Solution:
Given:
[tex]y=9x[/tex]This is a linear equation that relates distance, speed, and time.
where;
[tex]undefined[/tex](F.LE.5) The function f(x) = 7.75x models the amount of money that Jimearns for each hour of work. What does the lack of a constant tell us?A. There is no initial amount of money he gets paid prior to startingB. His hourly wageC. His total amount he gets paid for the dayD. The number of hours Jim has worked
In a linear model:
[tex]f(x)=mx+b[/tex]The coefficient of x, which is m, is the rate of change of the function f with respect to changes in the value of x. In the context of the problem, the coefficient of x tells us the amount of money that Jim earns per hour.
The constant term b is the initial value of the function f when x=0.
Since the given linear model has no constant term, it means that the initial value is 0. In other words, Jim will earn $0 if he works 0 hours.
Therefore, the correct choice is Option A) There is no initial amount of money he gets paid prior to starting.
The table shows the mean number of basketball goals made by four random samples of players from the school teamduring this year's season.Sample #Sample MeanNumber of Goals71243548Is a valid prediction for the mean of the population possible using these samples?A: No, there are not enough samples.B: Yes, the sample means are all less than 10.C: Yes, the variation of the sample means is small.D: No, the variation of the sample means is too great.
Answer:
Step-by-step explanation:
Find the Midpoint of AB*round to the nearest tenth if necessaryA6,-3), B(2,9)
Which pipe lengths could be joined to form a right triangle? 13 ft, 12 ft, 5 ft 19 ft, 16 ft, 2 ft 15 ft, 6 ft, 5 ft 40 ft, 20 ft, 10 ft
Answer:
13ft, 12ft, 5ft
Explanation:
Looking at the given options, the correct option is the one with 13ft, 12ft, and 5ft because if the longest side of the right triangle(the hypotenuse) is 13ft then the summation of the other two sides must be equal or greater than 13ft (Pythagorean Theorem);
[tex]12ft+5ft\ge13ft[/tex]Find the equation of the line thatis parallel to y = 2x – 7 andcontains the point (-3,6).y = [ ? ]x + []Enter
Answer:
y = 2x +12
Step-by-step explanation:
You want the line through point (-3, 6) that is parallel to y = 2x -7.
Parallel lineThe given line equation is in slope-intercept form ...
y = mx + b . . . . . line with slope m and y-intercept b
This allows us to see that its slope is 2.
The parallel line will have the same slope. All we need to do is find its y-intercept.
InterceptSolving the above equation for 'b', we get ...
b = y - mx
Using (x, y) = (-3, 6) and m = 2, we find 'b' to be ...
b = 6 -(2)(-3) = 12
EquationUsing the values for m and b that we now know, the desired equation is ...
y = 2x +12
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use trigaonamets functions as nessary to find the missing parts the triangle
Given a right angle triangle:
As shown on the acute angles is 21
So,
[tex]\begin{gathered} \cos \text{ 21=}\frac{adjacent}{\text{hypotenuse}}=\frac{6.4}{H} \\ \\ H=\frac{6.4}{\cos 21}=6.855 \end{gathered}[/tex]And:
[tex]\begin{gathered} \tan 21=\frac{opposite}{\text{adjacent}}=\frac{y}{6.4} \\ \\ y=6.4\cdot\tan 21=2.457 \end{gathered}[/tex]the third angle of the triangle =
[tex]90-21=69[/tex]This data set has two modes. Find the second mode of the data. 18, 12, 19, 15, 19, 18, 6 Mode: 18, [?]
The mode of a dataset is the data that happens most frequently. A dataset has more then one mode when the most frenquet data values happens the same number of times.
Let's put the dataset in ascending order:
[tex]18,12,19,15,19,18,6\to6,12,15,18,18,19,19[/tex]As we can see, most data happens once and 18 and 19 happens twice each. So, both are the modes.
Since the given one is 18, the second mode is 19.
Point M is the midpoint of segment AB. If the coordinates of Mare (2, 8) and the coordinates of Aare (10, 12), find the coordinates of B.B(x, y) =(
Using the formula
[tex](x_{m\text{ , }}y_m)\text{ = (}\frac{x_1+x_2}{2}\text{ , }\frac{y_1+y_2}{2})[/tex]x₁= 10 y₁=12 Xm=2 Ym = 8
x₂ = ? y₂=?
Substituting and solving for x₂
[tex]x_m=\frac{x_1+x_2}{2}[/tex][tex]2\text{ = }\frac{10+x_2}{2}[/tex]Multiply both-side of the equation by 2
4 = 10 + x₂
subtract 10 from both-side of the equation
-6 = x₂
x₂= -6
Similarly, substituting and solving for y₂
[tex]y_m=\frac{y_1+y_2}{2}[/tex][tex]8=\frac{12+y_2}{2}[/tex]Multiply both-side of the equation by 2
16 = 12 + y₂
Subtract 12 from both-side of the equation
4 = y₂
y₂= 2
Hence; coordinates of B are;
B(x,y) = ( -6, 2)
i need help with math
The value of 'y' for the parallel line drawn by the Amir is 25°.
Describe the term transversal?A transversal would be any line which intersects 2 straight lines at different point in geometry. In geometry, a transversal line connects two lines within the same plane at 2 separate points. Transversals contribute to the parallelism of two or more additional straight lines inside the Euclidean plane.For the given question;
There are two parallel line cut by the transversal drawn by the Amir.
Thus, the relation of the two angles are-
The supplement angle of (4y - 45) is 180 - (4y - 45).
And,
180 - (4y - 45) = y (vertical angles)
Simplify the equation;
180 - 4y + 45 = y
5y = 125
y = 25°
Thus, value of 'y' for the parallel line drawn by the Amir is y = 25°.
To know more about the transversal, here
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can you explain step by step how to solve this?
Remember that
the area of a parallelogram is equal to
A=b*h
in this problem
b=35 cm
h=44 cm
substitute
A=35*44
A=1,540 cm2Find out the perimeter
P=2*(35)+2*(47)
P=164 cmProblem N 2
we know that
the length of the wall is 170 inches
step 1
Find out the dimensions of the diagonal of the square
Applying the Pythagorean Theorem
d^2=12^2+12^2
d^2=2*12^2
[tex]d=12\sqrt[\square]{2}\text{ in}[/tex]Divide the length of the wall by the length of the diagonal
[tex]\frac{170}{12\sqrt[\square]{2}}=10.02[/tex]therefore
I need 11 (1/2 tiles)Note I rounded up because with 10 (1/2 tiles) the length is less than 170 inches4. Solve for y 2x - y = -8
The correct option is y = 2x + 8
You have $20,000 that you want to deposit into a savings account. You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Problem
You have $20,000 that you want to deposit into a savings account.
You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Solution
For this case we need to take in count the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P= 20000, r= interest rate in fraction and n= number of times that the rate is compounded in a year, t= 5 years and A is the future value
And the simple interest formula:
[tex]A=P(1+rt)[/tex]And compound continuosly:
[tex]A=\text{Pe\textasciicircum{}rt}[/tex]Let's calculate the final amount for each case
Bank A
[tex]A=20000(1+\frac{0.0425}{12})^{12\cdot5}=24726.038[/tex]Bank B
[tex]A=20000(1+\frac{0.06}{2})^{2\cdot5}=26878.328[/tex]Bank C
[tex]A=20000(1+0.055\cdot5)=25500[/tex]Bank D
[tex]A=20000e^{0.04\cdot5}=24428.055[/tex]And the best choice for this case seems to be Bank B since we will have more money at the end of the 5 year
How much do you owe at the end of five weeks ?
First, find the interest percentage. Divide the amount borrowed by the interest amount.
[tex]\frac{100}{10}=10[/tex]Then, divide the result by 100% to express it as a percentage.
[tex]\frac{10}{100}=0.10[/tex]Once we have the interest percentage as a decimal number, multiply it by the new borrowed amount.
[tex]0.10\times1100=110[/tex]Therefore, you owe $110 at the end of the five weeks.33 over r =11 over 2
Answer:
r=6
Step-by-step explanation:
33/r = 11/2
r/33 = 2/11 multiply both sides of the equation by 33
r = 33 * 2/11 = 6
find (x) 76° 6x-9 47°
There are two degrees, one variable and one number.
The 19% APR is the annual interest rate, but it is compounded monthly. What is the monthly interest rate ?
Answer:
1.583%
Step-by-step explanation:
19% divided by 12% (how many months there are) = 1.583%
Question 9 of 10Which of these is an example of numerical data?A. Type of petB. Favorite carC. Average speedD. Home state
Given:
Numerical data.
Find-: Numerical data.
Sol:
Average speed: Average speed define in numerical form and other options do not give any types of numerical data.
So answer is Average speed.
The family sized can of orange juice is 9 inches tall and has a diameter of 5 inches. If there areapproximately 58 cubic inches in a quart, how many 8 fluid ounce servings are in the can?
Volume of the can =
[tex]\begin{gathered} \text{ }\pir^2h \\ \text{ = (3.14)(5)}^2(9) \\ =706.5in^3 \\ \text{ 58 in}^3\text{ --------------------- 1 quart} \\ 706.5in^3\text{ -------------------- x} \\ \text{ x = (706.5 x 1) / 58} \\ x=12.18\text{ quarts} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \text{ 1 ounce ---------------- 0.03 quarts} \\ \text{ x ---------------- 12.18 quarts} \\ \text{ x = (12.18 x 1)(0.03} \\ \text{ x = 406 ounces} \end{gathered}[/tex]Maggie had a number of identical flowers for sale. She sold 70 of them with a 50% loss and sold the rest with a 80% profit. On the whole, Maggie still made a 10% profit. How many flowers did Maggie have at the beginning?
ANSWER:
130 flowers
STEP-BY-STEP EXPLANATION:
Let x be the total number of flowers, we can establish the following equation:
[tex]70\left(-50\%\right)+\left(x-70\right)\left(80\%\right)=x\left(10\%\right)[/tex]We solve for x:
[tex]\begin{gathered} 70\left(-0.5\right)+\left(x-70\right)\left(0.8\right)=x\left(0.1\right) \\ \\ -35+0.8x-56=0.1x \\ \\ 0.8x-0.1x=56+35 \\ \\ 0.7x=91 \\ \\ x=\frac{91}{0.7} \\ \\ x=130 \end{gathered}[/tex]The total number of flowers, that is, the ones it had at the beginning was 130
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 8z
Answer:
(0, 0)(0.1, 0.005)=====================
Given system2y = x² y = 5x³Substitute the value of y into first equation2*5x³ = x²10x³ - x² = 0x²(10x - 1) = 0x = 0 and 10x - 1 = 0x = 0 and x = 0.1Find the value of yx = 0 ⇒ y = 5*0³ = 0x = 0.1 ⇒ y = 5*(0.1)³ = 0.005Answer:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}2y=x^2\\ \;\;y=5x^3\end{cases}[/tex]
To solve by the method of substitution, substitute the second equation into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=5x^3 \implies 2(5x^3)&=x^2\\10x^3&=x^2\\10x^3-x^2&=0\\\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}10x^3-x^2&=0\\x^2(10x-1)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]x^2=0 \implies x=0[/tex]
[tex]10x-1=0 \implies x=\dfrac{1}{10}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=5(0)^3\\y&=0\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies y&=5\left(\dfrac{1}{10}\right)^3\\y&=5 \cdot \dfrac{1}{1000}\\y&=\dfrac{1}{200}\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{0,0} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{\dfrac{1}{10},\dfrac{1}{200}} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Acorn is tossed three times. An outcome is represented by a string of the sort HTT (meaning ahead on the first tos, followed by two tails). The outcomes areIsted in the table below. Note that each outcome has the same probability,Por each of the three events in the table, check the outcomes) that are contained in the event. Then, in the last column, enter the probability of the event.OutcomesmiተብህቡብProbability음THTTTHTTHTHTHITHTEvent At A tail on both the first andthe last tosses$?0Event : Two or more tails0Event Ci Alternating tail and head(with either coming frst)0ContinueSubmit Assignment2022 MID CARDSign out00
The outcome of tossing a coin is either a head or a tail.
Looking at the given table,
Event A = A tail in both the first and last tosses = THT, TTT
Event B = Two or more tails = TTH, TTT, HTT, THT
Event C = Alternating tail and head with either coming first = TTH, THH, HTT, HTH, THT. HHT
Recall,
probability = number of favorable outcome/number of total outcomes
Total number of outcomes = 8
Probability of event A = 2/8 = 1/4
Probability of event B = 4/8 = 1/2
Probability of event C = 6/8 = 3/4
The school budget allows no more than $360 to be spent on balls and bats.The cost of a ball is $6 and the cost of a bat is $24write the inequality to represent this information
Since the school budget allows no more than $360 to be spent on balls and bats, we have:
[tex]\text{total cost of balls and bats, in dollars }\le360[/tex]Now, let's call x the number of balls and y the number of bats that can be bought.
• The cost to buy x balls, in dollars, is 6x.
• The cost to buy y bats, in dollars, is 24y.
So, the total cost of balls and bats, in dollars, is 6x + 24y.
Now, we can use this expression in the above inequality to obtain the inequality:
[tex]\mathbf{6x+24y\le360}[/tex]20. A local children's center has 47 children enrolled, and 6 are selected to take a picture for the center's advertisement. How many ways are there to select the 6 children for the picture?
Given:
Total number of children enrolled = 47
Number of children to be selected = 6
Number of ways to select 6 children for the picture are:
[tex]=^{47}C_6[/tex]Formula for combination is given as:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Applying this, we get:
[tex]\begin{gathered} ^{47}C_6=\frac{47!}{6!(47-6)!} \\ =\frac{47!}{6!41!} \\ =10737573 \end{gathered}[/tex]Therefore, the required number of ways are 10737573.
How many different 7-digit telephone numbers can be made if the first digit cannot be7,8, 9 or 0?
The total amount of numbers that can be made is equal to the product of the amount of options for each digit.
The first digit has only 6 options: 1, 2, 3, 4, 5, or 6.
The other six digits have 10 options: 0,1,2,...,9.
Then, the total amount of different telephone numbers is six million:
[tex]6\times10\times10\times10\times10\times10\times10=6,000,000[/tex]if f(x) = 1/x and g(x) = x+1/x find(fog)(x).a) x +1/ x squared b) x / x + 1 c) x squared (x + 1)d) x + 1 / x cubed
We have the following:
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ g(x)=\frac{x+1}{x} \end{gathered}[/tex]now, (f(x) o g(x))
[tex]\mleft(f\: (x)\circ\: g(x)\mright)=\frac{1}{\frac{x+1}{x}}=\frac{x}{x+1}[/tex]The answer is the second option
[tex]\frac{x}{x+1}[/tex]if (x=5)and y=10 which expression has the greatest value
Let's assume the question was as stated below;
"If x=5 and y=10, which expression has the greatest value?"
a. xy
b. x + y
c. x-y
d. x/y
Answer:
Option A. Expression xy has the greatest value.
Explanation:
To determine which of the given options has the greatest value, let's go ahead and evaluate each of them;
Option A;
[tex]xy=x\ast y=5\ast10=50[/tex]Option B;
[tex]x+y=5+10=15[/tex]Option C;
[tex]x-y=5-10=-5[/tex]Option D;
[tex]\frac{x}{y}=\frac{5}{10}=\frac{1}{2}[/tex]We can see that the expression (xy) gives the greatest value.
Therefore, option A would be our correct answer.
On the plans for a treehouse, a beam represented by QR has endpoints Q(-6,2) and R (-1,8). A connecting beam represented by ST has endpoints S(-3,6) and T(-8,5). Are the beams perpendicular? Explain. (Hint:Graph the points if needed).
We have the next graph
QR is the beam in red
ST is the beam in blue
As we can see the beams are not perpendicular because they do not intercept each other and they don't form a 90° angle between each other
what kind of triangle is a triangle with the sides 8, 15, and 16? A. obtuseB. acuteC. right
Lets draw the following picture:
which corresponds to an acute triangle. In acute triangles, all the angles are less than 90°.
Jamir is training for a race and is running laps around a field. If the distance around the field is 450 yards,how many complete laps would he need to do to run at least 4 miles?laps
We have that Jamir is training for a race and is running laps around a field:
• The distance around the field is 450 yards (per lap).
,• He needs to run at least 4 miles.
1. Now we can proceed as follows to find the number of laps Jamir needs to run as follows:
[tex]\begin{gathered} 1\text{ Mile}=1760.0065617yards \\ \\ 4\text{ Miles=}4(1760.0065617yards)=7040.0262468yards \end{gathered}[/tex]Then we have that Jamir needs to run about 7040.0262468 yards.
2. Since the distance around the field is 450 yards (per lap), then we have:
[tex]7040.0262468yards*\frac{1lap}{450yards}=15.6445027707laps[/tex]Therefore, in summary, Jamir needs to run about 15.64 laps to run at least 4 miles (almost 16 laps - if we round the result to the nearest whole number).
Solve for V5/6= v-5 /4
Okay, here we have this:
Considering the provided equation, we are going to solve it to find the value of y, so we obtain the following:
5/6= v-5 /4
v-5 /4+ 5 /4=5/6 + 5/4
v= 5/6 + 5/4
v=(20+30)/24
v=50/24
v=25/12
Finally we obtain that v is equal to 25/12.