The quotient is 11/40.
What is a mixed number?It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.
2 3/4= 11/4
11/4 is divided by 10 then,
It becomes 11/40
So, the quotient is 11/40
Here, 11/40 cannot be converted into a mixed number.
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Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quaters, and 3 dollars. How much money does he have in total
He has 1999 cents that is equal to 20 dollars approximately as per money conversion theory that defines "The ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another."
What is money?Any tangible object or verifiable record that is commonly accepted as payment for goods and services as well as the repayment of debts, such as taxes, in a specific nation or socioeconomic setting is referred to as money.
Here,
Lynn has 54 pennies, 80 nickels, 22 dimes, 41 quarters, and 3 dollars.
1 Penny=1 cent
1 Nickel=5 cents
1 Dime=10 cents
1 Quarter=25 cents
1 dollar=100 cents
by this,
54 pennies=54*1=54 cents
80 nickels=80*5=400 cents
22 dimes=22*10=220 cents
41 quarters=41*25=1025 cents
3 dollars=3*100=300 cents
The total money he has=54+400+220+1025+300
=1999 cents
100 cents make to 1 dollar.
so 1999 cents will make to 19.99 dollars.
According to the money conversion theory, which states that "the ratio between two currencies, which is known as a conversion rate and is most frequently used in foreign exchange markets, indicates how much of one currency must be exchanged for the value of another," he has 1999 cents, which is approximately equal to $20.
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Diego is trying to write the expression 2 + 1 - in a way that makes it easier tocalculate. He says, “I can switch the order of 1 and and write 2+- 1 then I canget an equivalent expression that's easier to compute.Do you agree with Diego's reasoning? Why or why not?
While switching the order during adding or substraction,
How many radians are equal to 180 degrees 2piPi 1 2
Given: An angle of 180 degrees.
Required: To find the measure of the given angle in radians.
Explanation: The degree and radians measure of an angle is related by the following relation
[tex][/tex]I need help to simplify 3x (x² - x - 2) + 2x (3 - x) - 7x. I've tried to solve the problem three times and have gotten 2x² - 2x - 6, then, x² - 1x - 6, then, 3x³ - 5x² - 13x, I can't figure out what I'm doing wrong.
Given the initial expression,
[tex]3x(x^2-x-2)+2x(3-x)-7x[/tex]Simplify it as shown below
[tex]\begin{gathered} =3x*x^2-3x*x-3x*2+2x*3-2x*x-7x \\ =3x^3-3x^2-6x+6x-2x^2-7x \end{gathered}[/tex][tex]\begin{gathered} =3x^3-3x^2-2x^2-7x \\ =3x^3-5x^2-7x \end{gathered}[/tex]Thus, the answer is 3x^3-5x^2-7xO GEOMETRY Perimeter involving rectangles and circles A rectangular paperboard measuring 20 in long and 13 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.) Explanation +0 13 in 20 in Check 0 in X in² 5 in³ 3/5 ? Nikida E: 6 C E E 121
The perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
It is given to us that the measurement of rectangular paperboard are -
Length = 20in
Width = 13in
A semicircle is cut out of it.
We have to find out the perimeter of the paperboard that remains after the semicircle is removed.
Now, according to the given figure,
Radius of the semi circle = 1/2 (Width of the paperboard) ---- (1)
Let us say the radius of the semi circle is "[tex]r[/tex]".
So, from equation (1),
[tex]r = \frac{13}{2}\\ = > r = 6.5[/tex] in ---- (2)
Now, Perimeter of the paperboard that remains after the semicircle is removed =
Bottom length + Left width + Top length + Right circumference of the semicircle
= 20 + 13 + 20 + ([tex]\pi r^{2}[/tex]) [Circumference of semicircle = [tex]\pi r^{2}[/tex]]
= 53 + [[tex]\pi (6.5)^{2}[/tex]] [From equation (2), we have [tex]r = 6.5[/tex] in]
= 53 + 132.66
= 185.66 in
Thus, the perimeter of the paperboard that remains after the semicircle is removed is 185.66in.
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Enter the equation of the circle with the given center and radius. Center: (7,0); radius: 3 The equation is
Given data:
The given coordinate of centre of the circle is (7,0).
The given radius of the circle is r=(3)^(1/2).
The equation of the circle is,
[tex]\begin{gathered} (x-7)^2+(y-0)^2=(\sqrt[]{3})^2 \\ (x-7)^2+y^2=3 \end{gathered}[/tex]Thus, the equation of the circle is (x-7)^2 +y^2 =3.
what digit is in the
SOLUTION
Given the question in the image, the following are steps to solve the question.
Step 1: Write out the given function to be plotted on the graph.
[tex]x=6[/tex]Step 2: Plot the function on the graph. Please note that x=6 means that the line on the graph will pass through the point where x-axis is equal to 6. This can be better explained on the graph below.
The red line passing through x-axis at point 6 indicates x=6.
Which graph fits this line? O y= 2x + 1 O A O D. B. x / X E. # Oc. *
Answer: Option A
Given the above equation
y = 2x + 1
Firstly, we need to find the y and x - intercepts
To find y - intercept, make x = 0
y = 2(0) + 1
y = 0 + 1
y = 1
To find x - intercept, put y = 0
0 = 2x + 1
Collect the like terms
0 - 1 = 2x
-1 = 2x
Divide both sides by 2
2x = -1
2x/2 = -1/2
x = -1/2
Therefore, x = -1/2 and y = 1
(-1/2, 1)
Step 2: Graph the point
2 and the probability that event A occurs given 2 In an experiment, the probability that event B occurs is 3 6 that event B occurs is 7 What is the probability that events A and B both occur? Simplify any fractions.
In order to find the probability that events A and B both occurs, we can use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]So we have that:
[tex]\begin{gathered} \frac{6}{7}=\frac{P(A\cap B)}{\frac{2}{3}} \\ 7\cdot P(A\cap B)=6\cdot\frac{2}{3} \\ 7\cdot P(A\cap B)=4 \\ P(A\cap B)=\frac{4}{7} \end{gathered}[/tex]What is the average value of -2/5, 7/10, 1/2, -1/5
The average of numbers is equal to sum of values to number of values.
Determine the average value of observations.
[tex]\begin{gathered} a=\frac{-\frac{2}{5}+\frac{7}{10}+\frac{1}{2}-\frac{1}{5}}{4} \\ =\frac{\frac{-4+7+5-2}{10}}{4} \\ =\frac{\frac{6}{10}}{4} \\ =\frac{3}{20} \end{gathered}[/tex]So average value of the numbers is 3/20.
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
A trail mix recipe asks for 4 cups of raisins for every 6 cups of peanuts. Write a proportional equation where r represents the amount of raisins, and p represents the amount of peanuts.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
In this problem we have
p=kr
step 1
Find the value of k
k=p/r
we have the ordered pair (4,6)
substitute
k=6/4
k=1.5
therefore
the proportional equation is
p=1.5rGraph g(x)= 2|x-2|-3 and the parent function f(x)=|x|. Describe the transformations that occurred from f(x) to g(x). Then, describe the domain and range.
The first thing to do is to graph both equations, as follows:
It is possible to check from the equations that there is no restriction for the value of x in both equations, and from the graph, we see that for each value of x, there is always a value of Y well defined. For this reason, we are able to conclude that the domain of both equations is all the real numbers.
Now, for the range of each, we can see that the values of Y for both are restricted to real numbers higher than the minimum value. For equation g(x), the range is the real numbers higher or equal to -3, while for f(x) the range is the real numbers higher or equal to 0.
Two buses leave town 1404 kilometers apart at the same time and travel toward each other. one bus travels 12 km/h faster than the other. if they meet in 6 hours, what is the rate of each bus?rate of faster bus: km/hrate of slower bus: km/h
Let rate of faster bus be x km/h and rate of slower bus be y km /hr.
The relation between rate of slower and faster bus is,
[tex]x=y+12[/tex]Two bus are travelling in opposite direction so relative speed is,
[tex]x+y[/tex]Two buses meet in 6 hours so,
[tex]\begin{gathered} (x+y)\cdot6=1404 \\ x+y=234 \end{gathered}[/tex]Substitute y + 12 for x in the equation to obtain the value of y.
[tex]\begin{gathered} y+12+y=234 \\ 2y=234-12 \\ y=\frac{222}{2} \\ =111 \end{gathered}[/tex]Determine the value of x.
[tex]\begin{gathered} x=111+12 \\ =123 \end{gathered}[/tex]So answer is,
Rate of faster bus is 123 km/hr
Rate of slower bus is 111 km/hr.
Can you help me find the discriminant of this quadratic question aswell as the number and type of solutions?Problem: 2x^2+2=-5x
Given the quadratic equation:
[tex]2x²+2=-5x[/tex]we can write it like this:
[tex]2x²+5x+2=0[/tex]the discriminant is the expression b²-4ac. In this case, a = 2, b = 5 and c = 2, then, the discriminant is:
[tex]b²-4ac=(5)²-4(2)(2)=25-16=9[/tex]notice that the discriminant is 9 > 0, therefore, the quadratic function has two real solutions
I need help finding point slope form
We were given two points to find the equation of the line, these are (4,3) and (5,5).
We need to find the point-slope form, which can be writen as follow:
[tex]y-y_1=m\cdot(x-x_1)_{}[/tex]Where (y1,x1) is one point on the line and "m" is the slope of the line. We first need to find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (y1,x1) and (x2,y2) are the two known points. We can find the slope by applying the two points given to us:
[tex]m=\frac{5-3}{5-4}=2[/tex]We can know write the expression of the line:
[tex]y-5=2\cdot(x-5)[/tex]f(x) = 2x^3+4x^2+2x+1g(x) = x^3 –x^2+7x+9Find (f+g)(x):
Let's rewrite the functions:
[tex]\begin{gathered} f(x)=2x^3+4x^2+2x+1 \\ g(x)=x^3-x^2+7x+9 \end{gathered}[/tex]To get (f+g)(x), we just add them together:
[tex](f+g)(x)=f(x)+g(x)=2x^3+4x^2+2x+1+x^3-x^2+7x+9[/tex]We can simplify be pairing the terms with the same order:
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x)=2x^3+x^3+4x^2-x^2+2x+7x+1+9= \\ =(2+1)x^3+(4-1)x^2+(2+7)x+10=3x^3+3x^2+9x+10 \end{gathered}[/tex]So:
[tex](f+g)(x)=3x^3+3x^2+9x+10[/tex]write in slope intercept form and identity the slope and y intercept. a. x/3 + y/2 = 1b. 4x -3y + 2 =0c. x - y = 5(x - y)
Consider that the slope-intercept form of the straight line with slope (m) and y-intercept (c) is given by,
[tex]y=mx+c[/tex]a.
Modify the given equation as,
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=1 \\ \frac{y}{2}=-\frac{x}{3}+1 \\ y=-\frac{2}{3}x+2 \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=-\frac{2}{3}x+2[/tex]b.
Modify the given equation as,
[tex]\begin{gathered} 4x-3y+2=0 \\ 3y=4x+2 \\ y=\frac{4}{3}x+\frac{2}{3} \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=\frac{4}{3}x+\frac{2}{3}[/tex]c.
Modify the given equation as,
[tex]\begin{gathered} x-y=5(x-y) \\ x-y=5x-5y \\ 5y-y=5x-x \\ 4y=4x \\ y=x \end{gathered}[/tex]Thus, the equation in slope-intercept form can be written as,
[tex]y=x[/tex]6.Subtraction Solve: 4t+5=k t=6
We have the following:
[tex]\begin{gathered} 4t+5=k \\ t=6 \end{gathered}[/tex]replacing and solving:
[tex]\begin{gathered} 4\cdot6+5=k \\ k=24+5 \\ k=29 \end{gathered}[/tex]The value of k is 29
Write an expression for the measure of the given angle
Solution:
Remember that the angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference. According to this, we can deduce the following expression for the measure of the given angle:
[tex]m\angle UXY=\frac{arc\text{ }UZW}{2}[/tex]find the slope of the line. 5x-2y=7
Thus 5/2 is the slo
Solve and graph on a number line x - 2 > -5 and x - 2 < 4
ANSWER
Interval notation: (-3, 6)
Inequality form: -3 < x < 6
Number Line Graph:
EXPLANATION
[tex]\begin{gathered} x\text{ - 2 > - 5 OR x - 2 < 4} \\ x\text{ > - 5 + 2 OR x < 4 + 2} \\ x\text{ > -3 OR x < 6} \\ \end{gathered}[/tex]Hence, -3 < x < 6
17% of 800 is what number?
We want to obtain ;
[tex]17\text{ \% of 800}[/tex]That number would be
[tex]\begin{gathered} \frac{17}{100}\times800=\text{ }\frac{17\times800}{100} \\ =136 \end{gathered}[/tex]Therefore, 17% of 800 is 136.
Instructions: For the following real-world problem, solve using any method. Use what you've learned to determine which method would be best. Put your answer in the context of the problem and determine the appropriate final answer. A sprinkler is set to water the backyard flower bed. The stream of water and where it hits the ground at the end of the stream can be modeled by the quadratic equation -22 + 14x + 61 = 0 where x is the distance in feet from the sprinkler. What are the two solutions in exact form? 2 x V X or What are the rounded values (to two decimal places)? Which of these answers makes sense in context to be the value of the number of products? x =
Given the next quadratic equation:
[tex]-x^2+14x+61=0[/tex]we can use the quadratic formula to solve it, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-14\pm\sqrt[]{14^2-4\cdot(-1)\cdot61}}{2\cdot(-1)} \\ x_{1,2}=\frac{-14\pm\sqrt[]{196+244}}{-2} \\ x_{1,2}=\frac{-14\pm\sqrt[]{440}}{-2} \\ x_1=\frac{-14+\sqrt[]{440}}{-2}=\frac{-14}{-2}-\frac{\sqrt[]{440}}{2}=7-\sqrt[]{110} \\ x_2=\frac{-14-\sqrt[]{440}}{-2}=\frac{-14}{-2}+\frac{\sqrt[]{440}}{2}=7+\sqrt[]{110} \end{gathered}[/tex]The rounded values (two decimal places) are:
[tex]\begin{gathered} x_1=7-10.49=-3.49 \\ x_2=7+10.49=17.49 \end{gathered}[/tex]Since x is the distance, in ft, from the sprinkler, it cannot be negative, then the answer which makes sense in the context of this problem is 17.49 ft
Find the X-intercept and Y-Intercept of the line. Write your answer as exact values. do not write your answer as order pairs
The equation of the line is given as,
[tex]8x-5y=14[/tex]The intercepts are the points at which the curve intersects the coordinate axes.
The x-intercept of the line will be the value of 'y' at which the x-coordinate becomes zero. This can be calculated as follows,
[tex]\begin{gathered} 8x-5(0)=14 \\ 8x=14 \\ x=\frac{7}{4} \\ x=1.75 \end{gathered}[/tex]Similarly, the y-intercept is the point at which the line intersects the y-axis. This can be calculated as,
[tex]\begin{gathered} 8(0)-5y=14 \\ -5y=14 \\ y=\frac{-14}{5} \\ y=-2.8 \end{gathered}[/tex]Thus, the x-intercept and y-intercept are obtained as,
[tex]\begin{gathered} \text{ x-intercept}=1.75 \\ \text{ y-intercept}=-2.8 \end{gathered}[/tex]The triangle ABC shown on the coordinate plane below,is dilated from the origin by scale factor= 1/2. what is the location of triangle A'B'C'?
Explanation:
With a dialation about the origin of a scale factor of 1/2 every point of the dialated figure is now one half of the points from the original figure:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]We have this points:
• A: (3, 4)
,• B: (-7, 2)
,• C: (2, 2)
The new coordinates of these points will be:
Answer:
• A': (1.5, 2)
,• B': (-3.5, 1)
,• C': (1, 1)
1.) Your 3 year investment of $20,000 received 5.2% interested compounded semi annually. What is your total return? ASW
Let's begin by listing out the information given to us:
Principal (p) = $20,000
Interest rate (r) = 5.2% = 0.052
Number of compounding (n) = 2 (semi annually)
Time (t) = 3 years
The total return is calculated as shown below:
A = p(1 + r/n)^nt
A = 20000(1 + 0.052/2)^2*3 = 20000(1 + 0.026)^6
A = 20000(1.1665) = 23,330
A = $23,330
I know the first part but having trouble on the second part
Take into account that the standard deviation of a probability distribution table is given by:
[tex]\sigma=\sqrt[\placeholder{⬚}]{\Sigma\left(x-\mu\right)^2P\left(x\right)}[/tex]where x is each element of the first column of the table, μ is the mean and P(x) is the corresponding values of P(x) for each value of x in the second column.
By replacing the values of the table you obtain:
[tex]\begin{gathered} \sigma=\sqrt[\placeholder{⬚}]{\left(0-3.79\right)^2\lparen0.04)+\left(1-3.79\right)^2\left(0.23\right)+\left(3-3.79\right)^2\left(0.35\right)+\left(6-3.79\right)^2\left(0.15\right)+\left(7-3.79\right)^2\left(0.23\right)} \\ \sigma=\sqrt[\placeholder{⬚}]{5.6859} \\ \sigma\approx2.38 \end{gathered}[/tex]Hence, the standard deviation of the given data is approximately 2.38
Kristy is paid semimonthly. The net amount of each paycheck is$750.50. What is her net annual income?a. $18,012b. $4,503c. $19,513d. $9,006
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define semimonthly
A semimonthly payroll is paid twice in a month.
STEP 2: Calculate the net annual income
[tex]\begin{gathered} Net\text{ annual income means the total money received in a year.} \\ \text{If net amount of each paycheck is \$750.50 and it is a semimonthly payment, then;} \\ \text{monthly payment=\$750.50}\times2=\text{\$}1501 \\ \\ There\text{ are 12 months in a year,} \\ \text{If Kristy earns in month, then the amount earned in a year is:} \\ 12\times\text{\$1501=\$18,012} \end{gathered}[/tex]Hence, her net annual income will be $18,012
OPTION a
Please help me I don’t know how to solve this :(
You have already found the slope, which is 2
m =( y2-y1)/(x2-x1)
= (9200-9000)/(225-125)
= 200/100
= 2
The question tells us that it is a linear function
y = mx +b is the slope intercept form of a linear function
m is the slope and b is the initial value
c(n) = mn+b
c(n) = 2n+b
Using one of the points in the table we can find b
(125,9000)
9000 = 2(125) +b
9000 = 250+b
9000-250 = b
8750 = b
The initial value is 8750
This is also the estimate of c(0) because the initial value is when n=0
We can write the equation
c(n) = fixed cost + unit cost * number of units
The fixed cost is the initial value
the unit cost is the slope or m
c(n) = 8750 + 2n
Find the measure of Zx in the triangle.
21°
The measure of Zx is
(Simplify your answer. Type an integer or a decimal.)
...
The third angle of the triangle is 87°.
The Pythagorean Theorem is used for finding the length of the hypotenuse of a right triangle.
Pythagoras was a Greek mathematician who discovered that on a triangle abc, with side c being the hypotenuse of a right triangle (the opposite side to the right angle), that: a² + b² = c².Formula for the Base of an Isosceles Triangle
If you know the side length and height of an isosceles triangle, you can find the base of the triangle using this formula: b = 2√a² - h²Equate the sum of all the angle which is equal to 180°.
Sum of triangle = 180°
∠A + ∠B + ∠C =180°
21° + 72° + x = 180°
93° + x = 180°
x = 180° - 93°
x = 87°
Hence, the third angle of the triangle is 87°.
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