Given:
3(x-4)-5 = x - 3
Required:
To calculate which option is correct
Explanation:
[tex]\begin{gathered} 3(x-4)-5=x-3 \\ \\ 3x-12-5=x-3 \\ \\ 3x-17=x-3 \\ \\ 3x-x=-3+17 \\ \\ 2x=14 \\ \\ x=\frac{14}{2} \\ \\ x=7 \end{gathered}[/tex]Required answer:
Option D (x=7)
Suppose f(x) = x. Find the graph of f(x + 2).graph 1, 2, 3, or 4
-(1 – 7a) = 3(8a - 6)
Which is the better deal? Cheerios12 oz. for $ 1.9936 oz. for $2.5948 oz. for $3.9960 oz. $4.59
To calculate which is the best deal we must standardize all prices and compare them.
To do this we will divide the value by the number of ounces they have and thus choose the best one.
1.
[tex]\frac{1.99}{12}=0.165[/tex]2.
[tex]\frac{2.59}{36}=0.071[/tex]3.
[tex]\frac{3.99}{48}=0.083[/tex]4.
[tex]\frac{4.59}{60}=0.076[/tex]The price list by ounces would be as follows.
0.165
0.071
0.083
0.076
Best deal is number 2 0.071
Evaluate the expression when y= -4.y²-7y+2
Put y = -4 into the expression below:
[tex]y^2-7y+2[/tex]Hence,
[tex]\begin{gathered} y^2-7y+2=(-4)^2-7(-4)+2 \\ =16+28+2 \\ =46 \end{gathered}[/tex]Therefore, the value of the expression when y = -4 is 46
Use the Trapezoidal Rule to approximate ∫43ln(x2+9) dx using n=3. Round your answer to the nearest hundredth.
The Trapezoidal rule formula is given to be:
[tex]\begin{gathered} \int_a^bf(x)dx\approx\frac{\triangle x}{2}(f(x_o)+2f(x_1)+2f(x_2)+2f(x_3)+...+2f(x_{n-1})+f(x_n) \\ where \\ \triangle x=\frac{b-a}{n} \end{gathered}[/tex]The question gives:
[tex]\begin{gathered} f(x)=\ln(x^2+9) \\ a=3 \\ b=4 \\ n=3 \\ \therefore \\ \triangle x=\frac{1}{3} \end{gathered}[/tex]Therefore, divide the interval into n = 3 subintervals of length 1/3 with the following endpoints:
[tex]a=3,\frac{10}{3},\frac{11}{3},4[/tex]Evaluate the function at the endpoints:
[tex]\begin{gathered} f(x_0)=f(3)=2.89 \\ 2f(x_1)=2f(\frac{10}{3})=6.00 \\ 2f(x_2)=2f(\frac{11}{3})=6.22 \\ f(x_3)=f(4)=3.22 \end{gathered}[/tex]Sum up the calculated values and multiply by Δx/2:
[tex]\Rightarrow\frac{1}{3\times2}(2.89+6.00+6.22+3.22)=3.06[/tex]Therefore, the answer will be:
[tex]\int_3^4\ln(x^2+9)dx\approx3.06[/tex]Your sock drawer has 4 pairs of pink socks, 2 pairs of white socks, and 7 pairs of black socks. What is the probability that if you choose at random withough replacement you will not choose black socks 2 days in a row? a 1/12b 2/13c 3/8d 5/26
SOLUTION:
Case: Probability
Method:
To select socks that are not black without replacement,
Since there are a total of 6 pairs that are not black (NB)
[tex]\begin{gathered} Pr(NB) \\ =\frac{6}{13}\times\frac{5}{12} \\ =\frac{5}{26} \end{gathered}[/tex]Final answer:
5/26
16. – 2y+5=-1IIs 3 the solution?
We plug the value given to see tif the equation holds:
[tex]\begin{gathered} -2(3)+5=-1 \\ -6+5=-1 \\ -1=-1 \end{gathered}[/tex]Since the equation holds then, 3 IS the solution.
The average temperature on the planet A is 162°C. Convert this temperature to degrees Fahrenheit. Round to the nearestdegreeUse the formula F =+ 32162° Celsius is equivalent toFahrenheit.
Using the formula:
[tex]F=\frac{9}{5}c+32[/tex]We get:
[tex]\begin{gathered} F=\frac{9}{5}(162)+32 \\ F=323.6 \end{gathered}[/tex]162°C is equal to 323.6 F
The box plots represent the length of 100 randomly sampled commercial breaks for two different television stations Length of Commercial Breaks Channel 1 Channel 2 20 40 60 140 160 80 100 120 Time (seconds) Which statement about the difference in the medians of the two data sets is true?
Given data:
The length of the first commercial break is,
[tex]\begin{gathered} C_1=(120-90) \\ =30 \end{gathered}[/tex]The length of the second commercial break is,
[tex]\begin{gathered} C_2=(90-50) \\ =40 \end{gathered}[/tex]The expression for the diffrence compared to the first channel is,
Assume that random guesses are made for six multiple-choice questions on a test with five choices for each question so that there are n equals six trials each with the probability of success (correct) given by P equals 0.20. Find the probability of no correct answers.
Given in the question:
a.) Random guesses are made for six multiple-choice questions.
b.) There are five choices for each question.
c.) There are n equals six trials each with the probability of success (correct) given by P equals 0.20.
We will be using the Binomial Probability Formula:
[tex]P(X=k)=(_nC_k)(p^k)(1-p)^{n-k}[/tex]Where,
n = Number of trials = 6
P = Probability of success = 0.20
X = Correct answers
Let's evaluate the definition of binomial probability at k = 0 since we are tasked to find the probability of no correct answers.
[tex]P(X=0)=(_6C_0)(0.20^0)(1-0.20)^{6-0}[/tex][tex]P(X=0)\text{ = (}\frac{6!}{0!(6-0)!})(0.20^0)(0.80^6)^{}^{}[/tex][tex]P(X=0)\text{ = }0.262144\text{ }\approx\text{ 0.26}2[/tex]Therefore, the probability of no correct answers is 0.262 or 26.20%.
slove for y(13x-27)(9y + 19)(10x+6)
To obtain the value of y, we need to obtain the value of x first
Step 1: Finding x
(13x - 27) and (10x + 6) are equal (Alternate exterior angles)
so we can equate both angles
13x - 27 = 10x + 6
13x - 10x = 27 + 6
3x = 33
Divide both sides by 3
x = 33/ 3
x = 11
Step 2: Finding y
(9y + 19) and (10x + 6) are supplementary, hence they add up to 180
9y + 19 + 10x + 6 = 180
9y + 10x + 19 + 6 = 180
9y + 10x + 25 = 180
9y + 10x = 180 - 25
9y + 10x = 155
9y = 155 - 10x
substitute the value of x = 11 from step 1 into the equation
9y = 155 - 10 x 11
9y = 155 - 110
9y = 45
divide both sides by 9
y = 45/9
y = 5
1. An account is opened with a balance of $2800earning 4.25% simple interest. What will be thebalance in the account in 30 years?
Answer:
$6370
Explanation:
The simple interest formula gives us the final amount A given the principal amount P:
[tex]A=P(1+rt)[/tex]where r is the interest rate and t is the time interval.
Now in our case we have
P = 2800
r = 4.25/100
t = 30 years
therefore, the above formula gives
[tex]A=2800(1+\frac{4.25}{100}\cdot30)[/tex]which simplifies to give
[tex]\boxed{A=\$6370}[/tex]Hence, the account balance after 30 years will be $6370.
the chance of you having the same DNA as another person (other than an identical twin) is approximately 1 in 10 trillion (one trillion is a 1 by 12 zeros). Given the fraction,express this very small number using a negative power of 101/10,000,000,000,000
We are asked to write the quotient : 1/10,000,000,000,000 in a notation with powers of ten. This is called "scientific notation".
when we perform the division of 1 by that enormous number, we get:
0.0000000000001
This can be represented by a 10 to a negative exponent. Notice that we have 13 zeros in the denominator (which implies that we have to divide 13 times by ten)
so we can write the answer as: 1 * 10^(-13)
which with the appropriate equation editor becomes:
[tex]1\cdot10^{-13}[/tex]the base 10 with exponent -13 (negative 13)
Students in a science class recorded lengths of a stretched spring as shown in the table. Find the rate of change and explain what it means for this situation.
To find the rate of change;
Rate of change = change in y / change in x
= 10-0/ 2-0
=10/2
=5/1
=5
This means that the increase in w
Dustin boat traveled 36 miles downstream in three hours. The same boat traveled 30 miles upstream in five hours. What is the speed of the boat and the speed of the current
Answer:
The speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
Explanation:
Let's call x the speed of the boat and y the speed of the current.
The distance traveled is equal to the speed times the time, so the boat traveled 36 miles in three hours and we can write the following equation
(x + y)3 = 36
3(x + y) = 36
because when the boat traveled downstream, the total speed is the sum of x and y.
On the other hand, the boat traveled 30 miles upstream in 5 hours, so
(x - y)5 = 30
5(x - y) = 30
Therefore, the system of equations is
3(x + y) = 36
5(x - y) = 30
Solving the first equation for x, we get
[tex]\begin{gathered} 3(x+y)=36 \\ \\ \frac{3(x+y)}{3}=\frac{36}{3} \\ \\ x+y=12 \\ x+y-y=12-y \\ x=12-y \end{gathered}[/tex]Now, we can replace this expression on the second equation as follows
[tex]\begin{gathered} 5(x-y)=30 \\ \\ {\frac{5(x-y)}{5}}=\frac{30}{5} \\ \\ x-y=6 \\ \\ \text{ Replacing x = 12 - y} \\ 12-y-y=6 \\ 12-2y=6 \\ 12-2y-12=6-12 \\ -2y=-6 \\ \\ \frac{-2y}{-2}=\frac{-6}{-2} \\ \\ y=3 \end{gathered}[/tex]Then, the value of x is
x = 12 - y
x = 12 - 3
x = 9
So, the speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
Find the 38th term 359,352,345
Let's begin by listing out the information given to us:
1st term = 359, 2nd term = 352, 3rd term = 345
[tex]\begin{gathered} 359,352,345\ldots x_n \\ x_1=359,x_2=352,x_3=345 \\ x_1-x_2=x_2-x_3\Rightarrow359-352=352-345\Rightarrow7=7 \\ 7=7 \end{gathered}[/tex]This is an Arithmetic Progression (A.P.)
[tex]\begin{gathered} x_1=359 \\ x_2=359-7(2-1)\Rightarrow359-7(1)=359-7=352 \\ x_3=359-7(3-1)\Rightarrow359-7(2)=359-14=345 \\ x_n=x_1-7(n-1) \\ n_{38}=x_1-7(38-1)=359-7(37)=359-259=100 \\ n_{38}=100 \end{gathered}[/tex]USH financial is a small bank that is examining it’s customers use of its website. The numbers of online transactions made per day during the past 8 days are as follows.
Given:
The number of online transaction made per day during tha past 8 days are given as follows
51, 57, 71, 57, 55, 62, 51, 65
Find:
we have to find Mean, Median and mode of the given data.
Explanation:
(a)Mean
Mean of the given data is
[tex]\begin{gathered} Mean=\frac{51+57+71+57+55+62+51+65}{8} \\ Mean=58.6 \end{gathered}[/tex]Therefore, Mean is 58.6
(b) Median
Write the given data values in ascending order as following
51
51
55
57 Now n = 8
57 n/2 = 4
62 Median = Average of 4th and 5th items
65 Median = (57 + 57)/2 = 57
71
Therefore, Median is 57
(c)Mode
We know, the Mode is the value or values that occur most frequently.
Since 51 occurs 2 times and 57 also occurs 2 times.
Therefore, there are two modes, which are 51 and 57
Sue receives $7 per hour when she works at the book store. Last week she earned $259.How many hours did she work at her job?
1 hour = $7
Number of hours = Amount/7
Therefore, 259/7 = 37 hours
Solution: Sue worked for 37 hours last week.
my question:solve the equation or inequality.5t - 3 (7t + 1) < 93would the answer be 7 > -6?
Answer:
Explanation:
To solve the inequality for t, we first expand the left-hand side to get:
[tex]5t-21t-3<93[/tex]adding the like terms gives
[tex]-16t-3<93[/tex]adding 3 to both sides gives
[tex]-16t<96[/tex]At this point, we have to remember that dividing or multiplying an inequality by a negative number reverses its sign. So when we divide our inequality by -16, the inequality reverses sign and we get:
[tex]t>-\frac{96}{16}[/tex][tex]\boxed{\therefore t>-6.}[/tex]which is our answer!
Fidn the x intercept(s) and the coordinates of the vertex for the parabola y=x^2-8x+12 if there is more then one x intercept esperate them with commas!
To calculate the x-intercepts we replace y=0 and solve for x
[tex]x^2-8x+12=0[/tex]where a is 1, b is -8 and c 12
so factor the expression using
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]replacing
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(12)^{}}}{2(1)} \\ \\ x=\frac{8\pm\sqrt[]{64-48}}{2} \\ \\ x=\frac{8\pm\sqrt[]{16}}{2} \\ \\ x=\frac{8\pm4}{2} \\ \\ x=4\pm2 \end{gathered}[/tex]so x have two solutions because there are two x-intercepts
[tex]\begin{gathered} x_1=4+2=6 \\ x_2=4-2=2 \end{gathered}[/tex]then the x-intercepts are 6 and 2, the corrdinates are
[tex]\begin{gathered} (6,0) \\ (2,0) \end{gathered}[/tex]Vertex
the vertex is a point (x,y) to calculate x we use
[tex]x=\frac{-b}{2a}[/tex]and replace
[tex]\begin{gathered} x=\frac{-(-8)}{2(1)} \\ \\ x=\frac{8}{2}=4 \end{gathered}[/tex]now replace x=4 on the equation of the parable to find y
[tex]\begin{gathered} y=x^2-8x+12 \\ y=(4)^2-8(4)+12 \\ y=16-32+12 \\ y=-4 \end{gathered}[/tex]the coordinate of the vertex is
[tex](4,-4)[/tex]what is 6 5/6 as a decimal
the answer for 6 5/6
6.83
1 1 2. Consider 2 divided by 2 (a) Write a real-world problem for the division. (b) Create a model or write an equation for the division. (C) Find the quotient for the real-world problem in part (a). Show your work or explain your reasoning. Answer:
We will have the following:
a) His parents spent:
[tex]2.49\cdot6=14.94[/tex]So they spent $19.94.
b) They will spent the following in rental:
[tex]\frac{150}{8}=18.75[/tex]So, the hourly rate $18.75.
c) We will determine the amount spent:
[tex]182.53-150-14.49=18.04[/tex]So, it would be $18.04.
Need help solving question 34 via expanding and simplifying thanks
34. The equation is given as
[tex](x+y)^2-x(2-y)[/tex]Solving the equation by expanding and simplifying.
Use the identity,
[tex](a+b)^2=a^2+b^2+2ab[/tex][tex]x^2+y^2+2xy-2x+xy[/tex][tex]x^2+y^2-2x+3xy[/tex]Hence the answer is
[tex]x^2+y^2-2x+3xy[/tex]a backyard sandbox shaped like a right rectangular prisms is 0.45 meters high 2 m 2.6 m long if the sand is the box is 0.25 m deep what volume of sand is the box?
In order to determine the volume of the sand inside the box, take into account that the shape of the volume of the sand inside the box is the same that the rectangular prism. Then, you can use the folowing formula for the volume of the sand:
V = w·h·l
where w is the width, h the height and l the length. In this case, the height of the sand is 0.25m and the width and the length are the same of the box.
w = 2 m
l = 2.6 m
h = 0.25 m
replace the previous values of the parameters into the formula for V:
V = (2 m)(2.6 m)(0.25 m)
V = 1.3 m³
Hence, the volume of the sand inside the box is 1.3 m³
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each series with the equivalent series written in sima notation.
Step 1
Given;
Step 2
[tex]3(5)^0+3(5)^1+3(5)^2+3(5)^3+3(5)^4[/tex][tex]3+15+75+375+1875[/tex][tex]\begin{gathered} 4(8)^0+4(8)^1+4(8)^2+4(8)^3+4(8)^4 \\ 4+32+256+2048+16348 \end{gathered}[/tex][tex]\begin{gathered} 2(3)^0+2(3)^1+2(3)^2+2(3)^3+2(3)^4 \\ 2+6+18+54+162 \end{gathered}[/tex][tex]\begin{gathered} 3(4)^0+3(4)^1+3(4)^2+3(4)^3+3(4)^4 \\ 3+12+48+192+768 \end{gathered}[/tex]Answer:
Marc se come un sándwich de huevo para el desayuno y una hamburguesa grande para el almuerzo todos los días.
El sándwich de huevo tiene 250 calorías. Si Marc come 5,250 calorías en el desayuno y almuerzo en toda la
semana en total, ¿cuántas calorías tiene una hamburguesa grande?
lón de juegos la primera vez ella ganó 60 boletos. La segunda vez,
Answer:Hay 500 calorías en una Big Burger.
Step-by-step explanation:
En una semana (7 días), Mark come 7 sándwiches de huevo, que son 1750 calorías. Reste la cantidad total de calorías que consumió por la cantidad de calorías consumidas a través de sándwiches de huevo; 5250-1750=3500. 3500 es el número total de calorías que Mark consumió al comer una Big Burger todos los días durante 7 días. Divide 3500 entre 7 = 500. Hay 500 calorías en una Big Burger.
due today, i will mark as brainliest!
Step-by-step explanation:
y=2x-20 is the right answer mark brainliest
Answer:
[tex]\sf Y=2X-20[/tex]
Step-by-step explanation:
Given linear equation:
[tex]\sf X=\dfrac{1}{2}(20+Y)[/tex]
To express Y in terms of X, rearrange the equation to isolate Y.
Apply the distributive property of multiplication over addition:
[tex]\implies \sf X=\dfrac{1}{2} \cdot 20+\dfrac{1}{2} \cdot Y[/tex]
[tex]\implies \sf X=\dfrac{20}{2}+\dfrac{Y}{2}[/tex]
[tex]\implies \sf X=10+\dfrac{Y}{2}[/tex]
Subtract 10 from both sides of the equation:
[tex]\implies \sf X-10=10+\dfrac{Y}{2}-10[/tex]
[tex]\implies \sf X-10=\dfrac{Y}{2}[/tex]
Multiply both sides of the equation by 2:
[tex]\implies \sf 2(X-10)=2 \cdot \dfrac{Y}{2}[/tex]
[tex]\implies \sf 2(X-10)=Y[/tex]
[tex]\implies \sf Y=2(X-10)[/tex]
Apply the distributive property of multiplication over subtraction:
[tex]\implies \sf Y=2\cdot X- 2\cdot 10[/tex]
[tex]\implies \sf Y=2X- 20[/tex]
I would appreciate some help here, i’m bad at math
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
Considering the given line,
m = - 3 and c = - 1
By substituting these values into the slope intercept equation, the equation of the line is
y = - 3x - 1
We would substitute values of x into the equation and solve for corresponding values of y. It is shown below
For x = - 2, y = - 3 * - 2 - 1 = 6 - 1 = 5
For x = - 1, y = - 3 * - 1 - 1 = 3 - 1 = 2
For x = 0, y = - 3 * 0 - 1 = 0 - 1 = - 1
For x = 1, y = - 3 * 1 - 1 = - 3 - 1 = - 4
For x = 2, y = - 3 * 2 - 1 = - 6 - 1 = - 7
We would plot the corresponding x and y values on the horizontal and vertical axes of the graph respectively. The graph is shown below
J is the midpoint of HK . What are HJ, JK, and HK?
HJ=25
JK=25
HK=50
Explanation
Step 1
J is the midpoint, it means
[tex]HJ=JK[/tex]Step 2
replace andsolve for x
[tex]\begin{gathered} HJ=JK \\ 9x-2=4x+13 \\ \text{subtract 4x in both sides} \\ 9x-2-4x=4x+13-4x \\ 5x-2=13 \\ add\text{ 2 in both sides} \\ 5x-2+2=13+2 \\ 5x=15 \\ divide\text{ both sides by 5} \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \\ \end{gathered}[/tex]Step 3
finally replace the valure of X to find HJ and JK
[tex]\begin{gathered} HJ=JK=9x-2=9\cdot3-2=27-2=25 \\ HJ=25 \\ JK=25 \\ then \\ HK=HJ+JK=25+25 \\ \\ HK=50 \end{gathered}[/tex]I hope this helps you
ANSI’s bought 3 1/2 yards of ribbon she had 2 feet 10 inches of ribbon left after trimming some curtains how many inches did she used to trim the curtains
With the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
What is a conversion unit?If you want to change the units of a measured quantity without changing the value, you can do so by using a conversion factor, which is an expression representing the relationship between the units. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).So, inches of ribbon Ansi used in curtains:
1 yard = 36 inches
Now,
3½6+1/25/22.5Now, 2.5 yards in inches:
2.5 × 36 = 90 inchesNow, 1 foot = 12 inches.
Then, 2 feet and 10 inches:2 × 12 + 1024 + 1034 inchesInches of ribbon used:
90 - 34 = 56 inchesTherefore, with the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
Know more about conversion units here:
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