Answer:
(a)
f(x) = 30, for x ≤ 200
f(x) = 0.03(x - 200) + 30, for x > 200
(b) $34.50
(c) 356
Step-by-step explanation:
Let x = number of minutes.
(a)
f(x) = 30, for x ≤ 200
f(x) = 0.03(x - 200) + 30, for x > 200
(b)
Here, x = 350, so x > 200.
f(x) = 0.03(x - 200) + 30
f(350) = 0.03(350 - 200) + 30
f(350) = 0.03(150) + 30
f(350) = 4.5 + 30
f(350) = 34.5
$34.50
(c)
f(x) = 0.03(x - 200) + 30
0.03(x - 200) + 30 = 34.68
0.03(x - 200) = 4.68
x - 200 = 156
x = 356
The points A, B, and C, shown on the number line, have weights 0.5, 0.3, and 0.2 respectively.
H
в с
2 3 4 5 6 7 8
9 10
Which statement is true about the weighted average, w, of the points A, B, and C?
w lies before A.
w lies beyond C.
w lies between A and B.
w lies between B and C.
Answer:
"w" (and any subsequent words) was ignored because we limit queries to 32 words.
w = 0.33 so, w lies before A, B, and C.
Option A is the correct answer.
What is a number line?It is the representation of numbers in real order.
The difference between the consecutive numbers in a number line is always positive.
We have,
Average weight.
w = Sum of all the weight / 3
w = (0.5 + 0.3 + 0.2) / 3
w = 1/3
w = 0.33
Now,
A = 3, B = 6, and C = 7 on the number line.
0.33 lies before A, B, C
Thus,
w lies before A.
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PLEASE HELP!!!!!
Given that RS=18 and QR=6, identify the length of PS
Answer:
12 root 3
Step-by-step explanation:
first, you can say that QRP is similar to PRS
with the ratios, you can say that
[tex]\frac{QR}{PR} = \frac{PR}{RS}\\[/tex]
by substituting values, you have
[tex]\frac{6}{PR} = \frac{PR}{18}\\[/tex]
[tex]PR^2=108[/tex]
[tex]PR=6\sqrt{3}[/tex]
using pythagorean theorem, you can determine that
[tex]PS^2=(6\sqrt{3})^2+18^2[/tex]
[tex]PS^2=432[/tex]
[tex]PS=\sqrt{432}=12\sqrt{3}[/tex]
Answer:
12√3
Step-by-step explanation:
cos∠RSP = 18/PS
cos∠PSQ = PS/24
∠RSP=∠PSQ (the angle at S)
18/PS = PS/24
(PS)² = (18)(24) = 432
PS = √432 = 12√3
in the figure, OA/OC=OB/OD=1/4. the value of DC is 120 by the SAS test
The value of DC is of 80, hence the statement is false.
What are similar triangles?Similar triangles share these two features listed as follows:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The similar triangles for this problem are given as follows:
AOB and COD.
Hence the proportional relationship established between the side lengths is given as follows:
OA/OC = OB/OD = 1/4 = AB/DC.
Taking the last two terms, considering that AB = 20 cm, the length of DC is given as follows:
DC = 4 x AB
DC = 4 x 20 cm
DC = 80 cm.
Hence the statement is false, as the length is of 80 cm and not of 120 cm.
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Find the slope of the line between (19,-27) and (34,15)
After Julia has driven for a quarter of an hour, she was 170 miles east from Denver. After driving for 3 hours, she was only 100 miles east from Denver. Assume that Julia drove at a constant speed during the trip. Let be a function that gives Julia’s position east from Denver (measured in miles) after having driven for hours.
a) Determine a rule for the function .
b) Interpret the meaning of ^−1(16) and then find its value if it exists.
c) Interpret the meaning of ^−1(-141) and then find its value if it exists.
d) Determine a rule for ^−1 .
e) Construct a graph for ^−1 .
The rule for the function is P(t) = 170 + 680t
The time t after which Julia is 16 miles east from DenverThe time t after which Julia is -141 miles east from DenverThe inverse is P^-1(t) = (t - 170) / 680a) Determine a rule for the functionLet's call Julia's final position after t hours as P.
If she drove at a constant speed v (in miles per hour), then the distance traveled can be given as:
P - P0 = vt
Given that she was 170 miles east from Denver after driving for a quarter of an hour (0.25 hours), we can write the first equation:
170 = v * 0.25
v = 680
This means that her speed was 680 miles per hour.
Using this speed, we can write the second equation:
P = 680 * t
100 = 680 * t
t = 100 / 680 = 0.147
Combining the two equations, we can find the function that gives Julia's position east from Denver after t hours as:
P(t) = P0 + v * t ----- P0 = 170 i.e. her initial position
P(t) = 170 + 680 * t
So, the rule for the function P(t) is:
P(t) = 170 + 680t
The meaning of P^-1(16)P^-1(16) is the inverse of the function P(t) at the value 16.
In other words, it gives us the time t after which Julia is 16 miles east from Denver.
To find its value, we can use the equation of the function P(t):
P(t) = 170 + 680 * t
16 = 170 + 680 * t
-154 = 680 * t
t = -154 / 680
Time cannot be negative.
So, it does not exist
The meaning of P^-1(-141)P^-1(-141) is the inverse of the function P(t) at the value -141.
In other words, it gives us the time t after which Julia is 16 miles east from Denver.
So, we have
-141 = 170 + 680 * t
-311 = 680 * t
t = -311 / 680
Time cannot be negative.
So, it does not exist
Determine a rule for ^−1 .We simply make t the subject in P(t)
So, we have
P^-1(t) = (t - 170) / 680
The graph is attached
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PLEASE HELP!!!! BRAINEST IF CORRECT ONLY
Answer:
1. consistent independent
2. consistent dependent
3. inconsistent
Step-by-step explanation:
1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} \neq b_{1} :b_{2}[/tex]
2. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} = c_{1} : c_{2}[/tex]
1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} \neq c{1} : c_{2}[/tex]
Step-by-step explanation:
4x + y = 8
x + 3y = 8
consistent independent
both equations are lines with different slope.
so, they intersect at one point.
that is the solution.
-4x + 6y = -2
2x - 3y = 1
consistent dependent
both equations are actually identical lines.
multiply the second equation by -2.
and you see the equality.
that means every point is a solution.
there are infinitely many solutions.
5x - 2y = 4
5x - 2y = 6
inconsistent
both equations are lines with identical slopes.
but with different y-intercepts.
they are parallel and never intersect.
there is no solution.
there is no (x, y) that their sum has 2
different results.
How much money needs to be set aside today to purchase a new piece of equipment in 3 yrs? The money is expected to 9% interest compounded annually and the piece of equipemt is expected to increase by 3% per year. The present cost of the equipment is $75,000.00.
To calculate the amount of money that needs to be set aside today to purchase a new piece of equipment in 3 years, we need to find the future value of the equipment and calculate the present value of that future amount.
First, let's find the future value of the equipment:
The cost of the equipment is expected to increase by 3% per year, so after 3 years the cost will be:
$75,000 * (1 + 0.03)^3 = $78,225
Next, let's find the present value of that future amount:
The money is expected to earn 9% interest compounded annually, so to find the present value, we need to discount the future amount by the interest rate. We can use the formula:
PV = FV / (1 + r)^t
where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years.
Plugging in the values, we get:
PV = $78,225 / (1 + 0.09)^3 = $73,232.57
So, to purchase the equipment in 3 years, we need to set aside $73,232.57 today.
STRUCTURE Find the value of x for which PQ|| RS.
please help thank you so much!
Answer:
42
Step-by-step explanation:
If angle one equals 42, then angle 3 should too since they are the same angle.
hope it helps...
1/3 (4 x 3) + 2^3
Khan Academy question, please help !!
Answer:
12
Step-by-step explanation:
The answer for your question is 12
Answer:
=12
Step-by-step explanation:
1(4×3)/3+ 8=
1(12)/3+8=
12/3 + 8=
4 + 8 = 12
I hope I help you in this ans and tq.
The segments shown below could form a triangle.
OA. True
OB. False
The given statement exists true. A segment from the vertex of a triangle that is parallel to the other side.
What segments can form a triangle?The total of the lengths of any two segments must be greater than the length of the third segment in order to create a triangle. Any two sides of a triangle's lengths added together must be longer than the third side.
Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure.
A segment from the vertex of a triangle that is parallel to the other side. This section could be found on the triangle, inside it, or outside it.
There are three medians for every triangle, just as there are three altitudes, angle bisectors, and perpendicular bisectors. The lines that connect a triangle's vertices to the middles of its two opposite sides are known as the medians. The centroid of the triangle is the location where the three medians intersect.
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True. Since all the three combinations of segments when added the sum is greater than the third side the given segments can form a triangle.
How is this determined?According to the Triangle Inequality Theorem, a triangle's two side lengths added together are always greater than its third side. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
Given that the length of the three segments is:
AC = 9 units
CB = 4 units
BA = 11 units
According to the Triangle Inequality Theorem the sum of two sides of a triangle is always greater than third side. If this is true for all three combinations, then the triangle can be formed.
For the given segments:
AC + CB > BA
9 + 4 > 11
13 > 11 True
4 + 11> 9
True
9 + 11 > 4
Since all the three combinations when added the sum is greater than the third side the given segments can form a triangle.
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What is the value of x (x+30) 2x
Answer: 30
Step-by-step explanation:
Vertical angles are congruent.
[tex]x+30=2x \implies x=30[/tex]
Select all the statements that you agree with
Answer: 1 3 4
Step-by-step explanation:
100 POINTS! Please help
Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).
The axis of symmetry for each function is given as follows:
f(x): x = -4.g(x): x = 4.h(x): x = 1.Hence the rank from smallest to largest axis of symmetry is given as follows:
f(x), h(x), g(x).
How to obtain the axis of symmetry?The axis of symmetry of a quadratic function is given by the x-coordinate of the vertex of the quadratic function.
For function f(x), considering the vertex-form definition, the x-coordinate of the vertex is given as follows:
x = -4.
For function g(x), considering the standard definition, the x-coordinate of the vertex is given as follows:
x = -(-16)/2(4).
x = 16/4.
x = 4.
For function h(x), considering the graph of the function, the x-coordinate of the vertex is given as follows:
x = 1.
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In the following diagram, BC is parallel to DE. If AB=21, BD=7, and BC=15 then which of the following is the length of DE ? (1) 5 (2)10 (3) 20 (4) 25
The length of DE is 25. So correct option is (4).
What do you mean by parallel?In geometry, the term "parallel" refers to two lines that are equidistant from each other over their entire length and will never intersect, no matter how far they are extended. In other words, two parallel lines are parallel if they lie in the same plane and maintain the same distance between them at all times.
Since AB is parallel to DE and BD is perpendicular to both AB and DE, by alternate interior angles, we have:
angle BDA = angle DEC
Since BD is 7 and BC is 15, we have:
triangle BCD is a 7-15-17 right triangle (the Pythagorean theorem)
So, angle BDA = angle DEC = 90 - arctan(7/15) = arctan(15/7).
Also, since AB is parallel to DE, and BD is perpendicular to both AB and DE, we have:
angle ABD = angle CDE
So, by the vertical angles theorem, we have:
angle ABD = angle CDE = 90 degrees - arctan(15/7) = arctan(7/15)
Then, by the Pythagorean theorem, the length of DE can be found as:
[tex](DE)^{2}[/tex] = [tex](AB)^{2}[/tex] + [tex](BD)^{2}[/tex] = [tex]21^{2}[/tex] + [tex]7^{2}[/tex] = 441 + 49 = 490
So, DE = [tex]\sqrt{490}[/tex] = 2[tex]\sqrt{122}[/tex] = 2 * 11 = 22
Therefore, the length of DE is (4) 25.
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The A minor scale uses the white notes on the keyboard from A to A, but with G# instead of G.
A. True
B. False, the A minor scale uses all the white and black notes from C to C
C. False, the A minor scale uses the black notes on the keyboard from A to A
D. False, the A minor scale uses the white notes on the keyboard from C to C
"The A minor scale uses the white notes on the keyboard from A to A, but with G# instead of G." is True Option A
What is a minor scale?Generally, The tonic of a minor scale, which is the first note of the scale, is located a minor third above the root note of the scale. A minor scale is a sort of musical scale that consists of seven notes.
The A minor scale is a 7-note, the diatonic scale made up of the notes A, B, C, D, E, F, & G. It's the only minor scale that doesn't contain any sharps or flats.
A Natural Minor is A, B, C, D, E, F, G, A. Notice that the A Natural Minor Scale has no notes with accidentals. Let's build a G# Natural Minor Scale. Our starting note will be G#.
Therefore, Option A is true
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Macky wants to open a checking account. He is examining different banks and banking accounts. Then he will choose a bank account for his needs. Which of the following statements should not be one of Macky’s reasons for choosing a bank?
Answer:The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.
Step-by-step explanation:
The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.
66 out of the 75 employees at the water slides are temporary employees what percentage of the employees at the water slides are temporary
The percentage of the employees at the water slides are temporary is 88%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
To find the percentage of the employees that are temporary
66/75 x 100/1
=88%
Hence, 88% is the percentage of the employees at the water slides are temporary
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Mr.Bhavsar is buying a new Star Wars costume.it priced at $82 but he had a coupon for 25% off.the costume is subject to a 6% tax, and Mr.bhavsar has to pay $7 in shipping for his total order
The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The cost of the new Star Wars after a coupon for 25% off and a 6% tax will be given as,
⇒ $82 x (1 - 0.25) x (1 + 0.06)
⇒ $82 x 0.75 x 1.06
⇒ $65.19
The total cost after shipping will be given as,
Total cost = $65.19 + $7
Total cost = $72.19
The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.
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the square of the difference of 10 and j less than the product of ten cubed
The algebraic expression for "the square of the difference of 10 and j less than the product of ten cubed" is (10 - j)² < 10³.
How to write algebraic expressions?An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
The statement "the square of the difference of 10 and j less than the product of ten cubed" can be written as follow:
Step 1: Square the difference of 10 and j: (10 - j)²
Step 2: less than the product of ten cubed: (10 - j)² < 10³
Therefore, the algebraic expression is (10 - j)² < 10³
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Which of the following equations does not have any real solutions?
Answer:
4x² + 4x + 9 = 0 , has no real solutions
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
then the nature of the solutions can be determined using the discriminant.
Δ = b² - 4ac
• if b² - 4ac > 0 , then real solutions
• if b² - 4ac = 0 , then real and equal solutions
• if b² - 4ac < 0 , then no real solutions
4x² + 4x + 9 = 0 ← in standard form
with a = 4, b = 4 , c = 9
b² - 4ac
= 4² - (4 × 4 × 9)
= 16 - 144
= - 128 ← no real solutions
------------------------------------------
- 4x² + 56x - 196 = 0 ← in standard form
with a = - 4 , b = 56 , c = - 196
b² - 4ac
= 56² - (4 × - 4 × - 196)
= 3136 - 3136
= 0 ← has real solutions
-------------------------------------------
- 5x² - 10x + 10 = 0 ← in standard form
with a = - 5 , b = - 10 , c = 10
b² - 4ac
= (- 10)² - (4 × - 5 × 10)
= 100 - (- 200)
= 100 + 200
= 300 ← has real solutions
olve the word problem
For a period of time, an island's population grows at a rate proportional to its population. If the growth rate is 3.8% per year and the current population is 1543, what will the population be 5.2 years from now
Step-by-step explanation:
To solve this problem, we'll use the exponential growth formula:
P(t) = P0 * e^(rt)
Where P(t) is the population after t years, P0 is the initial population (1543), r is the growth rate (0.038), and t is the number of years (5.2).
P(5.2) = 1543 * e^(0.038 * 5.2)
Using a calculator or natural logarithm rules:
P(5.2) = 1543 * e^0.199
P(5.2) = 1543 * 1.22
P(5.2) = 1887.46
So the population will be approximately 1887.46 after 5.2 years.
A first-time homebuyer is comparing mortgage rates.
Option A offers the homebuyer 5.25% annual simple interest.
Option B offers the homebuyer the same interest rate but compounded semiannually.
If the repayment period is the same length for both loans, which option will result in the least amount of interest added to the loan?
O Option A will have the least amount of interest because simple interest generates earnings from both principal and interest.
O Option A will have the least amount of interest because simple interest generates earnings from principal only.
O Option B will have the least amount of interest because compound interest generates earnings from principal only.
O Option B will have the least amount of interest because compound interest generates earnings from both principal and interest.
If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.
What is the simple interest?The simple interest is the interest system that does not compute interest on accumulated interest.
Unlike simple interest, compound interest charges interest on accumulated interest.
Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.
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Answer: Option A will have the least amount of interest because simple interest generates earnings from principal only.
Step-by-step explanation: because it says it’s right on the computer;p
what is a non-example of scaling?
Answer:
A rate is two variables that relies on each other so a example would be a projectile and a cannon, in relation the cannon goes no where while the projectile is flying through the air
Step-by-step explanation:
Mathmatics For Calculus
The value of function f ' (2) is, 7/4.
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
We have to given that;
The function is,
⇒ f (x) = 7/x
Now, We an solve as;
⇒ f ' (2) = lim h → 0 ( f (2 + h) - f (2) / h )
⇒ f ' (2) = lim h → 0 ( 7 / (2 + h) - 7/2 / h )
⇒ f ' (2) = lim h → 0 ( 7/h (2 - 2 - h) / (2 + h)×2)
⇒ f ' (2) = lim h → 0 ( 7/h ( - h ) / 2 (2 + h) )
⇒ f ' (2) = lim h → 0 ( - 7 / 2 (2+ h))
⇒ f ' (2) = - 7/4
Thus, The value of function f ' (2) is, 7/4.
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Answer: a = 2 f(x) = x^5
Step-by-step explanation:
PLSSS HELP NOW!!!
what is the period of the sinusoidal function? enter your answer in the box.
Step-by-step explanation:
4
Ws
I need a bat to hit a ball with sport
Answer:
im confused are you asking a question or telling us about something?
A. Copy Theorem 2.3(theorem is the screenshot given) and apply it to the case when
n=7 and a=2.
B. Use the Desmos Graphing Calculator tool for
this part. Graph the function from PART A in the color blue. Use a red dotted line to
create the vertical asymptote associated with this graph. upload a
screenshot/picture of the graph with the equations you used.
The required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.
Limit, which can be defined as every nearby value of a variable for a function that exists, is called limits
Here,
According to the question,
[tex]y = \lim_{x \to \ a} 1/[x-a]^n[/tex]
Put a = 2 and n = 7
[tex]y = \lim_{x \to \ 2} 1/[x-2]^7[/tex]
As n = 7 is odd, from the theorem,
y = -∞, as 7 is an odd number.
Thus, the required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.
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PLEASE ASAP, DUE TODAY
Randy needs to buy school supplies. He needs a headset that costs $30.00. He also needs notebooks that cost $3.00 each.
Part 1
Complete the table to determine his total cost for a given number of notebooks.
Format your response using 2 decimal places and NO symbols. Example: 25.00
Unit 8: Polygons & Quadrilaterals
Homework 7: Trapezoids
Based on the given trapeziums, each problem's answers are:
∠J = ∠K = 44°; ∠L = ∠M = 136°x = 12; y = 5WX = 33AB = 15ML = 58GH = 15Let's discuss each problem we have:
1. The given trapezium is an isosceles trapezium, hence:
J = K = 7x + 2
M = L = 25x - 14
Since trapezium is a part of parallelogram, then:
∠J + ∠K + ∠L + ∠M = 360°
2∠J + 2∠M = 360°
2(7x + 2) + 2(25x - 14) = 360°
14x + 4 + 50x - 28 = 360°
64x - 24 = 360°
64x = 384
x = 6
∠J = ∠K = 7x + 2
∠J = ∠K = 7(6) + 2 = 44°
∠M = ∠L = 25x - 14
∠M = ∠L = 25(6) - 14 = 136°
2. Since EFGH is an isosceles trapezoid, then:
EH = FG
4x - 27 = x + 9
3x = 36
x = 13
EG = FH
3y + 19 = 11y - 21
40 = 8y
y = 5
3. It was given that:
PQ = 27
SR = 39
WX?
WX is the mig segment, where:
Mid segment = (base + top) / 2
WX = (PQ + SR) /2
WX = (27 + 39) / 2
WX = 66/2
WX = 33
4. It was given that:
MN = 22
DC = 29
AB ?
MN is mid segment
MN = (AB + DC) / 2
22 = (AB + 29) / 2
44 = AB + 29
AB = 15
5. JK = 3x + 11
NP = 45
ML = 10x - 12
NP is mid segmet
NP = (JK + ML) / 2
45 = [(3x + 11) + (10x - 12)] / 2
90 = (3x + 11) + (10x - 12)
90 = 13x - 1
13x = 91
x = 7
ML = 10x - 12
ML = 10(7) - 12
ML = 58
6. BC = 19
GH = 9x - 3
FE = 5x + 1
GH is mid segment
GH = (BC + FE) / 2
(9x - 3) = (19 + (5x + 1)) / 2
18x - 6 = 19 + (5x + 1)
18x - 6 = 20 + 5x
13x = 26
x = 2
GH = 9x - 3
GH = 9(2) - 3
GH = 15
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