Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Let
x -----> number of dimes coin
y -----> number of quarters coin
we have that
x=y ------> equation 1
and
0.10x+0.25y < 4 ------> inequality 1
substitute equation 1 in inequality 1
0.10x+0.25x < 4
solve for x
0.35x<4
x < 11.4
For 12 dimes
the value of x=12 not satisfy the inequality
that means
He couldn't have 12 dimes
what is 24 as a fraction or mixed number
Answer: 24/1
Step-by-step explanation:
Consider the following measures shown in the diagram with the circle centered at point A. Determine the arc length of CB.
Answer:
[tex]\frac{4}{3}\pi\; cm[/tex]Explanation:
If an arc of a circle radius, r is subtended by a central angle, θ, then:
[tex]\text{Arc Length}=\frac{\theta}{360\degree}\times2\pi r[/tex]In Circle A:
• The central angle, θ = 40 degrees
,• Radius = 6cm
Therefore, the length of arc CB:
[tex]\begin{gathered} =\frac{40}{360}\times2\times6\times\pi \\ =\frac{4}{3}\pi\; cm \end{gathered}[/tex]The correct choice is C.
mond Baware Infinits Piscais Angles and Angle Measure Name 5.2
If we want to find the reference angle, you have to find the smallest possible angle formed by the x-axis and the terminal line, going either clockwise or counterclockwise.
In this case, the angle 290° is in the fourth quadrant, so the reference angle can be drawn and calculated as:
The reference angle can be calculated as:
[tex]360-290=70\degree[/tex]Answer: the reference angle for 290° is 70°.
2.) Which equation represents the balance scale shown? 3x = 7 X-3 = 7 x/3 = 7 x + 3 = 7
As you can see from the figure,
There are 7 dots on the right side of the scale.
On the left side of the scale, there are 3 dots + x
So, we write these numbers on the left and the right side of the equality sign.
[tex]x+3=7[/tex]Therefore, the equation x + 3 = 7 represents the balance scale shown in the figure.
Compute the common and natural logarithms using the properties of logarithms and a calculator.Type the correct answer in each box. Round your answers to two decimal places.
(b)
[tex]\log _{}3.26[/tex]Using the calculator to compute the logarithm, we have;
[tex]\begin{gathered} \log \text{ 3.26 = 0.5132} \\ \log \text{ 3.26 = 0.51 (Round to two decimal places)} \end{gathered}[/tex](c)
[tex]\begin{gathered} \log \text{ 10000} \\ =\log _{10}10^4 \\ =4\log _{10}10 \\ =4\times1 \\ \log \text{ 10000}=4.00\text{ (Round to two decimal places)} \end{gathered}[/tex](d)
[tex]\begin{gathered} \ln 22=3.0910 \\ \ln 22=3.09\text{ (Round to two decimal places)} \end{gathered}[/tex]..Sam works 40 hours in one week and is paid $610. How much does Samearn per hour?
Answer:
Sam earns $15.25 per hour.
Explanation:
Sam works 40 hours in one week, and is paid $610
To know how much Sam earns per hour, we divide the amount earned by the number of hours worked.
This is:
[tex]\frac{610}{40}=15.25[/tex]Therefore, Sam earns $15.25 per hour.
On a map, the scale shown is1 inch : 5 miles. If a park is75 square miles, what is thearea of the park on the map?The park's area issquarelinches on the map.
We have the relationship between inches and miles is:
1 inch to 5 miles.
The park has an actual area of:
[tex]75mi^2[/tex]Now, to make the conversion to inches, we need to consider that 1 inch represent 5 miles. Thus:
[tex]\begin{gathered} 1in=5mi \\ 1in^2=25mi^2 \end{gathered}[/tex]We squared this amounts, if 1 inch is 5 miles, 1 inch squared will be equal to 5 squared which is 25.
Now we divide 75 miles squared by 25, to know how many inches squared will the park represent on the map:
[tex]\frac{75}{25}=3in^2[/tex]Answer: the area of the park on the map will be 3 inches squared.
500 books were sold the first day it went on sale. 150 books were sold each day after that. Write an equation to represent the total number of books sold. How many books were sold after 50 days?
Let x represent the number of days after release and y represent the number of books sold.
The first day there were 500 books sold, after that, 150 books were solf each passing day.
This means that for the first day y=500 ann each passing day 150 books were added, the equation is:
y=500+150x
Using this equation you have to calculate the number of books solf after x=50 days.
To do so replace in the equation above:
y=500+150*50
y=8000
After 50 days 8000 books were sold
If there are six servings in a 2/3 pound package of peanut which fraction of a pound is in each serving.
We will have the following:
If there are 6 servings in a 2/3 pound package, we will divide the pounds by the number of servings, that is:
[tex]\frac{(\frac{2}{3})}{6}=\frac{(\frac{2}{3})}{(\frac{6}{1})}=\frac{2\cdot1}{3\cdot6}=\frac{2}{18}[/tex][tex]=\frac{1}{9}[/tex]So, each serving has 1/9 of a pound.
***Explanation***
Since we have 6 servings and then the total value of pounds the package represents we will have that the weigth (in pounds) for each serving is given to us by dividing the total weight by the number of servings.
Now, in order to apply the division of a fraction by another fraction we rewrite the integer 6 as a fraction, and we know that 6 / 1 = 6 so, that is the fraction from for this number (At least the less complicated one) and we proceed with the "ear" opeation.
For the following line, name the slope and y-intercept. Then write the equation of the line in slope-interceptform.Slope= y - intercept = (0,_ ) Equation: y =
Given:
A line that passes the through the points (4, 0) and (0,-3).
Required:
Slope, y-intercept, and the equation of the given line.
Explanation:
As the line passes through the points (4, 0) and (0,-3), the slope is calculated as,
[tex]\begin{gathered} Slope\text{ = }\frac{y_2-y_1}{x_2-\text{ x}_1} \\ Slope\text{ = }\frac{-3\text{ - 0}}{0\text{ - 4}} \\ Slope\text{ = }\frac{-3\text{ }}{-4} \\ Slope\text{ = }\frac{3}{4} \end{gathered}[/tex]The y-intercept of the given line is the point through which the given line passes on the y-axis which is -3. Therefore the intercept of the given line is -3.
The equation of line in slope point form is given as,
[tex]y\text{ = mx + c}[/tex]Where m is the slope and c is the y-intercept. Therefore the equation of the line is given as,
[tex]y\text{ = }\frac{3}{4}x\text{ - 3}[/tex]Answer:
Thus the required equation of line is
[tex]y\text{ }=\text{ }\frac{3}{4}\text{x{\text{ - 3}}}[/tex]¿Cual es el resultado de efectuar (2x+5)³ + (x-2)(x-2)?
The equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
What is meant by binomial equation?A binomial number is an integer that can be produced by evaluating a homogeneous polynomial with two terms in mathematics, more specifically in number theory. It is a Cunningham number that has been generalized.
Let the equation be (2x + 5)² + (x -2)(x- 2)
By using binomial formula we get,
(a + b)³ = a³ + 3a²b + 3ab² + b³
The coefficient multipliers are located in row 3 of Pascal's triangle.
(2x + 5)³ + (x - 2)(x - 2)
= 8x³ + 60x² + 150x +125(x - 2)(x - 2)
8x³ + 60x² + 150x + 125 + x(x - 2) - 2(x-2)
8x³ + 60x² + 150x + 125 + x² - 2x - 2x +4
simplifying the above equation, we get
8x³ + 60x² + 150x + 125 + x² - 4x +4
8x³ + 60x² + 150x +129 + x² - 4x
8x³ + 60x² + 150x + 129 - 4x
8x³ + 60x² + 146x + 129
= 8x³ + 60x² + 150x +129
Therefore, by simplifying the equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
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Translate the sentence into an equation Three times the sum of a number and 2 is equal to 9 Use the variable y for the unknown number
Three times
multiply a value by 3
[tex]3\times()[/tex]The sum of a number and 2
We named the number "Y", then inside the parenthesis be the sum of x and 2
[tex]3\times(y+2)[/tex]Is equal to 9
we equal the equation to 9
[tex]3\times(y+2)=9[/tex]ratio of number of boys to girl is 5 to 4 there are 60 girls in choir how many boys are there
Since the ratio of boys to girls is 5:4 and there are 60 girls, let b be the number of boys and g be the number of girls. Then:
[tex]\begin{gathered} \frac{b}{g}=\frac{5}{4} \\ \Rightarrow\frac{b}{60}=\frac{5}{4} \\ \Rightarrow b=\frac{5}{4}\times60 \\ \Rightarrow B=75 \end{gathered}[/tex]Therefore, there are 75 boys in the choir.
Ava solved the compound inequality +7
Tell me if the inequalities are correct
x/4 + 7 < -1 2x - 1 >= 9
x/4 < -1 - 7 2x >= 9 + 1
x/4 < -8 2x >= 10
x < -32 x >= 10/2
x >= 5
The second option is the correct one
Dilate f (x) = (x+4)(x+2) by x
Given:
[tex]f(x)=(x+4)(x+2)[/tex]Dilate of function is:
[tex]\begin{gathered} f(x)=(x+4)(x+2) \\ =x(x+2)+4(x+2) \\ =x^2+2x+4x+8 \\ =x^2+6x+8 \end{gathered}[/tex]Two Column Proof. If you could write it on a piece of paper and send a picture, that would be great.
Let's suppose
∠1 =∠5 and ∠2 = ∠4
then
180° - ∠1 - ∠2 = ∠3
180° - ∠1 - ∠2 =
Answer the statistical measures and create a box and whiskers plot for the following set of data.1, 1, 2, 2, 5, 6, 11, 11, 12, 13, 14, 16, 17, 19
DEFINITIONS
A boxplot is a way to show the spread and centers of a data set.
The box and whiskers chart shows you how your data is spread out. Five pieces of information (the “five-number summary“) are generally included in the chart:
1) The minimum (the smallest number in the data set). The minimum is shown at the far left of the chart, at the end of the left “whisker.”
2) First quartile, Q1, is the far left of the box (or the far right of the left whisker).
3) The median is shown as a line in the center of the box.
4) Third quartile, Q3, shown at the far right of the box (at the far left of the right whisker).
5) The maximum (the largest number in the data set), is shown at the far right of the box.
SOLUTION
From the data set given, we have the following information:
1) Minimum Value: 1
2) First Quartile: The position for the first quartile is given by the formula
[tex]\Rightarrow\frac{n+1}{4}[/tex]where n is the number of data.
In the problem, there are 14 data values. Therefore, the position is:
[tex]\Rightarrow\frac{14+1}{4}=3.75th\text{ position}[/tex]Using the 3.75th position, we have
[tex]\begin{gathered} 3rd\Rightarrow2 \\ 4th\Rightarrow2 \\ \therefore \\ Q1=2 \end{gathered}[/tex]3) Median: The median position is given by the formula
[tex]\Rightarrow\frac{n+1}{2}[/tex]Therefore, the median position will be:
[tex]\Rightarrow\frac{14+1}{2}=\frac{15}{2}=7.5th\text{ position}[/tex]The 7.5th position will give:
[tex]\begin{gathered} 7th\Rightarrow11 \\ 8th\Rightarrow11 \\ \therefore \\ Med=11 \end{gathered}[/tex]4) Third Quartile: The third quartile's position is gotten using the formula:
[tex]\Rightarrow\frac{3}{4}(n+1)_{}[/tex]Therefore, the Q3 position will be:
[tex]\Rightarrow\frac{3}{4}\times15=11.25th\text{ position}[/tex]Therefore, the 11.25th position will give:
[tex]\begin{gathered} 11th\Rightarrow14 \\ 12th\Rightarrow16 \\ \therefore \\ Q3=14(0.75)+16(0.25)=14.5 \end{gathered}[/tex]5) Maximum: 19
Therefore, the boxplot is shown below:
For each of the following pairs of rational numbers, place a greater than symbol, >, a less than symbol, <, or an equality symbol, =, in the square to make the statement true.
I chow you how to solve for (d) and (i) and you could do the rest by yourself:
The best way to solve this operations is convert the numbers to a one form and then compare.
For (d)
[tex]\begin{gathered} \frac{7}{3}=\frac{6+1}{3}=\frac{6}{3}+\frac{1}{3}=2+\frac{1}{3}=2\frac{1}{3}=2.333 \\ \frac{13}{5}=\frac{10+3}{5}=\frac{10}{5}+\frac{3}{5}=2+\frac{3}{5}=2\frac{3}{5}=2.6 \\ So, \\ \frac{7}{3}<\frac{13}{5} \end{gathered}[/tex]Now for (i), take into account that this numbers are negative:
[tex]\begin{gathered} -11.5=-11.5\cdot\frac{4}{4}=-\frac{11.5\cdot4}{4}=-\frac{46}{4} \\ So,\text{ } \\ -\frac{46}{4}<-\frac{31}{4} \end{gathered}[/tex]Note that 46/4 is greater than 31/4, but -46/4 is lower than -31/4.
Also note that in this example I find to equalize the denominator of the numbers adn then you can compare the numerators.
What is 6 hundred thousand in hundreds
600,000 (Six hundred thousand)
1) If we divide 600,000 by 100 we'll have 6000
So 600,000 is equal to 6000 hundreds.
Rewrite each equation in slope-intercept form, if necessary, then determine whether the lines are parallel , perpendicular, or neither.A.) y=2×+1B.)2x+y=7The slope line A is _The slope of line B is _Lines A and B are _
You have the following equation of two lines:
A) y = 2x + 1
B) 2x + y = 7
the general form of an equation of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
The equation A is already written in the slope-intercep form. By comparing the equation with the general form you can notice that the slope is:
mA = 2
Next, you rewrite the equation B:
2x + y = 7 subtract 2x both sides
y = -2x + 7
by comparing with the general fom you have that the equation B has the following slope:
mB = -2
In order to determine if the lines are parallel,perpendicular, or neither, you calculate the quotien between the slopes of the lines.
mA/mB = 2/(-2) = -1
The quotient between the slopes is -1, this means that the lines are perpendicular
Math answers and how you got the answer to solve
Hello there. To solve this question, we'll have to remember some properties about functions.
Given the functions:
[tex]\begin{gathered} f(x)=x^3 \\ g(x)=6x^2+11x-2 \end{gathered}[/tex]We have to determine:
[tex]\begin{gathered} (f+g)(x) \\ (f-g)(x) \\ (fg)(x) \\ (ff)(x) \\ \left(\frac{f}{g}\right)(x) \\ \left(\frac{g}{f}\right)(x) \end{gathered}[/tex]And their domain.
Let's do each separately:
(f + g)(x)
In this case, this function is the same as adding f(x) and g(x):
[tex](f+g)(x)=f(x)+g(x)=x^3+6x^2+11x-2[/tex]And as it is a polynomial function, it has no holes or asymptotes, therefore its domain is all the real line. We write:
(f - g)(x)
In the same sense, it is equal to the difference between f and g:
[tex](f-g)(x)=f(x)-g(x)=x^3-(6x^2+11x-2)=x^3-6x^2-11x+2[/tex]Again, as it is a polynomial function, its domain is all the real line, just as before.
(fg)(x)
In this case, it is the same as the product of f and g:
[tex](fg)(x)=f(x)\cdot g(x)=x^3\cdot(6x^2+11x-2)=6x^5+11x^4-2x^3[/tex]Once again, its domain is all the real line.
(ff)(x)
In this case, it is the product of f and itself:
[tex](ff)(x)=f(x)\cdot f(x)=x^3\cdot x^3=x^6[/tex]As before, its domain is entire real line.
(f/g)(x)
In this case, it is the quotient between f and g, respectively:
[tex]\mleft(\frac{f}{g}\mright)(x)=\frac{x^3}{6x^2+11x-2}[/tex]But in this case, its domain is not the entire real line. We have to get rid of the holes and vertical asymptotes of the function.
This function has no holes, since we cannot simplify any terms in the fraction, but it has at least two vertical asymptotes (that we'll find by taking the roots of the denominator).
In fact, the name vertical asymptote stands for the values of x in which the function would not exist (its limit goes to either infinity, -infinity or would not exist).
These roots are given by:
[tex]6x^2+11x-2=0[/tex]Using the quadratic formula, we get:
[tex]\begin{gathered} x=\frac{-11\pm\sqrt[]{11^2-4\cdot6\cdot(-2)}}{2\cdot6}=\frac{-11\pm\sqrt[]{121+48}}{12}=\frac{-11\pm\sqrt[]{169}}{12} \\ \Rightarrow x=\frac{-11\pm13}{12} \\ \Rightarrow x_1=\frac{-11+13}{12}=\frac{2}{12}=\frac{1}{6} \\ x_2=\frac{-11-13}{12}=\frac{-24}{12}=-2 \end{gathered}[/tex]The roots are 1/6 and -2. They are the vertical asymptotes of the function.
The domain of (f/g)(x) is then given by subtracting these values from the real line:
Or also in interval notation:
We do the same to (g/f)(x):
It is equal to the quotient between g and f, respectively, thus
[tex]\left(\frac{g}{f}\right)(x)=\frac{g(x)}{f(x)}=\frac{6x^2+11x-2}{x^3}[/tex]And again in this case, we have no holes, but we do have a vertical asymptote.
Taking the roots of the denominator:
[tex]x^3=0[/tex]The only solution to it is:
[tex]x=0[/tex]And the domain is then given by:
∣+8∣−5=2Group of answer choicesv = -1 and v = -15v = -1 and v = -5No Solutionv = -15 and v = 15
Given:
[tex]|v+8|-5=2[/tex][tex]|v+8|=2+5[/tex][tex]|v+8|=7[/tex]case (1)
[tex]v+8=7[/tex][tex]v=7-8[/tex][tex]v=-1[/tex]Case (2)
[tex]-(v+8)=7[/tex][tex]-v-8=7[/tex][tex]v=-8-7[/tex][tex]v=-15[/tex]Therefore,
[tex]v=-1,-15[/tex]1st option is the correct answer.
If ABCD is dilated by a factor of 1/2coordinate of d' would be
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 8". Find P(A). Outcome Probability 1 0.01 2 0.04 3 0.4 4 0.01 5 0.08 6 0.07 7 0.21 8 0.07 9 0.11
For divisor of 8:
A be the event "the outcome is a divisor of 8".
Then P(A):
[tex]\begin{gathered} P(A)=P(1)+P(2)+P(4)+P(8) \\ P(A)=0.01+0.04+0.01+0.07 \\ P(A)=0.13 \end{gathered}[/tex]Which statement is true?123.466 > 132.4659.07 > 9.00850.1 < 5.013.37 < 3.368
In the given decimal inequality statements we can infer that only
9.07 > 9.008 is true.
The given statements are :
123.466 > 132.465
9.07 > 9.008
50.1 < 5.01
3.37 < 3.368
Let us take each statement and find out if it is true or false.
Statement 1: 123.466 > 132.465
Using the properties of decimals we see that 231<132 hence the statement is false.
Statement 2:
9.07 > 9.008
Here the second digit after decimal are 7 and 0. Since the first two significant digits are same , and 7>0 therefore 9.07>9.008 so it is true.
Statement 3:
50.1 < 5.01
Here 50 > 5 so the statement is false
Statement 4:
3.37 < 3.368
Here the first two significant digits are same. Again the digit in the hundredths place are 7 and 6, as 7>6, hence the statement is false.
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Complete the tables using the formula. Then, identify the starting amount and the amount you change by. These are linear, so the table should go up or go down by a constant amount.Y = 5x + 8
Part A
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point (y-intercept) = 8
Part C.
slope is 5.
STEP - BY - STEP EXPLANATION
What to find?
• The values of y at x=0,1,2,3,4,5, 6 and 7
,• Slope
,• Y- intercept.
Given:
y=5x + 8
To determine the values of y at each point of x, substitute into the formula given and simplify.
That is;
At x = 0
[tex]\begin{gathered} y=5(0)\text{ +8} \\ y=0+8 \\ y=8 \end{gathered}[/tex]At x = 1
[tex]\begin{gathered} y=5(1)+8 \\ =5+8 \\ =13 \end{gathered}[/tex]At x = 2
[tex]\begin{gathered} y=5(2)+8 \\ =10+8 \\ =18 \end{gathered}[/tex]At x = 3
[tex]\begin{gathered} y=5(3)+8 \\ =15+8 \\ =23 \end{gathered}[/tex]At x = 4
[tex]\begin{gathered} y=5(4)+8 \\ =20+8 \\ =28 \end{gathered}[/tex]At x = 5
[tex]\begin{gathered} y=5(5)+8 \\ =25+8 \\ =33 \end{gathered}[/tex]At x = 6
[tex]\begin{gathered} y=5(6)+8 \\ =30+8 \\ =38 \end{gathered}[/tex]At x=7
[tex]\begin{gathered} y=5(7)+8 \\ =43 \end{gathered}[/tex]Hence,
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point( y-intercept).
The y-intercept is the point at which x =0
Hence, from the values above, at x=0, y=8
Hence, the starting point (y-intercept) = 8
Part C
The changes in slope.
The slope is the changes in y-intercept, the y -values kept increasing by 5.
Hence, the slope is 5.
Sondra is going rock climbing. She starts at 12.25 yards above sea level. She ascends 38.381yards before lunch. She then descends 15.25 yards after lunch. What is Sondra's finalheight relative to sea level?
What we need to do is follow up with Sondra.
Starts at 12.15 yd
Ascendes 38.281, therefore:
[tex]12.15+38.5=50.65[/tex]A total 50.65 yd
Then, descends 15.25, therefore:
[tex]50.65-12.25=38.5[/tex]This means that the relative 38.5 - (15.25 - 12.25) = 38.5 - 3 = 35.5, it is means 35 1/2
The answer is 35 1/2
2,047÷41=sloveadd expression
The given expression is,
[tex]\frac{2047}{41}[/tex]On solving, we have,
[tex]\frac{2047}{41}=49\frac{38}{41}=49.93[/tex]Thus, 2,047÷41=49.93.
Suzie has cards in numbers 9-21 in a bag. What is the probability she will pull a card lower than 17?
She has cards that go from 9 to 21.
We assume she has one card with each number that goes from 9 to 21:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.
NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).
We have 17-9 = 8 cards that are lower than 17.
The total number is 22-9 = 13 cards (all the cards lower than 22).
Then, we can calculate the probability as:
[tex]P(C<17)=\frac{8}{13}[/tex]Answer: The probabilty she pull a card lower than 17 is P=8/13
Graph the parabola.Y = -2x^2 - 16x - 34Plat five points on a parable the vertex ,two points to the left of the vertex ,and two points to the right of the vertex . then click on the graph a function button.
The graph is shown below:
• The point (-4, -2) is the vertex
,• The points to the left are (-5, -4) and (-6, -10)
,• The points to the right are (-3, -4) and (-2, -10)