Given
$45 per month
$75 one-time starting fee
Find cost to join the gym for one year.
In 1 year, there are 12 months, so we multiply $45 by 12.
and since $75 fee is one time, we just need to add it after the monthly fee, which means that the cost to join the gym for one year is
(45 × 12) + 75 = c
please help me with this it's 12th grade math but I need it solved and the formula used
Amortization is the process of paying off debt with regular payments made over time.
Given that
[tex]A\text{ =P x}\frac{\frac{r}{n}(1+\frac{r}{n})^{nt}}{(1+\frac{r}{n})^{nt}-1}[/tex]where P = $20,000
r= 5% = 0.05
n = 4 (since it is compounded quarterly)
t = 11/12 (Since it is 11 quaterly payment)
[tex]\begin{gathered} \text{Therefore n x t = 4 x}\frac{11}{12}\text{ =}\frac{11}{3} \\ \end{gathered}[/tex]Also,
[tex]\frac{r}{n}=\frac{0.05}{4}=\text{ 0.0125}[/tex]Substituting these values
Evaluate 2a - b for a = 2 and b = 3. 1 04 19
Plugging the values given we have:
[tex]2(2)-3=4-3=1[/tex]Therefore the answer is 1.
Please help me!!! ASAP!!Using the points (2,1.5) and (0,4.5) write the equation of the line in slope intercept form.
Given the points (2 , 1.5 ) and ( 0 , 4.5 )
the slope of the line will be calculated as following :
So, the slope = -1.5
To write the equation of the line in slope intercept form
the form will be y = mx + b
where m is the slope and b is the y-intercept
y-intercept is the value of y at which x = 0
which is the point ( 0 , 4.5)
so, b = 4.5
so, the equation of the line will be:
y = -1.5 x + 4.5
At the beginning of an experiment, a scientist has 276 grams of radioactive goo. After 255 minutes, her sample has decayed to 17.25 grams.
ANSWER
[tex]\begin{gathered} a)t1\text{/2}=63.75\min \\ b)G(t)=276\cdot(\frac{1}{2})^{\frac{t}{63.75}} \\ c)131.65g \end{gathered}[/tex]EXPLANATION
a) At the start of the experiment, the scientist had 276 grams of radioactive goo and after 255 minutes, the sample decayed to 17.25 grams.
To find the half-life, we can apply the formula for half-life:
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{t1\text{/2}}_{}}[/tex]where N0 = initial amount
N(t) = amount after time t
t = time elapsed
t1/2 =half-life
From the question, we have that:
[tex]\begin{gathered} N(t)=17.25g \\ N_0=276g \\ t=255\text{ mins} \end{gathered}[/tex]We have to find the half-life, t¹/₂. That is:
[tex]\begin{gathered} 17.25=276(\frac{1}{2})^{\frac{255}{t1\text{/2}}} \\ \Rightarrow\frac{17.25}{276}=(\frac{1}{2})^{\frac{255}{t1\text{/2}}} \\ \Rightarrow0.0625=(\frac{1}{2})^{\frac{255}{t1\text{/2}}} \end{gathered}[/tex]Converting to logarithmic function:
[tex]\begin{gathered} \Rightarrow\log _{(\frac{1}{2})}0.0625=\frac{255}{t1\text{/2}} \\ \frac{255}{t1\text{/2}}=\frac{\log _{10}0.0625}{\log _{10}0.5} \\ \frac{255}{t1\text{/2}}=4 \\ \Rightarrow t1\text{/2=}\frac{255}{4} \\ t1\text{/2=63.75 mins} \end{gathered}[/tex]Therefore, the half-life is 63.75mins.
b) Therefore, using the half-life, we have that the equation G(t) for the amount of goo remaining at time t is:
[tex]G(t)=276\cdot(\frac{1}{2})^{\frac{t}{63.75}}[/tex]c) To find the amount of goo remaining after 68 mins, we have to find G(t) when t = 68.
That is:
[tex]\begin{gathered} G(t)=276\cdot(\frac{1}{2})^{\frac{68}{63.75}} \\ G(t)=276\cdot(\frac{1}{2})^{1.067} \\ G(t)=276\cdot0.477 \\ G(t)=131.65g \end{gathered}[/tex]That is the amount remaining after 68 minutes.
1. Find the probability of an event occurring, given the odds in favor of the event is 3:7.
correspondGiven an event A, the odds in favor of that event is 3:7. That is, for every 7 observations, 3 of them correspond to event A. We conclude that the probability is:
[tex]P(A)=\frac{3}{7}[/tex]What is the product of 0.42, 1.5, and 2.33?
Multiply decimals in the same way you multiply whole numbers, then add up the number of digits after decimal points and that number tells the number of decimal places has the answer.
To solve the given multiplication:
1. Multiply first 2 numbers:
2. Multiply the product you get in step 1 for the last number:
Then, the product of 0.42, 1.5 and 2.33 is 1.46790x/3>=-33 please help me
We need to solve the following inequality:
[tex]\frac{x}{3}\ge-33[/tex]To do that we need to isolate the "x" variable on the left side. This is done by changing the side of the other numbers so that the "x" stays alone there. When we change the sides of a number we need to invert its operation, from sum to subtraction and vice-versa or from product to division and vice-versa.
In this case there is a "3" dividing x, so we need to take it out from the left and multiply by that number on the right. We have:
[tex]\begin{gathered} x\ge-33\cdot(3) \\ x\ge-99 \end{gathered}[/tex]We found our result, x must be greater or equal to -99.
at them and then that in 'n (0 2. emewah of the followme equations represale with a walan rere radius (a) 10 (h) 1191 18 (a) ix'. '16 1 * Find the equation of the cinle which passes through (s) and is concentle with
Rewrite the equation in the standar form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]So:
[tex]\begin{gathered} x^2+y^2+2x-4y=0 \\ x^2+y^2+2x-4y=(x+1)^2+(y-2)^2-5 \\ so\colon \\ (x+1)^2+(y-2)^2=5 \end{gathered}[/tex]Since the circles are concentric they share the same center, therefore, for the other circle, the Center(h,k) is also:
[tex]C(h,k)=(-1,2)[/tex]Using the standard equation of the circle again:
[tex](x+1)^2+(y-2)^2=r^2[/tex]We need to find the radius, however, we know one of the points of the circle, which is:
[tex](x1,y1)=(5,3)[/tex]Evaluating the point into the equation:
[tex]\begin{gathered} (5+1)^2+(3-2)^2=r^2 \\ 36+1=r^2 \\ 37=r^2 \end{gathered}[/tex]Therefore, the equation is:
[tex](x+1)^2+(y-2)^2=37[/tex]what digit is in the
We need to write the number five hundred twenty-five thousand seven hundred seventy in standard notation using the form a x 10^b
Five hundred twenty-six thousand seven hundred seventy = 526.770
526.770
Move "the decimal point in your number until there is only one non-zero"
Then, count how many places you moved your decimal point
526770,0 = 5,26770
We move the decimal point five places
If you moved to the left side the exponent is positive in this case b
Read it as "a times 10 to the power of b."
So 526770= 5.2677x10^5
Erica is collecting cans for a school fundraiser. She collects 5 the first day, 10 the second day, and 15 the third day. if the pattern continues, how many cans will she collect on the tenth day? A) 50 cans B) 15 cans C) 100 cans D) 65 cans
A) 50 cans
1) We can write the sequence of collecting cans like this for Erica:
[tex](5,10,15,\ldots\text{.)}[/tex]2) Note that this is an Arithmetic Sequence and this can be described by the following explicit formula since the common difference is 5, the first element is 5:
[tex]a_n=5+(n-1)d[/tex]3) So let's find out the tenth term of that sequence
[tex]\begin{gathered} a_{10}=5+(10-1)5 \\ a_{10}=5+(9)5=50 \end{gathered}[/tex]Hence, on the tenth day She will collect 50 cans
Choose the definition for the function.-X –< - 2A.if x < -2if x 2 -2B.-X- - 4 if x < -2x + 2 if x > -2x + 4X + 4if x < -2if x 2-2C.D.X + 2-X - 4if x < -2if x = -2X-2
Solution
For this case we have a graph of a function given and we can see that the best option for this case is:
y= -x-2, x< -2
y= x+4, x>=2
Then the answer is:
A
7. Determine the value of y.A. 27°B. 24°C. 135°D. 45°I need this ASAP
step 1
we know that
the formula to calculate the sum of the interior angles in any polygon is equal to
S=(n-2)*180
where
n is the number of sides
in this problem n=5
so
S=(5-2)*180
S=3*180
S=540 degrees
step 2
we have that
S=90+135+82+z+5y
step 3
we have that
5y+45=180 -------> by form a linera pair
so
5y=180-45
5y=135
y=27 degrees
therefore
the answer isoption ANote
step 1 and step 2 are not necessary, because the question is the value of y
Read each question carefully and show work. Put your answer in the provided space._______ 1. Find the measure in degree of XZ_______ 2. Find the measure in degree of XYZ
XWZ is a central angle; the measure of the arc intersected by a central angle is equal to the measure of the arc.
Intersected arc XZ:
[tex]mXZ=115°[/tex]The total circumference (total arc) in a circle is 360°, use it and the measure of arc XZ to find the measure of arc XYZ:
[tex]\begin{gathered} mXYZ+mXZ=360 \\ \\ mXYZ=360-mXZ \\ mXYZ=360-115 \\ mXYZ=245 \end{gathered}[/tex]Then, the measure of XZ is 115° and the measure of XYZ is 245°Please factor this expression (7th grade):14y + 7xy
SOLUTION
We want to factor the expression
[tex]14y+7xy[/tex]Looking at the expression, we can see that 7 and y are common in
[tex]\begin{gathered} 14y+7xy \\ \end{gathered}[/tex]This makes the highest common factor to be 7y
So we have
[tex]\begin{gathered} 14y\div7y=2 \\ 7xy\div7y=x \end{gathered}[/tex]We have
[tex]\begin{gathered} 14y+7xy \\ 7y(2+x) \end{gathered}[/tex]Hence the answer is
[tex]7y(2+x)[/tex]Maya has $63,120 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will she earn in 5 years?
we can use the next formula in order to calculate the interest
[tex]M=C(1+i)^n[/tex]M is the quantity of the savings plus the interest
C is the initial capital
i is the compound interest rate
n is the number of periods during which compound interest is compounded
[tex]M=63120(1+0.02)^5=69689.58[/tex]the interest she will earn is
M-C= 69689.58-63120=6569.58
Suppose that 200 Bernoulli trials are performed with successprobability p= 1/4.Use the normal approximation to the binomial distribution to estimatethe probability that between 50 and 60, inclusive, successes occur.That is, estimate the probability P (50 < X < 60), where X is thenumber of successes.
Number of trials (n): 200
Probability of success (p): 1/4
We know that:
[tex]p+q=1\Rightarrow q=\frac{3}{4}[/tex]The distribution is B(200, 1/4), but since the number of trials is big, we can make the normal approximation:
[tex]N(np,npq)=N(200\cdot\frac{1}{4},200\cdot\frac{1}{4}\cdot\frac{3}{4})=N(50,37.5)[/tex]Now, we need to calculate the probability that between 50 and 60 (inclusive) successes occur. That is, our probability of interest is:
[tex]P(50\leq X\leq60)[/tex]Using the normal distribution, we standardize using the z-score formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where μ is the mean and σ is the standard deviation. Then:
[tex]\begin{gathered} Z_1=\frac{50-50}{\sqrt[]{37.5}}=0 \\ Z_2=\frac{60-50}{\sqrt[]{37.5}}=1.63299 \end{gathered}[/tex]Now, the probability becomes:
[tex]P(50\leq X\leq60)=P(0\leq Z\leq1.63299)[/tex]Using known values on tables:
[tex]P(50\leq X\leq60)=0.4485[/tex]Find the volume of a cone with a height of 9ft and a base diameter of 12 ft. Use the value 3.14 for n, and do not do any rounding. Be sure to include the correct unit in your answer.
Given:
it is given that thw height of a cone is 9 ft and base diameter is 12 ft.
Find:
we have to find the Volume of the cone.
Explanation:
we know the volume of the cone with height h and radius r is
[tex]V=\frac{1}{3}\pi r^2h[/tex]here height (h) = 9 ft
diameter d = 12 ft
Therefore, radius r = 12/2 = 6 ft
The Volume of the cone is
[tex]V=\frac{1}{3}\pi(6)^2\times9=\frac{1}{3}\times(3.14)\times36\times9=339.12\text{ }ft^3[/tex]Therefore, the volume of the given cone is 339.12 ft^3
What is equation? Define equation
ANSWER:
An equation is an algebraic equality in which letters (unknowns) appear with unknown value. The degree of an equation is given by the largest exponent of the unknown. Solving an equation is determining the value or values of the unknowns that transform the equation into an identity.
For example:
x + 2 = 31 + 2x
[tex]\blue{\huge {\mathrm{ EQUATIONS}}}[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
What is equation? Define equation.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
Equations are mathematical statements that show that two quantities are equal. They typically contain an equal sign (=) and one or more variables. Equations are used to express relationships between quantities and to solve problems in various fields of science, engineering, and mathematics.
Example equations include:
[tex]\sf -4t^2 - 16t = -8[/tex][tex]\sf -2x + 5 = 13[/tex][tex]\sf -\dfrac{y}{7} = 3[/tex]To solve an equation, we want to determine the value of the variable(s) that make the equation true.
There are different techniques to solve equations, but some common steps include:
1. Simplify both sides of the equation by combining like terms and using the order of operations if necessary.
2. Isolate the variable on one side of the equation by undoing any operations that were performed on it.
For example, if the variable is multiplied by a number, divide both sides of the equation by that number. If the variable is added to a number, subtract that number from both sides of the equation.3. Check the solution by plugging it back into the original equation to see if it makes the equation true.
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]
1. A barn roof has a 40° rise, and the barn is48 feet wide.a. How many feet does the roof rise?b. What length rafter is needed to have an8-inch overhang?
a) 40.27 approximately 40 ft
b) 40.94 approximately 41 ft
1) Let's sketch that to better grasp it
a. Let's use a trigonometric ratio for that rise of the roof since there's an angle of elevation. We'll use a tangent
[tex]\begin{gathered} \tan (40)=\frac{h}{48} \\ h=48\times\tan (40) \\ h\approx40.27\approx40\text{ ft} \end{gathered}[/tex]b). Since we want to know how can we have an 8" inch overhang, let's firstly convert that to feet:
1 ft ----------12 "
y ---------- 8"
y=8/12
y=2/3 ft = 8"
So let's find out the length of this rafter, assuming this rafter will be placed like this
[tex]\begin{gathered} h_{\text{rafter}}=40.276\text{ +0.666} \\ h_{rafter}=40.94\text{ ft} \end{gathered}[/tex]Geometry Please help! I was in a test and couldn’t pass this question, this is new material for me. I need a step by step tutorial, thank you!
Midpoint formula:
Xm = (x2-x1)/2
Ym= (y2-y1)/2
Where
xm and ym are the midpoints (-4,24)
(x1,y1)= (3,16)
x2,y2 = x,y
Replacing:
xm= (x2-x1)/2
-4 = (x-3)/2
-4(2)= x-3
-8= x-3
-8+3 =x
x =-5
Ym= (y2-y1)/2
24 = (y-16)/2
24(2)=y-16
48 = y-16
48+16 = y
y = 64
(-5,64)
solve the following system of equations algebraically for all values of x,y,z x+3y+5z=456x-3y+2z=-10-2x+3y+8z=72
The equations are given as shown below:
[tex]\begin{gathered} x+3y+5z=45\text{ ------------(1)} \\ 6x-3y+2z=-10\text{ ------------(2)} \\ -2x+3y+8z=72\text{ -------------(3)} \end{gathered}[/tex]From Equation (1):
[tex]x=45-3y-5z\text{ ----------(4)}[/tex]Substitute for x into equations (2) and (3):
[tex]\begin{gathered} \text{Equation 2:} \\ 6(45-3y-5z)-3y+2z=-10 \\ 270-18y-30z-3y+2z=-10 \\ -21y-28z=-10-270 \\ -21y-28z=-280 \\ \text{Dividing all through by -1} \\ 21y+28z=280\text{ -------------(5)} \end{gathered}[/tex][tex]\begin{gathered} \text{Equation 3:} \\ -2(45-3y-5z)+3y+8z=72 \\ -90+6y+10z+3y+8z=72 \\ 9y+18z=72+90 \\ 9y+18z=162 \\ \text{Dividing all through by 9:} \\ y+2z=18\text{ -------------(6)} \end{gathered}[/tex]Solving Equations (5) and (6) simultaneously:
From equation (6):
[tex]y=18-2z\text{ ------------(7)}[/tex]Substitute for y into equation (5):
[tex]\begin{gathered} 21(18-2z)+28z=280 \\ 378-42z+28z=280 \\ -14z=280-378 \\ -14z=-98 \\ z=\frac{-98}{-14} \\ z=7 \end{gathered}[/tex]Substitute for z into equation (7):
[tex]\begin{gathered} y=18-2(7) \\ y=18-14 \\ y=4 \end{gathered}[/tex]Substitute for y and z into equation 4:
[tex]\begin{gathered} x=45-3(4)-5(7) \\ x=45-12-35 \\ x=-2 \end{gathered}[/tex]The solutions are:
[tex]\begin{gathered} x=-2 \\ y=4 \\ z=7 \end{gathered}[/tex]Jonathan must determine the solutions of the quadratic equation0=4x²2²+3x+8.Which of the following is a solution to the equation?OA. 3+√394OB. 3+√134O C. -3-√218OD. -3-√1198
Given:
[tex]0=4x²+3x+8.[/tex]To find:
The solutions.
Explanation:
Here,
[tex]\begin{gathered} a=4 \\ b=3 \\ c=8 \end{gathered}[/tex]Using quadratic formula,
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ =\frac{-3\pm\sqrt{(-3)^2-4(4)(8)}}{2(4)} \\ =\frac{-3\pm\sqrt{9-128}}{8} \\ =\frac{-3\pm\sqrt{-119}}{8} \\ =\frac{-3\pm i\sqrt{119}}{8} \end{gathered}[/tex]Thus, the solution is,
[tex]\frac{-3-i\sqrt{119}}{8}[/tex]Final answer:
The correct option is D.
[tex]\frac{-3-i\sqrt{119}}{8}[/tex]A worm cancrawl 6 feet 8inches in 1 1/2hour. What is theworm's unitrate?
This problem involves proportions and also different units of measure.
So, first, let's write the distance the worm can crawl in 1 1/2 hour using inches.
We know that 1 foot = 12 inches. So, we have:
6 feet 8 inches = 6 * 12 inches + 8 inches
= 72 inches + 8 inches
= 80 inches
Also, notice that:
1 1/2 hour = (1 + 1/2) hour = 1.5 hour
Now, we have the proportions:
distance (in inches) time (in hour)
80 1.5
x 1
Now, we cross multiply those values to find:
1 * 80 = 1.5 * x
80 = 1.5 x
80/1.5 = 1.5x/1.5
80/1.5 = x
x = 80/1.5
x ≅ 53.33
So, we found that the worm can crawl approximately 53.33 inches per hour.
If we want to know its rate in feet per hour, we need to divide the result by 12:
1 foot = 12 inches
1/12 foot = 1 inch
53.33 inches = 53.33 (1/12 foot)
= (53.33/12) feet
≅ 4.44 feet
Therefore, the worm's rate is approximately 4.44 feet per hour.
The two roots a + b and e- Vb and 3-6 are called ______ radicals. ??
Conjugate radicals
A conjugate is a binomial with an apposite se
Part A: Write a system of Linear Equations that represents this situation Part B:Will your friend’s hair ever be as long as her cousin’s hair? If so, in what month?
EXPLANATION
The system of linear equations that we could use to represent this situation is shown as follows:
Assuming that x represents the number of inches, the equation would be
y = mx + c
Thus, from the table we get
7 = 3m + c (1)
9 = 8m + c (2)
Subtracting (1) from (2):
-2 = -5m
m = -2/-5
Substituting for m into equation (1) gives:
7 = 3(0.4) + c
Then, c=7 - 1.2 = 5.8
In conclusion, the equation representing the growth of the cousin's hair is represented as y = 1.2x + 5.8
the meaning of point of intersection depends on what the graph is describing Examine each of the graphs below and write a brief story that describes the information on the graph include a sentence explaining what point of intersection represents
The graph represents the cost associated with producing a given number of tortillas, there are two scenarios, handmade and machine-made tortillas, for the handmade scenario, we can see that as the number of tortillas increases the cost remains the same, and for the machine-made scenario, we can see that as the number of tortillas increases, the cost decreases.
The point of intersection, in this case, is the cost associated with producing 0 tortillas, this can be interpreted for the machine-made case as the cost of starting the equipment (the machine) that makes the tortillas.
is this linear or non-linear?y=7x+6
The given expression is,
[tex]y=7x+6[/tex]An equation with maximum degree of a term is one is called linear equation.
So the given exprssion is linear.
3(2c+d)-4(c-d)+d squared when c=1 d=3 please explain
We need to find the value of the expression 3(2c+d)-4(c-d)+d² when c = 1 and d = 3.
So we just need to apply those values to the variables and then calculate the expression:
[tex]\begin{gathered} 3\left(2c+d\right)-4\left(c-d\right)+d^2 \\ 3(2\cdot1+3)-4(1-3)+3^2 \\ 3(2+3)-4(-2)+9 \\ 3\cdot5+8+9 \\ 15+8+9 \\ 32 \end{gathered}[/tex]So the value of the expression is 32.
Write an equation for the linear function f with the given value: f(–3) = 3 and f(3) = –1.
Given:
f(-3) = 3
f(3) = -1
Let's write an equation for the linear function.
For example:
f(x) = y
We have the point:
(x, y)
From, f(-3) = 3, we have the point:
(-3, 3)
From f(3) = -1, we have the point:
(3, -1)
Thus, we have the points:
(x1, y1) ==> (-3, 3)
(x2, y2) ==> (3, -1)
To write a linear equation, applt the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, apply the formula:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{-1-3}{3-(-3)} \\ \\ m=\frac{-1-3}{3+3} \\ \\ m=\frac{-4}{6} \\ \\ m=-\frac{2}{3} \end{gathered}[/tex]The slope is -⅔
[tex]y=-\frac{2}{3}x+b[/tex]To solve for the y-intercept, b, susbstitute either of the points for the value of x and y.
Take the point: (-3, 3), substitute -3 for x and 3 for y:
[tex]\begin{gathered} 3=-\frac{2}{3}\ast-3+b \\ \\ 3=2+b \\ \\ \text{Subtract 2 from both sides:} \\ 3-2=2-2+b \\ \\ 1=b \\ \\ b=1 \end{gathered}[/tex]The y-intercept, b is = 1
Therefore, the equation for thr linear function is:
[tex]y=-\frac{2}{3}x+1[/tex]ANSWER:
[tex]y=-\frac{2}{3}x+1[/tex]Toretto has 7 cars and Brian has 3 cars. Rome has p more than the product of Toretto and Brian's cars. Write an expression for the number of cars Rome has
(7 x 3) + p
Explanations:The number of cars Toretto has = 7
The number of cars Brian has = 3
The product of Toretto and Brian Cars = 7 x 3
The product of Toretto and Brian Cars = 21
Rome has p cars more than the product of Toretto and Brian's cars
The expression for the number of cars Rome has will be:
Number of Rome's cars = (7 x 3) + p
which can also be simplified as 21 + p