The formula indicates how the price of the meal after taxes is calculated.
[tex]T=P+rP[/tex]Where
T is the total price
P is the price without taxes
r is the tax rate, this value is always expressed as a decimal value.
Amy paid a total of $30.60 plus a $10 gift certificate, the total cost of the bill is:
[tex]\begin{gathered} T=30.6+10 \\ T=40.6 \end{gathered}[/tex]To express the tax rate as a decimal value you have to divide the percentage by 100:
[tex]\begin{gathered} r=\frac{9}{100} \\ r=0.09 \end{gathered}[/tex]Replace both values on the formula:
[tex]P+0.09P=40.60[/tex]Now we have established an equation with one unknown "P", to solve the equation for P, the first step is to simplify both terms on the left side of the equation. To do so, add both terms:
[tex]\begin{gathered} P+0.09P=40.60 \\ 1.09P=40.60 \end{gathered}[/tex]Divide both sides by 1.09 to determine the value of P
[tex]\begin{gathered} \frac{1.09P}{1.09}=\frac{40.60}{1.09} \\ P=37.249\approx37.25 \end{gathered}[/tex]The cost of the family's dinner before taxes w
11. Algebra The total cost of the Fatigato
family's two cars was $71,482. The cost of
one car was $38,295. Write an equation
using a variable to represent the cost of
the family's other car.
Answer:
$33,187
Step-by-step explanation:
Our total is 71,482 so let's set our equation to 71482=_________
Now we have $38,295 for one car, and we will subtract it from the total to find the other car, as there are 2 cars.
Equation:
71482-38295=x OR 71482=38295+x
X is the cost of the second car.
fill in the missing numbers along the sides of the triangle so that it contains each of the numbers from 4 through 12 exactly once. furthermore each side of the triangle should contain four numbers whose sum is 32the pair of numbers that can be used for A and B is ___. the pair of numbers that can be used for C and D is ____. and the pair of numbers that can be used for E and F is___.
Answer:
For A and B, we have (10, 6)
For C and D, we have (12, 8)
For E and F, we have (12, 8)
Explanation:
To determine the missing numbers along each side of the triangle, we have to
*Add the two numbers at the vertex
*Subtract it from 32
*Divide it by 2
*Add 2 to it to have the 1st number
*Subtract 2 from it to have the 2nd number
So to find the pair of numbers that can be used for A and B, we'll have;
[tex]\begin{gathered} 12+4=16 \\ 32-16=16 \\ \frac{16}{2}=8 \\ 8+2=10 \\ 8-2=6 \end{gathered}[/tex]Therefore the missing numbers for A and B are 10 and 6.
So to find the pair of numbers that can be used for C and D, we'll have;
[tex]\begin{gathered} 4+8=12 \\ 32-12=20 \\ \frac{20}{2}=10 \\ 10+2=12 \\ 10-2=8 \end{gathered}[/tex]Therefore the missing numbers for C and D are 12 and 8.
So to find the pair of numbers that can be used for E and F, we'll have;
[tex]\begin{gathered} 12+8=20 \\ 32-20=12 \\ \frac{12}{2}=6 \\ 6+1=7 \\ 6-1=5 \end{gathered}[/tex]So to avoid repetition of any of the numbers between 4 and 12, we have to add and subtract 1 instead of 2.
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
The given inequality has the following solution set
9.52 ≤ x ≤ 22.22
If we express this as an interval, we get [9.52, 22.22].
Here is the inequality which is Kali's earning potential
200 ≤ 15.75x + 50 ≤ 400
To solve the inequality, we must isolate the variable in the center; if we remove 50 from each of the three sides, we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we must divide both totals by 15.75, yielding:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the inequality's solution; the solution set expressed as an interval will be [9.52, 22] or 9.52 ≤ x ≤ 22.22
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
The greatest common factors of 2^5 · 5· 11 and 2^3· 5^2 · 7 is equivalent to 2^3 * 5
What are greatest common factors?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor.
This factor must be able to divide all the terms of the expression withour remainder.
Given the numbers 2^5 · 5· 11 and 2^3· 5^2 · 7. Find the factors;
2^5 · 5· 11 = 2^3 * 2^2 * 5 * 11
2^3· 5^2 · 7= 2^3 * 5 * 5 * 7
Since the number 2^3 * 5 is common to both factors, hence the GCF of these numbers 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 * 5
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find an equation of the circle that has center (1,-5) and passes through (2,1)
1) Since the equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And we've been told the Center (1,-5) and one point located at the circumference, (2,1). So let's find the radius, i.e. the distance from the center to any point to the circumference.
2) Let's use the Formula for the distance between (1,-5) and (2,1), derived from the Pythagorean Theorem:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(2-1)^2+(1_{}+5)^2} \\ d=\sqrt[]{37} \end{gathered}[/tex]3) So d = radius, and now we can plug those pieces of information into the formula of the circle:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-1)^2+(y+5)^2=(\sqrt[]{37})^2 \\ (x-1)^2+(y+5)^2=37 \end{gathered}[/tex]So we now have the formula for that circle.
Answer:
Radius (R) is equal to the distance between the points (-2,1) and (3,1)
R² = (1 - 5)² + (1 - 1)² = (-24)² + 0 = 579
R = 23.16
One month Tony rented 5 movies and 3 video games for a total of $32. The next month he rented 2 movies and 12 video games for a total of $83. Find therental cost for each movie and each video game.Rental cost for each movie:Rental cost for each video game:
Let x represent the rental cost for each movie.
Let y represent the rental cost for each video game.
We were told that One month Tony rented 5 movies and 3 video games for a total of 532. This means that
5x + 3y = 32
Also, the month, he rented 2 movies and 12 video games for a total of $83. This means that
2x + 12y = 83
Dividing through by 2, we have
x + 6y = 41.5
x = 41.5 - 6y
Substituting x = 41.5 - 6y into 5x + 3y = 532, we have
5(41.5 - 6y) + 3y = 32
207.5 - 30y + 3y = 32
- 30y + 3y = 32 - 207.5
- 27y = - 175.5
y = - 175.5/- 27
y = 6.5
x = 41.5 - 6(6.5) = 41.5 - 39
x = 2.5
Rental cost for each movie = $2.5
Rental cost for each video game = $6.5
what is the value of a in the equation 5a – 10b = 45, when b =3?a)3b)15c)21d)39
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]5a-10b=45[/tex]STEP 2: Substitute 3 for b in the equation
[tex]5a-10(3)=45[/tex]STEP 3: Simplify the equation to solve for a
[tex]\begin{gathered} 5a-30=45 \\ 5a=45+30 \\ 5a=75 \\ a=\frac{75}{5} \\ a=15 \end{gathered}[/tex]Hence, the value of a is 15
Whats a ratio for 5ml and 120ml
Step 1:
The ratio for 5ml to 120ml
Step 2:
The symbol of ratio is :
Therefore,
[tex]\begin{gathered} 5ml\text{ ratio 120ml} \\ =\text{ 5 : 120} \\ =\text{ }\frac{5}{120} \\ =\text{ }\frac{1}{24} \\ =\text{ 1 : }24 \end{gathered}[/tex]Step 3
Final answer
1 : 24
Write the quadratic function in vertex form. Then identify the vertex.
g(x)=x^2+12x+37
The vertex form is y= (x+ 6)²+1.
What is Vertex form?The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
a=1
b=12
c=37
Consider the vertex form of a parabola.
a(x+ d)²+e
Now, d= b/2a
d=12/ 2
d=6
and, e= c-b²-4a
e= 37 - (12)²/4x1
e= 37 - 36
e= 1
Then, the vertex form is
y = a(x+ d)²+e
y= 1(x+ 6)²+1
y= (x+ 6)²+1
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Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour. After how long are the two trains exactly 300 miles apart?
After 2.14 hours the trains are exactly 300 miles apart.
How to find the time the trains travel 300 miles apart?Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour.
The time both of them will travel 300 miles can be calculated as follows:
Therefore,
speed = distance / time
distance = speed × time
The train that travel west:
let
t = time of the train that travel west
distance = 60t
The train that travel south:
distance = 80t
Therefore,
total distance = 60t + 80t
300 = 140t
t = 300 / 140
t = 2.14285714286
t = 2.14 hours
Therefore,
time taken = 2.14 hours
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Write the equation of the line with the given information in point-slope form. (-5, 11) and (-2, 1)
Answer
The equation in point-slope form is
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
We can calculate the slope of the line and then use any of the two points given to serve as the point (x₁, y₁) in the equation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-5, 11) and (-2, 1)
x₁ = -5
y₁ = 11
x₂ = -2
y₂ = 1
[tex]\text{Slope = }\frac{1-11}{-2-(-5)}=\frac{-10}{-2+5}=\frac{-10}{3}[/tex]Slope = m = (-10/3)
Using the point (-2, 1) as (x₁, y₁), we can write the equation of the line
y - y₁ = m (x - x₁)
y - 1 = (-10/3) (x - (-2))
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Hope this Helps!!!
Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.
Solution
Step 1
The terminal side, containing point (-3, 4) is located in Quadrant 2.
sine is positive
cosine and tangent are both negative.
Step 2
Draw a diagram to illustrate the information
Step 3
[tex]\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }\sqrt{25} \\ \text{d = 5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} sine\text{ = }\frac{Opposite}{Hypotenuse} \\ Sin\theta\text{ = }\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} Cosine\text{ = }\frac{Adjacent}{Hypotenuse}\text{ = }\frac{x}{d} \\ Cos\theta\text{ = }\frac{-3}{5} \end{gathered}[/tex][tex]\begin{gathered} tangent\text{ = }\frac{Opposite}{Adjacent}\text{ = }\frac{y}{x} \\ tan\theta\text{ = }\frac{-4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} sin\theta\text{ = }\frac{4}{5} \\ cos\theta\text{ = }\frac{-3}{5} \\ tan\theta=\frac{-4}{3} \end{gathered}[/tex]a=460 rounded to the nearest 10 b=11.9 rounded to 1 dp find the minimum (to 2 dp) of a / b
The minimum result (to 2 dp) of a / b is 38.66
What is rounding decimals?The term "rounding decimals" refers to the accurate rounding of decimal figures. When rounding a decimal number, certain principles must be followed. Simply put, if the last digit is less than 5, round down the previous digit. However, if it is 5 or greater, round the previous digit up.Given:
a=460 rounded to the nearest 10
b=11.9
Now, substitute the values of a and b in a/b,
a/b = 460/11.9
Multiply the same integer(10) by both the numerator and denominator,
a/b = 4600/119
Round the number obtained
a/b ≅ 38.66
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Find the largest of three consecutive odd integers whose sum is 111.
The largest of three consecutive odd integers whose sum is 111 is 39
What is an integer?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.
Odd integers that follow each other grow (or shrink) by a factor of 2. Consider the numbers 1, 3, and 5. Add two to the preceding number to move from one to the following. You don't know where to begin, and that is the issue here. In actuality, you are searching for the least of the three integers, therefore this is your unknown.
x + (x + 2) + (x + 4) = 111
x + x + 2 + x + 4 = 111
3x + 6 = 111
3x = 105
x =[tex]\frac{105}{3}[/tex]
x = 35
35 ,37,39
The largest of three consecutive odd integers whose sum is 111 is 39
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a firm uses a trend projection and a seasonal factor to simulate sales for a given time period. it assigns 0 if sales fall 1 if sales are steady 2 if sales rise moderately and 3 if sales rise a lot. the simulator generates the following output
0102000103200002123120203002101
estimate the probability that sales will remain steady. express as a fraction and as a decimal
The probability that the sales will will remain steady is; 7/30 or 0.233
What is the probability of occurrence?We are given the numbers generated by the simulator for the sales as;
0, 1, 0, 2, 0, 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 1, 2, 3, 1, 2, 0, 2, 0, 3, 0, 0, 2, 1, 0, 1
Now, we are given the following implications of the simulator as;
If it assigns 0, then it means that sales fall.If it assigns 1, then it means that sales are steady.If it assigns 2, it means that sales rise moderately.If it assigns 3, it means that sales rise a lot.Now, we want to find the probability that the sales will will remain steady which is the point at which it assigns 1 from the 30 numbers generated. Thus;
P(sales will remain steady) = 7/30 = 0.233
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8. A car costs $10,500, and you're offered a loan that requires $800 down and a monthly payment of $187.53 for 60 months, how much will you pay in interest? Round your answer to the nearest dollar.$
The Solution:
Given that a car that cost $10500 was offered as a loan with a down payment of $800.
This means the loan balance will now be:
[tex]\text{Loan baleance=10500-800= \$9700}[/tex]The loan payment plan is a monthly payment of $187.53 for 60 months.
[tex]\text{Total Payment=187.53}\times60=\text{ \$11251.80}[/tex]We are required to find how much was paid in interest.
We shall take the difference between the total payment and the loan balance.
[tex]\begin{gathered} \text{Interest paid=Total payment-Loan balance} \\ \text{Interest paid=11251.80-9700= \$1551.80}\approx\text{ \$1552} \end{gathered}[/tex]Therefore, the correct answer is $1552
A. The printer prints the entire report in 152 minutes
B.The printer prints 3 more pages per minutes in colored ink than black ink.
C.The printer prints 3 fewer pages per minute in colored ink than black ink.
D.The printer prints the same number of pages per minute in either type of ink.
Answer:
C
Step-by-step explanation:
the function calculates the number of pages left to print. that means for every minute it subtracts a number of pages from the total of pages (that total being 152 pages).
the colored print only manages 30 pages per minute, while the pure black ink printing manages 33 pages per minute.
If z varies inversely as w, and z=20 when w=6, find z when w=3.
Z=
I have watched 32% of the episodes of my favorite show. I have watched 8 episodes. How many episodes are there?
Answer:
There are 35 episodes in the show
Yesterday, grace drove 28 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
Answer: 22.8 miles or 22 4/5
Step-by-step explanation:
To find the unit rate you do
28.5 ÷ 1.25 = 22.8
Find X. Circumscribed Angles
The value of of angle x of the circumscribing circle is x° = 140°
In the above question, the following figure is given, where
The angle inside the circle made by the intersection of two line segments is = 40°
We need to find the angle x made by the angle made by the tangents outside the circle
A line that touches a curve or a circle at one point is said to be tangent.
The point of tangency is the intersection of the tangent line and the curve.
We'll find the value of of angle x using the theorems of the circumscribing circle.
The sum of opposite angles of a circumscribing quadrilateral is always 180°
Using this property we can write,
40° + x° = 180°
x° = 180° - 40°
x° = 140°
Hence, the value of of angle x using the theorems of the circumscribing circle is x° = 140°
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41 points 3 games how many points 11 games
Answer:
33by 11
Step-by-step explanation:
in 41 3 games firstly we find 1 point it is 3by41
The half-life of a radioactive kind of copper is 3 hours. if you start with 2,352 grams of it, how much will be left after 9 hours??
Answer:
294 grams
Explanation:
The amount of radioactive material left after t hours given that the half-life is to hours is
[tex]A=P(0.5)^{\frac{t}{t_0}}[/tex]Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives
[tex]A=2352(0.5)^{9/3}[/tex][tex]A=294g[/tex]which is our answer!
Hence, the amount of radioactive copper left after 9 hours is 294 grams.
Brittany has 34,011 in a savings account that earns 6% annually. the interest is not compounded. How much interest will she earn in 4 years? use the formula I = PRT, where I is the interest earned, p is the principal, r as the interest rate expressed as a decimal, and T is the time in years.
Notice that we are dealing with simple interest, and therefore given by the formula:
I = P * R * T
where P = $34,011
R = 6% in "decimal" form (0.06)
T = 4 (for 4 years)
Then, we have:
I = 34011 * 0.06 * 4 = $8162.64
This is the interest Brittany earned in 4 years.
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeee!!!
Answer:
I think it is y
Step-by-step explanation:
what is the product of [tex] ( - \frac{3}{4} ) \times ( - \frac{7}{8} )[/tex]
What is the product of
In the multiplication of fractions, you multiply the numerators with each other and the denominators with each other
( - 3/5) *(-7/8)
= -3*-7 / (5*8) = (positive)
= 21/40
_____________________
Answer
= 21/40
_____________________
Do you have any questions regarding the solution?
Convert each slope-intercept or point slope equation into standard form.
y - 3 = 1/5(x + 6)
The Standard form of the equation will be;
⇒ x - 5y = -21
What is Standard form of equation?
The standard form of the equation is defined as;
Ax + By = C
Where, A, B and C are integers.
Given that;
The equation in slope - intercept form as;
⇒ y - 3 = 1/5 (x + 6)
Now,
We convert the equation in standard form as;
Since, The equation in slope - intercept form as;
⇒ y - 3 = 1/5 (x + 6)
Change into standard form as;
⇒ y - 3 = 1/5 (x + 6)
Multiply by 5 both side, we get;
⇒ 5( y - 3) = (x + 6)
⇒ 5y - 15 = x + 6
Add 15 both side, we get;
⇒ 5y - 15 + 15 = x + 6 + 15
⇒ 5y = x + 21
Subtract 21 both side, we get;
⇒ 5y - 21 = x + 21 - 21
⇒ 5y - 21 = x
Subtract 5y both side, we get;
⇒ 5y - 21 - 5y = x - 5y
⇒ - 21 = x - 5y
⇒ x - 5y = -21
Therefore,
The Standard form of the equation will be;
⇒ x - 5y = -21
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Need help with absolute value please
Answer:
let's say you need to find the absolute value of -5 the answer would be 5.
Step-by-step explanation:
Since the distance between -5 and 0 in a number line is 5. This would also be applied If you you were trying to find the absolute value of 5. it would also be 5.
When in math, I figured out negative number's absolute value will always be positive. absolute value numbers of positive numbers will stay the same.
Describe the shape, orientation, and vertex of
each parabola relative to the graph of y=x².
Sketch each graph.
a) y=-0.5x² + 2
c) y = -0.1x² - 6
e) y=-3x²-5
g)y=8x²+4
b) y = 2x²
d)y=x²+4
f) y=0,1x² +2
h) y=-0.7x²-3
The parabola y = - 0.5x² + 2 opens downwards and the vertex is at (0,2) .
A parabola is a mirror-symmetric planar curve with a rough U-shape. It can be defined by many seemingly unrelated mathematical descriptions that all relate to the same curves.
One way to interpret a parabola is with a line and a point (the focus) (the directrix). The directrix is less significant. The parabola lies between the directrix or the focus and the endpoints in this plane that are uniformly spaced apart.
a) y=-0.5x² + 2 vertex is at (0,2)
c) y = -0.1x² - 6 vertex at (0,6)
d)y=x²+4 vertex at (0,-4)
e) y=-3x²-5 vertex at (0,5)
g)y=8x²+4 vertex at (0,-4)
h) y=-0.7x²-3 vertex at (0,3)
A parabola can also be thought of as a conic section formed by joining a right circular conical area with a plane perpendicular to another axis.
The graph of the parabola is attached below.
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A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers. Determine the expected number of the real workers in any sample of size 50?
The expected number of the real number in any sample size is 150.
What is sample size?
In statistics, the sample size refers to the group of people whose data is analyzed during calculation. Depending upon the constraints, the data is analyzed for the measurement. The analysis of samples is perform with the help of Binomial distribution.
According to the question, the given random sample can be solved with the help of Binomial distribution:
The sample size of teachers: n = 50
Percentage of ghost workers: 30%
Percentage of real workers: 70%
For ghost workers: n = 50 and p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69
Now, to calculate the expected number of the real workers as per given samples:
For real workers: n = 50 and p = 0.70 and q = 1 - p = 1 - 0.70 = 0.30
Expected number is: (n)(q) = (50)(0.30) = 150
Hence, the expected number of the real number in any sample size is 150.
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