hello
let's write out all the numbers from 20 - 40
[tex]20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]what we need to find out here is basically all the numbers having unit digit (ones) from 3 upwards for the 20's and 4 upwards for the 30's
if we count carefully, we have 13 numbers in there that the units (ones) are greater than the tens digit
During the year Juanita spend $480 for electricity she paid the same amount each month how much did she pay monthly for electricity 1 year =12 month’s
Given:
The electricity bill year = $480
Find-:
How many amounts each month
Explanation-:
The amount is
[tex]1\text{ Year}=480[/tex]In 1 Year is 12 months.
[tex]\begin{gathered} 1\text{ Year}=12\text{ Months} \\ \\ 1\text{ Year}=480 \\ \\ 12\text{ Months}=480 \\ \\ 1\text{ Month}=\frac{480}{12} \\ \\ \end{gathered}[/tex]The 1 Month's salary is
[tex]\begin{gathered} 1\text{ Month}=\frac{480}{12} \\ \\ 1\text{ Month }=40 \end{gathered}[/tex]So, each month's bill is $40.
The box contains red, white, and blue balls. The probability of pulling a red ball out of the box is 1/4,White - 3/20. Calculate the probability that one ball accidentally pulled out is:(a) blue; (b) red or white; (c) red or blue; (d) not white.
We have to find the listed probabilities.
We have red, white and blue balls.
Red balls have a probability of 1/4.
White balls have a probability of 3/20.
The complement of these probabiities correspond to blue balls.
a) We then can calculate the probability of a blue ball by calculating 1 minus the probability of not being a blue ball, which means red or white.
We can do it as:
[tex]\begin{gathered} P(B)=1-P(not\text{ }B) \\ P(B)=1-(P(R)+P(W)) \\ P(B)=1-(\frac{1}{4}+\frac{3}{20}) \\ P(B)=1-\frac{5+3}{20} \\ P(B)=1-\frac{8}{20} \\ P(B)=\frac{20-8}{20} \\ P(B)=\frac{12}{20} \\ P(B)=\frac{3}{5} \end{gathered}[/tex]b) We now have to calculate the probability of the ball being red or white.
As it can be either of the two we can add the probabilities:
[tex]\begin{gathered} P(R\cup W)=P(R)+P(W) \\ P(R\cup W)=\frac{1}{4}+\frac{3}{20} \\ P(R\cup W)=\frac{8}{20} \\ P(R\cup W)=\frac{2}{5} \end{gathered}[/tex]NOTE: It could have also being calculated as the complement of the probability of the ball being blue.
c) We now calculate the probability that the ball is red or blue. We will calculate it as the complement of the ball being white:
[tex]\begin{gathered} P(R\cup B)=1-P(W) \\ P(R\cup B)=1-\frac{3}{20} \\ P(R\cup B)=\frac{20}{20}-\frac{3}{20} \\ P(R\cup B)=\frac{17}{20} \end{gathered}[/tex]d) In this case, we will got the same result as in (c), as the event of the ball being red or blue its the same event as the ball being not white. So the probability is:
[tex]P(not\text{ W})=P(R\cup B)=\frac{17}{20}[/tex]Answer:
a) 3/5
b) 2/5
c) 17/20
d) 17/20
Use the system of equations below to answer the questions 1-4. -2x + y = 4 2x + 3y = 20 1) Which of the following problems is created by using the elimination method on the system above? a) 4x + 4y = 24 b) 4y = 24 c) -4x + 3y = 24 d) -2y = 16 Ha a "79.4 2) Find the value of y. Show ALL of your work. O 3) Find the value of x. Show ALL of your work. W O P II search
To answer this question, we can proceed as follows:
1. We need to solve the next system of linear equations using the elimination method.
In this method, we can eliminate one of the variables from the system adding both equations, and previously (in some cases) multiply one of the equations by a number.
Then, we can solve this system as follows:
After adding both equations, we can eliminate the variable x. We do not need to multiply one of the equations by any number since -2x+2x = 0. We obtain a value for y after adding y + 3y = 4y, and 4 + 20 = 24. We solved the equation for y, and finally, we got y = 6.
In part 1, we have that the problem created by using the elimination method is option b:
4y = 24 (as we obtained above).
2. The value for y is given above, and this value is y = 6.
3. To obtain the value for x, we can substitute the value of y in the second equation of the given system, that is:
[tex]2x+3(6)=20\Rightarrow2x+18=20[/tex]To solve this equation, we can subtract 18 from both sides of the equation:
[tex]2x+18-18=20-18\Rightarrow2x+0=2\Rightarrow2x=2[/tex]Finally, to find the value for x, we need to divide both sides of the equation by 2:
[tex]2x=2\Rightarrow\frac{2x}{2}=\frac{2}{2}\Rightarrow x=1[/tex]In summary, we have that the values for x = 1, and for y = 6, using the elimination method above.
Consider the line x+9y= -5Find the equation of the line that is parallel to this line and passes through the point (6, 1)Find the equation of the line that is perpendicular to this line and passes through the point (6, 1) Equation of the parallel line: Equation of the perpendicular line:
We want to write a parallel line and another perpendicular to
[tex]x+9y=-5[/tex]That passes through the point (6, 1).
Parallel lines have the same slope. To determinate the slope of our line, let's rewrite it in slope intercept form. The slope intercept-form is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
Rewritting our line:
[tex]\begin{gathered} x+9y=-5 \\ 9y=-x-5 \\ y=-\frac{x}{9}-\frac{5}{9} \end{gathered}[/tex]The slope of this line is -1/9.
The set of parallel lines, since they have the same slope, have the following form
[tex]y=-\frac{x}{9}+c[/tex]The y-intercept of our desired parallel line can be determinated by using the point we know that it belongs to the parallel line. Making the substitution, we have
[tex]\begin{gathered} 1=-\frac{6}{9}+c \\ \Rightarrow c=\frac{15}{9}=\frac{5}{3} \end{gathered}[/tex]The equation for the parallel line is:
[tex]y=-\frac{x}{9}+\frac{5}{3}[/tex]For the perpendicular line, the idea is almost the same. The difference is the slope is not the same, it is minus the inverse of our line.
[tex]m_{\perp}=-(m)^{-1}\Rightarrow m_{\perp}=-(\frac{-1}{9})^{-1}=9[/tex]The set of perpendicular lines is
[tex]y=9x+d[/tex]The y-intercept of our desired pperpendicular line can be determinated by using the point we know that it belongs to the perpendicular line. Making the substitution, we have
[tex]\begin{gathered} 1=9\times6+d \\ 1=54+d \\ d=-53 \end{gathered}[/tex]The equation for the perpendicular line is:
[tex]y=9x-53[/tex]Answer: y=1/9x+5/3
Step-by-step explanation:
1. What is the value of 3/10 + 3/100?a. 43/100 b. 33/100 c. 33/10 d. 6/10
Explanation:
The question asked to solve the expression below
[tex]\frac{3}{10}+\frac{3}{100}[/tex]Step 1:
Find the L.C.M of 10 and 100
The L.C.M od 10 and 100 is
[tex]=100[/tex]Step 2:
Simplify the expression to get a single fraction below as
[tex]\begin{gathered} \frac{3}{10}+\frac{3}{100} \\ \frac{30+3}{100} \\ =\frac{33}{100} \end{gathered}[/tex]Hence,
The final answer is
[tex]\frac{33}{100}[/tex]OPTION B is the correct answer
The coordinates of three vertices of a square are (1, 4), (1, 8) and (4, 4). What are the coordinates of the fourth vertex?
Three vertices of a rectangle are located at (1, 4), (1, 8), and (4,4),
The figure is shown below:
From (1, 4) to (4, 4) there are 4 - 1 = 3 units.
From (1, 4) to (1, 8) there are 8 -4 = 4 units
The fourth point must be located at (4, 8):
A. The graph of g(x) is 12 units below the graph of f(x).B. The graph of g(x) is 12 units to the right of the graph of f(x).C. The graph of g(x) is 12 units above the graph of (x).D. The graph of g(x) is 12 units to the left of the graph of (x).
We are given an initial function:
[tex]f(x)=x^2[/tex]And we are given the function:
[tex]g(x)=(x-12)^2[/tex]The relationship between the two functions is the following:
[tex]g(x)=f(x-12)[/tex]When we have this type of relationship:
[tex]g(x)=f(x-a)[/tex]This means that the graph of g(x) is the translation of "a" units to the right of the graph of f(x).
Therefore, the graph of g(x) is 12 units to the right of the graph of f(x)., The right answer is B
in the formula A=1/2h•b solve for b
hello
to solve this problem, we'll make b the subject of formula
[tex]a=\frac{1}{2}h\times b[/tex]step 1
multiply both sides by 2
this is done so as to eliminate 1/2 on that side of the equation
[tex]\begin{gathered} a=\frac{1}{2}h\times b \\ 2\times a=2\times(\frac{1}{2}hb) \\ 2a=hb \end{gathered}[/tex]step 2
divide both sides by h
this done to make b the subject of formula
[tex]\begin{gathered} 2a=hb \\ \text{divide both sides by h} \\ \frac{2a}{h}=\frac{hb}{h} \\ b=\frac{2a}{h} \end{gathered}[/tex]therefore, b = 2a / h
A new eye clinic sold 47 pairs of eyeglasses the 1st month it was open. Thenumber of pairs of eyeglasses sold increases by 25% each month thereafter.The equation f(x) = 47(1.25)*1 gives the number of pairs of eyeglasses soldeach month after the clinic's opening.About how many pairs of eyeglasses will be sold in the 10th month?
We have that the function that describes the number of eyeglasses sold is :
[tex]f(x)=47\cdot(1.25)^x[/tex]after 10 months, we have that the glasses sold are
[tex]f(10)=47\cdot1.25^{10}\approx438[/tex]your job in a company is to fill quart sized bottles of oil from a full 25 gallon of oil drum . then you are to pack 6 quarts of many cases of oil can you get from a 25 drum of oil?
To determine the cases of oil can you get from a 25 drum of oil:
Step 1: 1 gallon = 4 quarts
Hence from 25 gallon oil drum, 25 x 4 = 100 quart-size bottles can be filled.
Step 2: One case will pack 6 quart size bottles.
[tex]\begin{gathered} 1\text{ gallon}\Rightarrow\text{ 4 quarts} \\ 25\text{ gallon }\Rightarrow\text{ 25 x 4 = 100 quarts} \end{gathered}[/tex]1 case will pack 6 quarts
[tex]\begin{gathered} 1\text{ case }\Longrightarrow\text{6 quarts} \\ x\text{ case }\Longrightarrow\text{ 100 quarts} \\ 6x=100 \\ x=\frac{100}{6} \\ x=16.67\text{ cases} \\ x\approx17\text{ cases} \end{gathered}[/tex]Therefore number of cases from a 25 drum of oil = 17 cases of oil
Hence the correct answer is Option B
A Mason lays 84 bricks in 4 hours. At this rate how many bricks can he lay in 9 hours?
Manson lays 84 bricks in 4 hours
In 1 hour, he will lay 84/4 = 21 bricks
The work rate per hour is 21 bricks per hour
In 9 hours, he will lay 21 x 9 = 189 bricks
The answer is 189 bricks
funtion 1 is defined by the equation y = -2t+6funtion 2 is defined by line h shown on the graph which funtion has a more negative slope
To determine which function has a more negative slope we have to calculate the slope of line h, with the following expression and two points given in the graph:
(0, 4) (4, 0)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-4}{4-0} \\ m=-\frac{4}{4}=-1 \end{gathered}[/tex]The slope of line h is -1, and for function 1 we know that the slope-intercept form is given by:
y=mx+b
where, m is the slope of the line, so in this case the slope is -2.
So, the slope of function 1, -2 is more negative than function 2 (line h).
3 3/8 divided by 3/4 using cross multiplication algorithm
Answer
3 3/8 ÷ (3/4) = (9/2) = 4 ½
Explanation
We are asked to evaluate 3 3/8 divided by 3/4 using cross multiplication algorithm.
The algorithm will need us to put the mixed fraction in definite fraction form (improper fraction) and to evaluate the division, we change the division sign into multiplication sign and the fraction after the division sign changes into its reciprocal.
3 3/8 = (27/8)
(3 3/8) ÷ (3/4)
= (27/8) ÷ (3/4)
[tex]\begin{gathered} \frac{27}{8}\div\frac{3}{4} \\ =\frac{27}{8}\times\frac{4}{3} \\ =\frac{108}{24} \\ \text{Divide numerator and denominator by 12} \\ \frac{108}{24}=\frac{9}{2} \end{gathered}[/tex]Hope this Helps!!!
May I please get help with part a? I have tried multiple ways to find the answers but still could not get the correct answers
Use the fact that the sum of the three angles of any triangle is equal to 180 degrees.
Consider triangle ABC.
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The formula for the slope(m) is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let us solve for the slope of PQ
[tex]\begin{gathered} P\rightarrow(-2,4) \\ Q\rightarrow(4,5) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Slope(m)=}\frac{\text{5-4}}{4--2}=\frac{1}{4+2}=\frac{1}{6} \\ \therefore Slope\text{ of PQ=}\frac{1}{6} \end{gathered}[/tex]Let us now solve for the slope of RS
[tex]\begin{gathered} R\rightarrow(4,2) \\ S\rightarrow(-2,0) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Slope of RS=}\frac{\text{0-2}}{-2-4}=\frac{-2}{-6}=\frac{1}{3} \\ \therefore\text{Slope of RS}=\frac{1}{3} \end{gathered}[/tex]Hence, the slope of line PQ is 1/6 and the slope of RS is 1/3 so figure PQRS is not a parallelogram because opposite sides are not parallel.
Larry found a house for $120,500. He pays a 20% down payment. How much does Larry pay for the down payment? I assume 120,450?
Larry found a house for $120,500. He pays a 20% down payment. How much does Larry pay for the down payment?
we have that
$120,500 ------> represents 100%
20%=20/100=0.20
Multiply $120,500 by 0.20
120,500*0.20=$24,100
the answer is $24,100a cell phone company dropped the prices on their phones by 9% how would you write the expression of the new price of the phones
let the old price be x
9% of the old price= 9/100 X x = 0.09x
so the new price will now be x - 0.09x
Question 7Points 2Find whether the function y =-2x2 - 4x + 7 opens upward or downward. Also, fincwhether it has a maximum or minimum point.
First, let's compare the given equation with the standard form of a quadratic equation, so we can find the parameters a, b and c:
[tex]\begin{gathered} y=ax^2+bx+c\\ \\ y=-2x^2-4x+7\\ \\ a=-2,b=-4,c=7 \end{gathered}[/tex]The value of a indicates if the graph opens upward or downward:
a > 0: graph opens upward.
a < 0: graph opens downward.
Since a = -2 is negative, the graph opens downward.
Also, if the graph opens downward, the vertex of the graph is a maximum point.
Therefore the correct option is the third one.
11) y = V.x - 1 A) Domain: { All real numbers. } Range: { All real numbers. } B) Domain: xs-1 Range: y = 0 C) Domain: 1 z 1 Range: y = 0 D) Domain: x 20 Range: y 2-1
the square root function is defined for:
[tex]D\colon\mleft\lbrace x\in R\colon x\ge0\mright\rbrace[/tex]In this sense, the output values will be greater than or equal to 0, however, since the graph is translated 1 unit down, the range is:
[tex]R\colon\mleft\lbrace x\in R\colon y\ge-1\mright\rbrace[/tex]The graph of g(x) is a translation of y = 3x.Which equation represents g(x)?O g(x) = 3 x-454+Og(x) = 3x + 432+9.O g(x) = }+ 1.51+Og(x) = 3/- 1.5-10 -8 -6 -4 -24N68 10 x-3-5
Take into account that g(x) is a horizontal translation of y.
Moreover, consider that a horizontal translation is given by the transformation of the form:
y => g(x - a)
where g(x-a) is y translated a units to the right.
Then, based on the given graph, you can conclude:
[tex]g(x)=\sqrt[3]{x-4}[/tex]can you please explain ratios and rational numbers to me? im not really smart and im a very disappointing kid to my folks
A ratio is simply the way we compare things quantitatively. For instance, if the number of shoes a student has is 6 and the number of books he has is 20. We can use ratios to compare the two quantities.
We say, the ratio of shoes to books is 6:20, the colon sign is used in-between, to separate the quantities.
Rational numbers are numbers that can be expressed in fractional forms. For instance, 0.5 can be expressed as 5/10 or 1/2. Therefore, it is a rational number.
Solve the following quadratic equation by applying square roots y=-2x^2+ 128
Given the equation:
[tex]\text{ y = -2x}^2\text{ + 128}[/tex]In solving the quadratic equation by applying square roots, let's only focus at -2x^2 + 128 and disregard y, then we find x by generating this:
[tex]-2x^2\text{ + }128\text{ = 0}[/tex][tex]-2x^2\text{ = -128 }\rightarrow x^2\text{ = }\frac{128}{2}[/tex][tex]\text{ x}^2\text{ = 64 }\rightarrow\text{ x = }\sqrt[]{64}[/tex][tex]\text{ x = }\pm\text{ 8}[/tex]Therefore, the answer is letter D.
Angie ate 1/4 of a pizza with a diameter of 10 inches. How many square inches of pizza did she eat?
first let's find the are of the whole pizza
The pizza is circular in shape
So we can find its area using the formula of area of a circle
[tex]A=\pi r^2[/tex]where r is the radius
From the question, diameter = 10
Radius is half of diameter, hence r = 5 cm
Substitute the value of r = 5 and pie =22/7 in the formula and evaluate
[tex]A=\frac{22}{7}\times5^2[/tex][tex]=78.571[/tex]Since Angie ate 1/4 of the pizza, we will find 1/4 of 78.571
= 19.64 square inches
What is the best classification for 10.0 ?Whole numberIntegerRational numberNatural Number
the number 10 can be calssified as a natural number.
A natural number is any whole number from 1 upwards
natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,.............to infinity
Luella has a bag with three Hershey Kisses, two Reese's Cups, five York Peppermint Patties, and a Jolly Rancher. What is the probability that Luella will pull out a York Peppermint Pattie, replace it, and then pull out a Hershey Kiss? answer as a percent to the nearest tenth.
The probability is 15 percent
Explanation:The bag contains 3 Hershey Kisses, 2 Reese's Cups, 5 York Peppermint Patties, and a Jolly Rancher.
The probability of pulling out a York Peppermint Pattie is, replace it, and then pull out a Hershey Kiss is:
5/10 * 3/10 = 15/100
This is 15 percent
EQUATIONS AND INEQUALITIESSolving a word problem with two unknowns using a line
ANSWER
225 hamburguers
EXPLANATION
First, we have to name the variables:
• x: number of hamburgers sold
,• y: number of cheeseburgers sold
We know that they sold a total of 503, so one of the equations is x + y = 503.
Also, we know that the number of cheeseburgers is 53 more than the number of hamburgers, so the other equation is y = x + 53.
We have to solve the system,
[tex]\begin{cases}x+y=503 \\ y=x+53\end{cases}[/tex]Since we have to solve for x, we can use the substitution method. Replace y with the second equation in the first equation,
[tex]x+(x+53)=503[/tex]Add like terms,
[tex]\begin{gathered} (x+x)+53=503 \\ 2x+53=503 \end{gathered}[/tex]Subtract 53 from both sides,
[tex]\begin{gathered} 2x+53-53=503-53 \\ 2x=450 \end{gathered}[/tex]And divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{450}{2} \\ \\ x=225 \end{gathered}[/tex]Hence, 225 hamburgers were sold on Tuesday.
the table below show the number of jean sold at a store at different prices
Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital amount of C-14 (at time=t = 0)N== amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the fossile to the nearest year.
SOLUTION
We have been given the equation of the decay as
[tex]\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}[/tex]So we are looking for the time
Plugging the values into the equation, we have
[tex]\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}[/tex]Taking Ln of both sides, we have
[tex]\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}[/tex]Hence the answer is 4308 to the nearest year
twice the sum of a number and six.
Let x represent the number
Twice the number would be 2x
The expression for twice the sum of the number and 6 would be
2x + 6
I need help filling in the blank spaces. *clicking on the photo enhances quality*
Chebyshev's Theorem states that at least 3/4 of the data lie within two standard deviations of the mean; therefore, in our case, the answer to part 3 is k=2.
4) Calculating the interval within two standard deviations of the mean,
[tex]\begin{gathered} \bar{x}\pm2s \\ \Rightarrow\bar{x}+2s=120+2*15=150 \\ and \\ \bar{x}-2s=120-2*15=90 \end{gathered}[/tex]Thus, the answer to part 4) is 90 and 150