.
→ You have to determine the probability of drawing an "8" given that the card is a club. There is only one 8 of clubs between the 13 cards of the suite, the probability is equal to the number of successes divided by the total number of outcomes:
[tex]P(8|Club)=\frac{1}{13}[/tex]→ You have to determine the probability of drawing a 10 or an ace, given that the card is a club. Once again, since you know that the card's suit is a club, you have to calculate the probability considering the 13 ranks that conform to the suit.
The events "drawing the 10 of clubs" and "drawing the ace of clubs" are mutually exclusive, which means that the probability of the union between both events is equal to the sum of their individual probabilities:
[tex]P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club)[/tex]There is only one 10 within the 13 ranks of the suit, the probability can be expressed as follows:
[tex]P(10|Club)=\frac{1}{13}[/tex]You can calculate the probability of drawing the Ace of Clubs using the same logic:
[tex]P(Ace|Club)=\frac{1}{13}[/tex]Now you can calculate the union between both events:
[tex]\begin{gathered} P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club) \\ P((10|Club)\cup(Ace|Club))=\frac{1}{13}+\frac{1}{13} \\ P((10|Club)\cup(Ace|Club))=\frac{2}{13} \end{gathered}[/tex]What are the domain and range of the function f of x is equal to the quantity x squared plus 6x plus 8 end quantity divided by the quantity x plus 4 end quantity?
A. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 0}
B. D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
C. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 2}
D. D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
The domain and range of [tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex] is D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2} .
The domain of a function f(x) is set of the value of x for which it is defied and Range of function is set of values f takes .
The rational number [tex]f(x) = \frac{p(x)}{q(x)}[/tex] where p(x) and q(x) are polynomial in terms of x and q(x) ≠ 0 . The domain of rational number is set of values that do not cause denominator equal to zero .
The given function is :
[tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex]
we need to find domain and range of function,
For domain put denominator equals to zero
x+4 = 0
x = -4
so, domain is every real number except number making it zero
domain = (-∞,-4)∪(-4,∞) and x ≠ -4
For range ,factoring numerator
x²+6x+8 = x²+2x+4x+8
x(x+2)+4(x+2) = (x+4)(x+2)
Putting numerator back,
[tex]f(x) = \frac{(x+4)(x+2)}{x+4}[/tex]
Cancelling factor (x+4) from numerator and denominator
[tex]f(x) = x+2[/tex]
Putting x+2 = 0
[tex]x +2 = 0\\x = -2[/tex]
range = (-∞,-2)∪(-2,∞) and f(x) ≠ -2
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D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
I took the test
How would you write the equation for the following sentence: 3 hot dogs and 4 sodas cost $20. * Do not put spaces or dollar signs in your answer. Your answer
3h + 4s = 20
1) Let's write an equation for that, calling hot dogs by h and sodas by s.
3h + 4s = 20
Note that in this equation we are relating prices, of hot dogs and sodas and the total cost of them. Similar reasoning is used to set a linear system of equations.
Find the measureOf an act intercept by and inscribed whose measure is 75°Hent, draw a picture and label it,
From the arc-angle relationships, we know that the inscribed angle is half of the intercepted arc, that is,
[tex]75=\frac{arcAB}{2}[/tex]Then, by moving the denominator to the left hand side, we get
[tex]\begin{gathered} 2\times75=arcAB \\ \text{arcAB}=150 \end{gathered}[/tex]then, the arcAB measure 150 degrees.
During a special one-day sale, 600 customers bought the on-sale sandwich. Ofthese customers, 20% used coupons. The manager will run the sale again the nextday if more than 100 coupons were used. How many coupons were used andshould she run the sale again?80 coupons were used; no, she should not run the sale again140 coupons were used; yes, she should run the sale againOOO115 coupons were used; yes, she should run the sale again120 coupons were used; yes, she should run the sale again
Answer:
120 coupons were used; yes, she should run the sale again
Explanation:
The total number of customers = 600
The percentage that used coupon = 20%
[tex]\begin{gathered} 20\%\text{ of 600} \\ =\frac{20}{100}\times600 \\ =120 \end{gathered}[/tex]Thus, 120 coupons were used.
Since more than 100 coupons were used, the manager should run the sale again.
Find the area under the graph of f(x) = e-2ln(x) on the interval [1, 2]. (2 points)0.51.52.3331.75
Explanation:
To solve the question, we will need to re-express the given function as follow:
[tex]f(x)=e^{-2\ln (x)}[/tex]Will become
[tex]f(x)=e^{-2\ln (x)}=e^{\ln x^{-2}}[/tex]Thus
[tex]f(x)=e^{\ln x^{-2}}=x^{-2}[/tex]This simply means that we will find the area under the curve:
[tex]f(x)=x^{-2}\text{ within the interval \lbrack{}1,2\rbrack}[/tex]Thus
The area will be
[tex]\int ^2_1f(x)dx=\int ^2_1x^{-2}dx[/tex]This will then be
[tex]\lbrack\frac{x^{-2+1}}{-2+1}\rbrack^2_1=\lbrack\frac{x^{-1}}{-1}\rbrack^2_1[/tex]This will be simplified to give
[tex]-\lbrack\frac{1}{x}\rbrack^2_1=-\lbrack(\frac{1}{2})-(\frac{1}{1})\rbrack=-1\lbrack-\frac{1}{2}\rbrack=\frac{1}{2}[/tex]Therefore, the area under the curve will be
[tex]\frac{1}{2}=0.5[/tex]Thus, the answer is 0.5
Find the height of the cone. Round to the nearest hundredth, if necessary. Show your work.
The height of the cone is 6.16 inches
Explanation:Given:
diameter of the cone = 4 inches
Angle BAC = 72°
To find:
the height of the cone
To determine the height of the cone, we will use the right-angled triangle formed in the cone:
Diameter = 2(radius)
radius = diameter/2
radius = 4/2
radius = 2 inches
Height = BC
To get the height, we will apply the tan ratio (TOA):
[tex]tan\text{ 72\degree = }\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} tan\text{ 72\degree = }\frac{BC}{2} \\ BC\text{ = 2\lparen tan 72\degree \rparen} \\ BC\text{ = 2\lparen3.0777\rparen} \end{gathered}[/tex][tex]\begin{gathered} BC\text{ = 6.1554} \\ \\ The\text{ height of the cone is 6.16 in} \end{gathered}[/tex]what is the volume of a sphere with a radius of 3.3m rounded to the nearest tenth in cubic meters
For this exercise you need to use the following formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where "r" is the radius of the sphere.
In this case you can identify that:
[tex]r=3.3m[/tex]Then, you can substitute this value into the formula:
[tex]V=\frac{4}{3}\pi(3.3m)^3[/tex]Finally, evaluating, you get that the volume of the sphere (rounded to the nearest tenth in cubic meters) is:
[tex]V\approx150.5m^3[/tex]The answer is:
[tex]V\approx150.5m^3[/tex]Good morning can someone help me with my math
Part A
Angles 1 and 2 (<1 and <2 ) are alternate angles
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines
Therefore < 1 and < 2 are equal
Part B
AC and BD are Arc angles
AC = 2 x < 1
BD = 2 x < 2
Since < 1 and < 2 are equal
Then AC = BD
Part C
Parallel lines AB and BC will intercept the AC and BD arcs
Is (5, 1) a solution to the equation y = 1? yes no
Since the coordinates are written as (x,y), for the point (5,1) we have that:
[tex]\begin{gathered} x=5 \\ y=1 \end{gathered}[/tex]Therefore, this is a solution to the equation y=1.
Then, the answer is yes.
I need to find the solution to 5x-2 divided by 6
Given:
[tex](5x-2)\div6[/tex]To find:
Solve the given expression.
Explanation:
Rewrite the given expression,
[tex]\frac{5x-2}{6}[/tex]Expand the fraction into 2 simpler fractions with common denominator 6,
[tex]\frac{5x}{6}+\frac{-2}{6}[/tex]Simplify the expression, we will get:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]Final answer:
Hence, the required solution is:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]
Rewrite the equation by completing the square.X^2 + 11x + 24 = 0
Solution
For this case we can complete the square on this way:
[tex]x^2+11x+(\frac{11}{2})^2+24-(\frac{11}{2})^2[/tex]and if we simplify we got:
[tex](x+\frac{11}{2})^2+24-\frac{121}{4}=(x+\frac{11}{2})^2-\frac{25}{4}[/tex]We can use this property:
[tex](a^2+2ab+b^2)=(a+b)^2[/tex]For this case:
[tex]a=x,b=\frac{11}{2}[/tex]Answer:
(x+11/2)^2 = 25/4
did it on khan, hope this helps<3
Given the equation y = 1.3* Growth a. Does this equation represent growth or decay? 1.3 b. What is the growth or decay factor? e. What is the rate of growth or decay? d. What is the initial value?
Answer:
a. Growth
b. 1.3
c. 30%
d. 1
Explanation:
The exponential equation given can be written in the form
[tex]y=1.3^x=1(1.3)^x[/tex]From this form, we see that
a. the function represents a growth since 1.3 > 1
b. the growth factor is 1.3
c. The rate of growth is (1.3 - 1) * 100% = 30%
d. the initial value is 1.
Hence, the answers
a. Growth
b. 1.3
c. 30%
d. 1
The side lengths of a triangle are shownbelow. How many other triangles with thesemeasurements could be made?A. None just this unique triangleB. Two trianglesC. Many triangles84 mm96 mm60 mm
Given the side lengths of some triangle:
[tex]\begin{gathered} L_1=84 \\ L_2=96 \\ L_3=60 \end{gathered}[/tex]Let us suppose that there exists another triangle with these side lengths:
[tex]\begin{gathered} L_1^{\prime}=84 \\ L_2^{\prime}=96 \\ L_3^{\prime}=60 \end{gathered}[/tex]Based on these, we can say that:
[tex]\begin{gathered} L_1\cong L_1^{\prime} \\ L_2\cong L^{\prime}_2 \\ L_3\cong L^{\prime}_3 \end{gathered}[/tex]Then, using the Side-side-side theorem, we conclude that both triangles are congruent, so this triangle is unique
Number of balls madeHow many games had 11 or fewer balls made?
The number of games that had 11 or fewer balls made = 6
Explanations:The number of games that have 11 or fewer balls made will be the number of games that have between 0 to 11 balls made.
Number of games that had 0-3 balls made = 0
Number of games that had 4 - 7 balls made = 1
Number of games that had 8-11 balls made = 5
The number of games that had 11 or fewer balls made = (Number of games that had 0-3 balls made) + (Number of games that had 4-7 balls made) + (Number of games that had 8-11 balls made)
The number of games that had 11 or fewer balls made = 0 + 1 + 5
The number of games that had 11 or fewer balls made = 6
Answer:
6
Step-by-step explanation:
The period of a pendulum is the time the pendulum
The period of the pendulum is 11.11 seconds.
EXPLANATION
From the given equation,
L= 0.81t² -----------------------------------------(1)
But L= 100 feet
Substitute the value of L into equation (1)
That is;
100 = 0.81t²
Divide both-side of the equation by 0.81
[tex]\frac{\cancel{0.81}t^2}{\cancel{0.81}}=\frac{100}{0.81}[/tex][tex]t^2=123.45679[/tex]Take the square root of both-side of the equation.
[tex]t\approx11.11[/tex]T= 11.11 seconds.
Hence, the period of the pendulum is 11.11 seconds.
Can anyone help me pls this is my last grade for algebra and Ik failing the class right now I need this grade to be able to pass my class pls help
For every room added, the price increase is $50, therefore the slope is equal to 50.
Since the value for one room is $125 and we know that each room costs $50, then the y-intercept is the value for 1 room minus 50.
[tex]b=125-50=75[/tex]Now we can create the function for this situation:
[tex]f(x)=50\cdot x+75[/tex]Where f(x) is the price and x is the number of rooms to be cleaned. Since the function is linear, the unit rate is equal to the slope, so the unit rate is 50.
The amount charged to drive to the client's home is the fixed part of the price, so it is equal to the y-intercept. The price is $75.
To find the cost of 8 rooms we need to make x = 8 and calculate the value of the expression.
[tex]f(8)=50\cdot8+75=475[/tex]The value would be $475.
use the information to answer the following questionsmr. ramirez purchased 20 concert tickets for a total of $225.the concert tickets cost $15 for adults and $10 for children under the age of 12 part A: write a system of equations to represent the given scenario. use the variables "a" for adults and "c" for children.
Answer:
a + c = 20
15a + 10c = 225
Explanation:
If 'a' is the number of tickets for adults and 'c' is the number of tickets for children, we can write the following equation:
a + c = 20
Because Mr. Ramirez purchased a total of 20 concert tickets.
In the same way, if the cost of the tickets is $15 for adults and $10 for children, we can write the following equation:
15a + 10c = 225
Because 15a is the total cost for adults, 10c is the total cost for children and 225 is the total cost in general.
Therefore, the system of equations that represents the given scenario is:
a + c = 20
15a + 10c = 225
The total profit (in dollars) from the sale of a espresso machines is P(x) = 160x - 0.85x^2 + 25.Evaluate the marginal profit at the following values to 4 decimal place accuracy if necessary:(A) P'(60) =(B) P'(65) =
We will have the following:
[tex]\begin{gathered} P(x)=160x-0.85x^2+25 \\ \\ \Rightarrow P^{\prime}(x)=160-1.7x \end{gathered}[/tex]So:
A) P'(60):
[tex]P^{\prime}(60)=160-1.7(60)\Rightarrow P^{\prime}(60)=58[/tex]B) P'(65):
[tex]P^{\prime}(65)=160-1.7(65)\Rightarrow P^{\prime}(65)=49.5[/tex]Benchmark estimate of 6.34 + 3.95
The value of 6.34 + 3.95 using benchmarks estimating is 10.
BenchmarksBenchmarks to estimate means rounding to the nearest whole number
Step 1: If the value after decimal is 5 or more than round off it to successive whole number other wise round off it to preceding whole number
Step 2: We need to round 6.34 and 3.95 to the nearest whole number
6.34 will be rounded to 6.
3.95 will be rounded to 4.
Since we have gotten the rounded number to be 6 and 4 then;
Benchmark estimate = 6 + 4
= 10
Therefore, Benchmark estimate 6.34 + 3.95 =10.
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The function g is graphed below. At what numbers in the interval (-4,4) is g discontinuous?
The graph has discontinuity if the curve or the line is not continuous.
From the graph shown, The graph stopped at (-1, 0) and then starts again at (-1, 4), stopped again at (3, 2)
then gone with (3, 3) and continues up to (4, -2)
So graph g discontinuous at -1 and 3
kenji mixes 1/5 clay soil with 1/8 bale of straw to make an Adobe brick how much soil will he need to use the whole bale of straw.
Clay soil = 1/5
bale of straw = 1/8
Clay soil needed = x
Bale of straw needed = 1
Clay soil : Bale of straw (rate)
1/5 : 1/8 = x : 1
1/5 ÷ 1/8 = x / 1
1/5 × 8/1 = x / 1
8/5 = x / 1
Cross product
8 * 1 = 5 * x
8 = 5x
Divide both sides by 5
x = 8/5
Greatest common factor of 9 and 11
Answer:
1
Step-by-step explanation:
Since, 1 is the only common factor between 9 and 11. The Greatest Common Factor of 9 and 11 is 1.
The Jordan family budgeted 16% of their disposable annual income of $44,000 for food, but found they needed $35 more per week. How much of their income should now beadded to their food budget?$1,587.00$1,820.00$1,924.00$2,042.00None of these choices are correct.
Given:
The percentage of income budgeted for food, R=16%.
The income of the family, I=$44,000.
The extra amount for food needed per week, x=$35.
The amount budgeted by the family for food in an year is,
[tex]\begin{gathered} A=\frac{R}{100}\times I \\ =\frac{16}{100}\times44000 \\ =7040 \end{gathered}[/tex]There are 365 days in an year and 7 days in a week.
The number of weeks per year is,
[tex]N=\frac{365}{7}[/tex]The extra amount added by the family for food is,
[tex]\begin{gathered} A_w=xN \\ =35\times\frac{365}{7} \\ =1825 \end{gathered}[/tex]Hence, the family should add $1825 to their food budget.
So, none of these choices are correct.
(0,2)-5The function g(x) = -3x - 6. Compare the slopes.A. The slope of f(x) is the same as the slope of g(x).B. The slope of f(x) is undefined, and the slope of g(x) is negative.Ο ΟC. The slope of f(x) is greater than the slope of g(x).D. The slope of f(x) is less than the slope of g(x).
To solve the exercise, first we are going to find the slope of the function f(x). Since we have a graph of the function, we can see two points through which the line passes:
[tex]\begin{gathered} (x_1,y_1)=(0,2) \\ (x_2,y_2)=(1,-1) \end{gathered}[/tex]Now we can use this formula to find the slope:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex][tex]\begin{gathered} m_{f(x)}=\frac{-1-2}{1-0} \\ m_{f(x)}=\frac{-3}{1} \\ m_{f(x)}=-3 \end{gathered}[/tex]Then, the slope of the function f(x) is -3.
On the other hand, the function g(x) also describes a line and is written in slope-intercept form, that is:
[tex]\begin{gathered} y=mx+b\Rightarrow\text{ slope-intercept form} \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}[/tex]Then, you can see that the slope of the function g(x) is -3, because
[tex]\begin{gathered} g(x)=-3x-6 \\ m_{g(x)}=-3 \\ \text{and} \\ b=-6 \end{gathered}[/tex]Therefore, the slope of f(x) is the same as the slope of g(x) and the correct answer is option A.
I need to know number 6SP please I need to find the mean
The mean absolute deviation is given by the next formula:
[tex]\text{MAD}=\frac{1}{n}\sum ^{\square}_i|x_i-\bar{x}|[/tex]Where n is the number of points in the data set and x with a bar on top is the mean.
In our case,
[tex]\bar{x}=\frac{1}{25}(5\cdot1+5\cdot2+4\cdot3+4\cdot4+6\cdot5+6\cdot1)=\frac{79}{25}[/tex]and n=25.
Then,
[tex]\text{MAD}=\frac{1}{25}(5|1-\frac{79}{25}|+5|2-\frac{79}{25}|+4|3-\frac{79}{25}|+4|4-\frac{79}{25}|+6|5-\frac{79}{25}|+|6-\frac{79}{25}|)[/tex]Finally,
[tex]\text{MAD}=\frac{862}{625}\approx1.4[/tex]The answer is 1.4 once rounded.
were would he be at in 6 seconds
6 seconds later we can say that dwyane was running to the left of zero, because if he was running at 4 meters per second to the right when he passed the zero point, hence 6 seconds later he was on the left of the zero at the point -2.
the function h(t)=-4.9t^2+19t+1.5 describes the height in meters of a basketball t seconds after it has been thrown vertically into the air.what is the maximum height of the basketball? round your answer to the nearest tenth
we have
h(t)=-4.9t^2+19t+1.5
This function represent a vertical parabola open downward
The vertex represent a maximum
using a graphing tool
see the attached figure
please wait a minute
The vertex is the point (1.94, 19.92)
therefore
the maximum height of the basketball is 19.9 meters
Suppose a charity received a donation of $17.3 million. If this represents 41% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Using the concept of percentage, the total amount that was donated to charity is $42.195 million.
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviation used to represent percentages is the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
According to the data, the charity got a donation of $17.3 million, or 41% of its total donations.
Let x serve as a symbol for the total sum.
This will be shown as follows:
41% × x = $17.3million
0.41x = $17.3 million
Divide by 0.41
x = $17.3million / 0.41
x = $42.195 million
The total amount that is donated to charity is $42.195 million
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List the odd counting numbers between 4 and 14
ANSWER
[tex]5,7,9,11,13[/tex]EXPLANATION
We want to list the odd counting numbers between 4 and 14.
Odd numbers are numbers that are not divisible by 2 and counting numbers are natural numbers.
Therefore, odd counting numbers between 4 and 14 are:
[tex]5,7,9,11,13[/tex]That is the answer.