Answer:
On Friday it saved 1,024
Step-by-step explanation:
The computation of the amount saved on friday is given below:
GIven that
On Monday it saved P4
On Tuesday it saved P16 (P4 × 4)
On Wednesday it saved P64 (P16 × 4)
On Thursday it saved 256 (P64 × 4)
On Friday it saved 1,024 (P256 × 4)
On a recent trip to the convenience store, you picked up 2 gallons of milk, 6 bottles of water, and 7 snack-size bags of chips. Your total bill (before tax) was $25.65. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.90 more than a bottle of water, how much does each item cost?
Answer:
The water costs $1.90, the chips are $.95 and the milk is $3.80.
Step-by-step explanation:
Let m = milk
Let w = water
Let c = chips
2m+6w+7c =25.65 w = 2c m = w + 1.90
For the first equation, substitute w for 2C and m for w + 1.90 to get:
2(w+1.90) +6(2c) + 7c = 25.65
2w+3.8+12c+7c=25.65
2w+19c = 21.85
Now substitute 2c for w:
2(2c)+19c =21.85
4c + 19c = 21.85
23c = 21.85
c = .95 Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.
w = 2c
w=2(.95) = 1.90
m = w + 1.90 = 1.90+1.90 = 3.80
We know for a fact that the equation:
[tex]|z+z'| \leqslant |z|+|z'|[/tex]
holds for any 2 complex numbers
I came up with the conclusion that:
[tex]|z+z'|=|z|+|z'|[/tex]only holds when z and z' are pure imaginary or pure real numbers of the SAME sign.
How can i prove this algebraically/geometrically?
Note: Irrelevant answers will be reported
They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].
Let [tex]z=z'=a+bi[/tex]. Then
[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]
[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]
so [tex]|z+z'|=|z|+|z'|[/tex].
The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].
In the triangle below M, Z, and P are the midpoints of the sides. Name a segment that is parallel to the one given. Pay attention to the order of the points used in the given side.
Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
What is the Triangle Midsegment Theorem?The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.
In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:
MP which is parallel to XY, also, MP = 1/2(XY)
PZ which is parallel to WX, also, PZ = 1/2(WX)
MZ which is parallel to WY. also, MZ = 1/2(WY)
Thus, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
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The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 Which equation best compares the y-intercepts of f(x) and g(x)? The y-intercept of f(x) is equal to the y-intercept of g(x). The y-intercept of f(x) is equal to 2 times the y-intercept of g(x). The y-intercept of g(x) is equal to 2 times the y-intercept of f(x). The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x). Question 12(Multiple Choice Worth 1 points) (01.04 MC) A store manager can spend at most $1,000 a day for operating costs and payroll. It costs $100 each day to operate the store and $30 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most: 30x + 100 ≤ 1000 x ≥ 30 x ≥ 33 x ≤ 33 x ≤ 30 Question 13(Multiple Choice Worth 1 points) (02.01 LC) Which of the following tables represents a function? x 1 −1 4 −4 y 8 8 10 10 x 2 2 3 3 y 6 −6 7 7 x 5 −5 5 −5 y 10 11 12 13 x 2 2 7 7 y 2 3 4 5 Question 14(Multiple Choice Worth 1 points) (01.06 LC) Joy needs 8 feet of fabric for a project she is working on, but the store only sells the fabric in meters. One meter of fabric costs $1.15. How much will the fabric cost? [1 ft = 0.305m] $9.20 $2.12 $2.81 $30.16 Question 15(Multiple Choice Worth 1 points) (04.02 LC) What is the solution to the following system of equations? x − 3y = 5 2x + y = 10 (5, 0) (0, 5) (7, 0) (0, 7) You must check the box below prior to submitting your exam! Check this box to indicate you are ready to submit your exam Instructors monitor ALL areas of a student's account Student e-mail accounts are to be used for FLVS course-related email only and not for general introductions or spamming of people in your address book. Please remember to click the Logoff link when you have completed your work in the course. FDK191.12
Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)
What is the examination of the y-intercept?The value of the function at the point where the value of x is equal to zero is known as the y-intercept.
f(x)=-6(1.05)^x
Considering x
x=0
f(0)=-6(1.05)^0
f(0)=-6(1)
f(0)=-6
Therefore, the y-intercept is point (0,-6)
Generally, the equation for the function of the y-intercept of g(x) is mathematically given as
From table
at x=0
The y-intercept is the point (0,-3)
Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)
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Express the formula in terms of the height, Use that formula to find the height when the volume is and the radius is
The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5
How to change the subject of the formula?We are given the formula for volume of a cylinder as;
V = πr²h
where;
h is height
r is radius
To make h the subject, let us divide both sides by πr² to get;
V/(πr²) = h
At V = 45π and r = 3, we have;
h = 45π/(πr²)
h = 45/3²
h = 5
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Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9
Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]
Simplify
18÷[7+2{7+2(7-6)}+2
Answer is
[tex] \frac{2}{3} [/tex]
Show me the steps by steps
Answer:
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
=18÷[7+2{7+2(7-6)}+2]
=18÷[7+2{7+2×1}+2]
=18÷[7+2×9+2]
=18÷[7+18+2]
=18÷27
=[tex] \frac{18}{27} [/tex]
=9 two is 18 and 9 three is 27
So,
=[tex] \frac{2}{3} [/tex]
I need some help please
The values of x and y that can represent the equation is illustrated.
How to illustrate the information?The equation given us 32 = xy + 16
The table will be:
x. y
4. 4
16. 1
2. 8
32. 0.5
For example, when x and y are 4. This will be:
= xy + 16
= (4 × 4) + 16
= 32
Other values of x and y will also give 32.
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How do u solve for X?
Answer:
x = 70
Step-by-step explanation:
x and 2x - 30 are supplementary angles , sum to 180° , then
x + 2x - 30 = 180 ( add 30 to both sides )
3x = 210 ( divide both sides by 3 )
x = 70
Answer:
2x - 30 and x degrees should add up to 180 degrees
2x - 30 + x = 180
3x = 210
x = 70 degrees
The correct answer would be D
According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48
Option A, The option that has the same potential roots according to the rational root theorem is 3x5 – 2x4 – 9x3 + x2 – 12.
How to solve for the rootsWe have p, this is the factors of the number 12.
The factors are ±(1, 2, 3, 4, 6, 12)
We have factors of q = 3
= ±(1, 3)
The rational roots are the roots that have the same factors that are contained in the question.
Hence the answer is A.
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Answer:
The Answer is A
Step-by-step explanation:
Did it on edge :)
write the whole number as an equivalent fraction with the given denominator.
3= 4
Answer: 12/4
Step-by-step explanation: whole number = 3. given denominator = 4. 4/4 = 1. 1 times 3 = 3. 4 plus 4 plus 4 = 12. therefore answer is 12/4
A number is negative if and only if it is less than 0.
p. A number is negative.
q. A number is less than 0.
Which represents the inverse of this statement? Is the inverse true or false?
~p4~9
The inverse of the statement is sometimes true and sometimes false.
Oq+p
The inverse of the statement is true.
q→P
~q→ ~p
The inverse of the statement is false.
The inverse statement is:
¬q ⇒ ¬p
Which is true.
How to get the inverse statement?
Here we have the biconditional statement:
A number is negative if and only if it is less than zero.
Where:
p = a number is negative.q = a number is less than 0.So we can write the statement as:
p ⇔ q
The inverse statement is:
if not q, then not p.
or
¬q ⇒ ¬p
Replacing p and q, we have:
"if a number is not less than zero, then the number is not negative".
This is true, if the number is not less than zero, then the number is 0 or larger, so that number is not negative.
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Answer:
D.
∼p↔∼q
and
G.
The inverse of the statement is true.
Step-by-step explanation:
Rewrite as an exponential equation.
In 5 = y
The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
How to rewrite the expression?The natural logarithm equation is given as:
ln 5 = y
Rewrite as:
ln(5) = y
Take the exponent of both sides
[tex]e^{ln(5)} = e^y[/tex]
Evaluate the expression
[tex]5 = e^y[/tex]
Rewrite as:
[tex]e^y = 5[/tex]
Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
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Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.
The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.
Notice that the Angles of a Triangle add up to 180° That is
∠A + ∠B + ∠C = 180°
Thus,
∠C = 180° - 32° - 109°
= 39°
Recall the Sine Theorem which indicates;
a/SinA = b/SinB = c/SinC
thus given that
AC = 1,523m
We have
AC/SinB = BC/SinA
BC = AC/SinB * SinA
= 1523/Sin109° * Sin32°
BC =854m
Therefore
AC/SinB = AB/SinC
Thus,
AB = AC/SinB * SinC
= 1523/Sin109° * Sin39°
AB ≈ 1,014m
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12 ft
8 ft
8 ft
Find the area of the kite
The area of the kite exists 48 sq. ft.
How to estimate the area of kite?The area of a kite exists half the outcome of the lengths of its diagonals. The formula to define the area of a kite exists:
Area = ½ × p × q.
Given that a kite contain diagonals of lengths 12 ft and 8 ft.
We know that the area of a kite having diagonals of length 'p' units and 'q' units exists
Area of kite = ½ (p × q)
Here, p = 12 ft and q = 8 ft.
Area of kite = ½ (p × q)
= (12 × 8)/2
= 96/2 = 48
Therefore, the area of the kite will be 48 sq. ft.
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The figure shows two parallel lines PQ and ST cut by the transversals PT and QS:
Answer:
triangle PQR is similar to triangle TSR because the measure of angle 3 is congruent to the measure of angle 4 and the measure of angle one is congruent to the measure of angle 5
Step-by-step explanation:
angle 3 and angle 4 are congruent because they are vertical pairs.
Angles 1 and five are congruent because they are alternate interior angles
Please answer fast!
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Answer:
x = 15 & y = 35
Step-by-step explanation:
[tex]y = x + 20[/tex]
[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]
[tex]y = x + 20 = (15) + 20 = 35[/tex]
what is the measure of this
Answer:
60
Step-by-step explanation:
140-80=60
Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
The value of y in the triangle is B. 6✓3.
How to calculate the value?From the information given,
NU = 9
UM = 3
MN = 3 + 9 = 12
NT² = 9 × 12 = 108
NT = ✓108
NT = 6✓3
Therefore, y is 6✓3.
The value of y in the triangle is 6✓3.
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Answer:
B
Step-by-step explanation:
DATE PAGE No. Demand 10 a) A ratio of two number is equal to 3:8. If the smaller number is 12, find the greater number:
From ratio concept, the greater number number is 32 .
What is the greater number from concept of ratio ?A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)
Let the greater number be x .
The ratio given is 3:8 .
Thus, by the concept of ratio -
⇒ 3/8 = 12/x
⇒ x = (8/3 * 12)
∴ x = 32
Therefore, from ratio concept, the greater number number is 32 .
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PLEASE NEED HELP
A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. Boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. What percentage of filled boxes of rice are rejected for distribution?
Find the z-table here.
4.0%
24.2%
75.8%
96.0%
Answer:
D) 96%
Step-by-step explanation:
If you take 96% of 28.6 you get 27.6 so it fits
Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.
THE REAL ANSWER IS $107, 270
First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1
The total interest is $107,270
What is monthly payment formula?
The formula for monthly payment is:
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
We can find total interest as shown below:
Value of property = $475,000
Money available as a deposit = $80,000
P = 475,000-80,000
= 395000
t = 25 year
r = 2% = 0.02
n = 25*12 = 300
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
Putting the value of P, t, r, and n in the above formula
[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]
after solving the above expression
M = $1674.22
Interest = M*n-P
Putting the value of P, n and M
= 1674.22*300-395000
= 502266-395000
= 107,266
Rounding to nearest ten dollar
= $107,270
Hence, the total interest is $107,270.
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Answer:
Step-by-step explanation:
Question 9(Multiple Choice Worth 5 points)
(04.06A LC)
What is the slope of the line segment?
15
12
9
6
63
0123
0-3
0-13/1
O
O
1/3
3
5
Answer: 3
Step-by-step explanation:
[tex]\frac{3-0}{1-0}=3[/tex]
PLEASE HELP!!
From the triangle below, if AD=2 and CD=8. Find the Length of side AB
which quantity is scalary
Step-by-step explanation:
find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14. How old were the bones at the time they were discovered?
Therefore, the bones were 6612.5 years old at the time they were discovered.
Half lifeGiven that the radioactive element carbon-14 has a half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:
50 = 5750100 = 1150057.5 = X57.5 x 11500 / 100 = X6612.5 = XTherefore, the bones were 6612.5 years old at the time they were discovered.
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Answer:Therefore, the bones were 6612.5 years old at the time they were discovered.
Step-by-step explanation:
An advertiser claims that 74% of people stream their TV, 12% have cable, and the rest do not watch TV. A test is conducted to evaluate the claim and the conclusion is fail to reject
using alpha = 0.1. What is your interpretation of the test result?
Considering the hypothesis tested, the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
What are the hypothesis tested?At the null hypothesis, we test if the percentages are as advertised.At the alternative hypothesis, we test if the percentages are different than advertised.We fail to reject the null hypothesis, hence the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
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In what statistical measurement would you be most interested when considering housing prices in a particular city?
Answer:
Median
Explanation:
Real estate prices are virtually usually biased to the right. If we estimate the price of a typical home in a city at $500,000. We would have no trouble locating properties for $2 million and $3 million, and perhaps even some $5 or $6 million residences. However, you won't find houses for under $1.5 million. Because of this, the mean value is pulled toward the high end more than the median value.
Which equation could possibly represent the graphed function?
Answer: A
Step-by-step explanation:
The polynomial has roots at [tex]x=-4, -2, 4[/tex].
So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].
This eliminates everything except for A.
A role-playing game uses an 11-sided die that displays the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 What is the probability that someone throws the 11-sided die one time and rolls a number 9 or higher? Express your answer as a percentage rounded to one decimal place
Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:
p = 3/11 = 0.273 = 27.3%.
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