The cost of the basic portrait package = $55
The cost of the deluxe portrait package = $97
What is a system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Here, we let
x = the cost of the basic portrait package
y = the cost of the deluxe portrait package
Eighth graders from Dover Elementary School ordered 82 basic portrait packages and 73 deluxe portrait packages, for a total of $11,591:
82x + 73y = 11591
The seniors at Clarksville High ordered 85 basic portrait packages and 70 deluxe portrait packages, for a total of $11,465:
85x + 70y = 11465
by solving the system of equations:
82x + 73y = 11591
85x + 70y = 11465
We get
x = $55
y = $97
Hence, the cost of the basic portrait package = $55
the cost of the deluxe portrait package = $97
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Area and
Circumference
The area of the circle is 25.12 unit² and the circumference is 17.75 units.
Define a circle's area and circumference.The space a circle takes up on a two-dimensional plane is known as the area of the circle. The region included by the circle's radius or perimeter is another way to define the circle's area.
A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant π.
The given points of radius are
(x₁, y₁) = (2, 3)
(x₂, y₂) = (4, 1)
The formula for the distance between the specified points is
r = [tex]\sqrt{(y_{2}-y_{1})^{2} + (x_{2}-x_{1})^{2} }[/tex]
r = [tex]\sqrt{(1-3)^{2} + (4-2)^{2} }[/tex]
r = [tex]\sqrt{4+4}[/tex]
r = 2[tex]\sqrt{2}[/tex] units
The area of the given circle will be given by the formula A = πr²
A = 3.14 × (2√2)²
= 3.14 × 8
= 25.12 unit²
The circumference of the given circle will be given as
C = 2πr
C = 2 × 3.14 ×2√2
C = 12.56√2
C = 12.56 × 1.414
C = 17.75 unit
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V=πh^(r-h/3) make r the subject formula
If we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)
In this question, we have been given a formula V=πh^(r-h/3)
We need to make r the subject formula
This means we need to rewrite formula for r.
V = πh^(r-h/3)
h^(r-h/3) = V/ π
r - h/3 = log_h(V/π)
r = log_h(V/π) + (h/3)
Therefore, if we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)
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Please help! This unit is stressing me out!! I will give you brainliest answer!
What is the mean in hypothesis testing?
Answer:
t = (x - μ) / SE. where x is the sample mean, μ is the hypothesized population mean in the null hypothesis, and SE is the standard error. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic.
Step-by-step explanation:
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The mean in hypothesis testing is the parent population from which the samples are drawn.
What is hypothesis testing?In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population parameter. The analyst's methodology is determined by the nature of the data and the purpose of the analysis. Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis.
Hypothesis testing is a type of statistical inference that employs sample data to draw conclusions about a population parameter or probability distribution. First, an educated guess is made about the parameter or distribution.
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At the beginning of the year 2005, a person invests some amount in a bank. At the beginning of 2010, the accumulated interest was 10000 and at the beginning of 2015, the accumulated interest became 25000. The interest rate is compounded annually and the annual interest rate is fixed. What is the principal amount
Answer:23000
Step-by-step explanation:
The principal amount is ₹20000.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Let the money at beginning of the year 2005, a person invests in a bank be x.
At the beginning of 2010, the accumulated interest was ₹10000.
Now, x(1+r/100)⁵=x+10000 ------(I)
Let x(1+r/100)⁵=A
At the beginning of 2015, the accumulated interest became ₹25000.
So, x(1+r/100)¹⁰=x+25000 ------(II)
From the equation (I),
x(A-1)=10000 ------(III)
From equation (II), we get
x×A²=x+25000
x(A²-1)=25000 ------(IV)
From equation (III) and (IV), we get
10000(A+1)=25000
A=1.5
Put A=1.5 in equation (III), we get
0.5x=10000
x=10000/0.5
x=₹20000
Therefore, the principal amount is ₹20000.
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The Haddads expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85, but did not know by how much. Their
account showed a previous balance of $417.80, $350.00 in deposited checks,
an automatic deposit of $150.00, and $5.25 in interest. If the Haddads' present
balance is $555.82, by how much did this month's gas bill exceed last month's bill?
The gas bill exceeded $87 from last month to this month.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, The Haddad expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85 but did not know by how much.
Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.
∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.
Haddads' present balance is $555.82,
∴ The gas bill is $(858.69 - 555.82) = $302.87.
So the gas bill s exceeded by $(302.87 - 215.85) = $87.
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Find the product of (3 x 10 9) and (2 x 10 9). Write the final answer in scientific notation.
6 x 10 81
6 x 100 18
6 x 10 18
6 x 10 9
Answer:
6 x 10^18
Step-by-step explanation:
3 x 2 = 6
10^9 * 10^9 = 10^(9+9) = 10^18
Rounded to the nearest tenth, what is the perimeter of the triangle?
60°
5 cm
30°
Answer:
11.0 cm
Step-by-step explanation:
Answer:
11.8 cm
Step-by-step explanation:
2.5 + 5 + 2.5√3 = 7.5 + 2.5√3 = 11.8 cm
Three rectangular prisms have the same based area but different heights. As the heights of the these prism increase, the volume increases. Identify the independent variable in this situation.
Responses
width of the prism
volume of the prism
area of the prism
height of the prism
length of the prism
The independent variable in this situation is C. area of the prism.
What is a variable?In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent, by some law or rule, on the values of other variables.
The term "independent variable" means exactly what it sounds like. It is a variable that is independent of the other variables you are attempting to measure. For example, age could be an independent variable.
In this case, the area doesn't change in relation to others. It's independent.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
When a transversal crosses a pair of parallel lines same side interior angle pair are supplementary.
What is parallel lines?
Two lines in same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both lateral and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks. Different shapes' sides run parallel to one another. The single arrow lines in the rectangle below are parallel to one another, and the double arrow lines also are parallel to one another.
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tan^2x+1=sec^2x
how do i prove the identity
The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.
How to prove a derivate trigonometric formula
In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.
Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:
sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x
Step 2 - Divide each side of the formula by cos² x:
sin² x / cos² x + cos² x / cos² x = 1 / cos² x
(sin x / cos x)² + 1 = (1 / cos x)²
Step 3 - Use the definition of the two trigonometric functions:
tan² x + 1 = sec² x
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Can you guys help out and awnser this chart with the following questions:(
1) Saleena worked for 20 hours in total.
2) She earned $220 during the week.
Define time.Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Given,
Saleena has a part time job.
a) On Monday
Start time = 4: 30 pm
End time = 9:00 pm
Hours worked = 4 : 30 hours
b) On Tuesday
Start time = 3: 00 pm
End time = 9 : 00 pm
Hours worked = 6 hours
c) On Thursday
Start time = 4: 30 pm
End time = 9: 00 pm
Hours worked = 4 hours 30 minutes
d) On Saturday
Start time = 10:30 pm
End time = 3 : 30 pm
Hours worked = 5 hours
Total hours worked = 4:30 + 6 + 4: 30 + 5
1) Saleena worked for 20 hours in total.
2) She earns $11/h
Saleena worked for 20 hours in total.
Multiplying by $11 for per hour
20 × 11
220
2) She earned $220 during the week.
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Hi can someone please find the area of this circle? Thank you!
If a statement is given that angle A and angle B are complementary, which fact would be needed to prove that this geometric relationship is true?
The geometric relationship sum of ∠A+∠B = 90° as they are complementary.
What is are complementary?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.
It is given that angle A and angle B are complementary.
Hence, The geometric relationship sum of ∠A+∠B = 90°
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Is the function 4y = 24 linear or nonlinear?
The given function is linear and constant because your equation is represented by the standard form for the linear equation.
Which is a Linear Function?
A linear function can be represented by an equation. The standard form for the linear equation is: y= mx+b , for example, y=6x+4. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=6 and b=4.
An equation is classified as nonlinear when it is not represented by the standard form for the linear equation. For example, 2x²+x+10, x², x³, x³ +2, etc.
The given equation is 4y=24. Firstly, you should rewrite it to the standard form for the linear equation is: y= mx+b. Therefore,
4y=24
y=24/4
y=6
If the standard form for the linear equation is y= mx+b, for the given equation m=0 and b=6. Thus, the given equations is linear and constant. It can be classified for constant because for any value of x, the value of y always be equal to 6.
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Imagine that your school planted two trees when it was first opened. One tree, a ficus, was 6 feet 6 feet tall when it. was planted and has grown 1.5 feet 1.5 feet per year. The other tree, an oak, was grown from an acorn on the ground and has grown 2 feet 2 feet per year. When will the trees be the same height? How tall will the trees be when they are the same height?
The height of the two trees will be same after 13 years and the height of the trees will be 24 feet.
According to the question,
We have the following information:
One tree, a ficus, was 6 feet tall when it. was planted and has grown 1.5 feet per year. The other tree, an oak, was grown from an acorn on the ground and has grown 2 feet per year.
So, for first tree, we have:
6, 7.5, 9, ...
Now, this is an arithmetic progression.
So, for the second tree, we have:
0,2,4, ...
Now, this is again an arithmetic progression.
Formula to find nth term of an A.P.:
an = a+(n-1)d where a is the first term and d is the common difference
6+(n-1)1.5 = 0+(n-1)2
6+1.5n-1.5 = 0+2n-2
4.5 = 2n-1.5n-2
6.5 = 0.5n
n = 13 years
Now, we have the height of the trees after 13 years:
an = 0+(13-1)2
an = 12*2
an = 24 feet
Hence, the height of the two trees will be same after 13 years and the height of the trees will be 24 feet.
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Moloch The Destroyer is looking to save up for an evil lair. He has placed $104,828 in an account with 1.02% interest compounded monthly. How much will he have after 2
years?
Moloch have $133,737.75 after 2 years at the interest of 1.02% per month.
What is compound interest?Interest accrued on both the principal sum of money and the interest already earned.
The formula for compound interest is A= p(1+r/100)ⁿ
Where A is amount, p is principal, r is rate and n is time.
Given that,
The amount Moloch placed in account = $104,828
The rate of interest = 1.02% per month
time = 2 years,
To find total amount Moloch has after 2 year,
Use formula
Amount = [tex]p(1+r/100)^{nt}[/tex]
= 104,828 (1+1.02/100)²ˣ¹²
= 104,828 (1+0.0102)²⁴
= 104,828 (1.0102)²⁴
= 104,828×1.27578
= 133,737.75
After 2 years, Moloch have $133,737.75 in account.
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A coin 22 mm in diameter contains 66 mm³ of metal. How thick is the coin? [Take
[tex]\pi[/tex]
=3.142]
Answer:
3000/17281 mm
Step-by-step explanation:
We can model this as a cylinder with a volume of 66 mm³, a radius of 11 mm, and an unknown height [tex]h[/tex] mm.
Using the formula for the volume of a cylinder,
[tex]V=\pi r^2 h \\ \\ 66=11^2 \pi h \\ \\ h=\frac{66}{121\pi} \\ \\ h=\frac{6}{11\pi} \\ \\ h \approx \frac{6}{11(3.142)} \\ \\ h \approx 3000/17281[/tex]
Answer:
0.17 (2d.p)
Step-by-step explanation:
volume of cylinder= πr^2Xh
22/2=11 which is radius
11^2=121
121X3.142=380.182
380.182Xh=66
h=66/380.182=0.1736010648
Solve x − 7y = 8 for x.
Answer:
x=7y+x
Step-by-step explanation:
Isolate x on one side
x-7y=8
+7y. +7y
x=7y+8
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true or false Two planes intersected by a third plane are parallel
Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.
Define parallel.Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Given,
Two planes intersected by a third plane are parallel.
Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.
A line is formed by the intersection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot meet at a single place. Stack a hardcover book on your desk and open the two hard covers at any random angle. The coverings' planes are not parallel to one another but are individually perpendicular to the desk top (or necessarily perpendicular to each other).
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How many permutations are there in BOOKKEEPING
Answer: There are 151200 permutations
Answer:
In the word "bookkeeping" there are approximately 151,200 permutations.
Step-by-step explanation:
Permutations:
Is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.
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Alonso went to the store to buy some almonds. The price per pound of the almonds is $7.25 per pound and he has a coupon for $3.50 off the final amount. With the coupon, how much would Alonso have to pay to buy 5 pounds of almonds? Also, write an expression for the cost to buy pp pounds of almonds, assuming at least one pound is purchased.
Answer:
It costs 32.75 for five pounds. and the expression would be p7.25-3.50
Step-by-step explanation:
5*7.25 = 36. 25. 36.25-3.50=32.75
c=p7.25-3.50 would be the expression. :)
Write the following ratio using two other notations.
5 to 2
Use only the numbers above (not any others).
The ratio 5 to 2 is written in other notations as
5 : 25 / 2What are ratios?Mathematicians use the term "ratio" to compare two or more numbers.
It serves as a comparison tool to show how big or small an amount is in relation to another.
In a ratio, division is used to compare two amounts.
The ratio 5 is to 2 can be represented as a fraction to 5 / 2
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find the missing terms of the arithmetic sequence __ -6 __ __ 15 __
The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
an = a1, a2, a3, a4, a5, a6
formula for nth term is :
an = a + (n - 1)d
where
an = last term
a = a1 = first term
n = number of terms
d = difference between two terms
here
a2 = a + d
- 6 = a + d ....(1)
a5 = a + 4d
15 = a + 4d .......(2)
on solving equation we get :
- 6 = a + d ....(1)
15 = a + 4d .......(2)
(-) (-) (-)
- 21 = - 3d
d = 21/3
d = 7
using the value of d in equation the value of a is :
- 6 = a + d
-6 = a + 7
a = -6 -7 = -13
then
a1 = a = -13
a2 = a + d = -13 + 7 = -6
a3 = a + 2d = -13 +2 x 7 = 1
a4 = a + 3d = -13 + 3 x 7 = 8
a5 = a + 4d = -13 +4 x 7 = 15
a6 = a + 5d = -13 +5 x 7 = 22
The missing terms of the arithmetic sequence -13, - 6, 1 , 8 , 15, 22.
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Damon is saving for a vacation. He estimates that he’ll need about $2,500 for the trip. He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal. In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation. Review his work, and select the true statement. Step 1: y = 500 + 400x Step 2: y − 500 = 500 + 400x − 500 Step 3: y − 500 = 400x Step 4: y − 500 400 = 400 x 400 Step 5: y − 500 400 = x Step 6: 2 , 500 − 500 400 = x Step 7: 5 = x A. Damon used the multiplication property of equality in step 2. B. Damon used the subtraction property of equality in step 3. C. Damon used the division property of equality property in step 4. D. Damon used the associative property in step 5. E. Damon used the addition property of equality in step 6.
By reviewing Damon's work, the true statement is, Damon used the subtraction property of equality.
what is true statement?
A statement is true if the assertion it makes is true, and it is false if the assertion it makes is untrue. For example, the statement "The trains are always late" is only accurate if the situation it describes—that is, if the trains are indeed always late—actually exists.
As given, Damon is saving for a vacation.
He estimates that he’ll need about $2,500 for the trip.
He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal.
In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation.
The statements are,
Step 1: y = 500 + 400x
Step 2: y - 500 = 500 + 400x - 500
Step 3: y - 500 = 400x
Step 4: y - 500/400 = 400x/400
Step 5: y - 500/400 = x
Step 6: 2500 - 500/400 = x
Step 7: 5 = x
Therefore, the true statement is Damon used the subtraction property of equality in step 3.
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Help please I will give you 100 points
The angles of the given figure are:
∠1 = 128°
∠2 = 52°
∠3 = 47°
∠4 = ∠5 = 81°
What are corresponding angles?
Corresponding angles are those created when a transversal line crosses two straight lines. When two or more straight lines and a transversal intersect, corresponding angles are found at the intersection.According to the corresponding angles rule, a transversal cutting two parallel lines results in corresponding angles that are equal.The angle is supplementary(∠5)
52° + ∠5 + 47° = 180°
∠5 + 99° = 180°°
∠5 = 180° - 99°
∠5 = 81°
Then the ∠1 and 52° are supplementary (Interior adjacent angles)
∠1 + 52° = 180°
∠1 = 180° - 52°
∠1 = 128°
Now, ∠2
∠2 + ∠5 + 47° = 180°
∠2 + 81° + 47° = 180°
∠2 = 180° - 128°
∠2 = 52°
Based on interior opposite angles are equal. Then
∠5 = ∠4 and ∠3 = 47°
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A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.
What is the velocity of the car when t = 6? Please show your work and include units in your answer.
The velocity experimented by the car is equal to - 1 feet per second.
What is the velocity of a car at a given time?
Herein we have the graph of the position of the car (y), in feet, versus time (t), in seconds. The graph shows a linear equation, that is, the position is described by a polynomial of the form:
y = m · t + b
Then, the functions for the velocity and acceleration are shown below:
Velocity
dy / dt = m
The slope represents the velocity of the car.
Acceleration
d²y / dt² = 0
Then, the velocity of the car is found by means of the secant line formula:
dy / dt = (0 ft - 10 ft) / (10 s - 0 s)
dy / dt = - 1 ft / s
The velocity of the car is - 1 feet per second.
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Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
A. y=-2² +4
B. y= 2²
C. y=log₂ (x+2)+1
D. y= log₂ (x+2)
A) Y = [tex]-2^{x}+4[/tex] is the equation which have real zero(s) corresponding to the x-intercept(s) of the graph below
What does a mathematical coordinate mean?
a set of numbers used to represent the horizontal and vertical divisions of the positions of two reference axes in a coordinate plane. often shown as the combination of x-values and y-values (x,y).
What is the Slope Intercept Form Equation?
The slope intercept equation can be used to find the general equation of a straight line using its slope and the point of its y-axis junction. The equation in slope intercept form is Y = mx + b.
You must enter y=0 for the x intercept.
in equation A we can see that at x=2 , y=0
so hence answer is option A) Y =[tex]-2^{x}+4\\[/tex]
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09.
If X = 12, Y = ¹/3, and T = 6
Evaluate XY - YT.
Answer:
XY - YT = 2
Step-by-step explanation:
substitute the given values into the expression
XY - YT
= (12 × [tex]\frac{1}{3}[/tex] ) - ([tex]\frac{1}{3}[/tex] × 6 )
= 4 - 2
= 2
The sum of two binomials is 5z + 6. If one binomial
is 3z - 4, what is the other binomial?
Answer: 2z+2
Step-by-step explanation:
