The equation which can be used to represent the total tolls Stephanie will pay is y = 1.35x
Equationlet
Number of 3 1⁄2 miles = xCost of each toll = $1.35Total tolls paid = yy = 1.35x
If the number of 3½ miles on the route is 5
Then, the total toll paid is
y = 1.35x
= 1.35(5)
= $6.75
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Find the mean of the list of data 43,69, 48,37,85,57,95,102
enter your answer in scientific notation
It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
Scientific notations have some of the profits as:
Better readability due to compact representation
Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
A comet is about [tex]5.1 \times 10 ^9[/tex] km from the sun.
Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.
[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]
= [tex]1.7 \times 10 ^4[/tex]
Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.
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a²-b when a = 8 and b = 7
Answer:
[tex]57[/tex]
Step-by-step explanation:
You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]
Answer:
57
Step-by-step explanation:
a = 8
b = 7
a² - b
= 8² - 7
= (8*8) - 7
= 64 - 7
= 57
1 pts
The Dingles have some friends drop in. They wish to serve sherry but do nor have enough to serve
all the same kind. So they mix some which is 20% alcohol with some which is 14% alcohol and have
5 quarts which is 16% alcohol. How much of each kind of sherry did they have to mix?
Write
2660
1000
as a decimal.
Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f.
The function that is a tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]
What is the concept of integral?The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.
Knowing that :
40x + y = 0 is tangent of f(x)slope of the line = -40therefore, f'(x)|x=a = -40, so only look for a we have:
[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]
if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:
[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]
Therefore,
[tex]f(x) = (5/4)x^4+60[/tex]
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A bank loaned out $11,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled $1500, how much was loaned at
The amount loaned at 8% is $4800.
The amount loaned at 18% is $6,200.
What are the linear equations that represent the question?a + b - 11,000 equation 1
0.08a + 0.18b = 1500 equation 2
Where:
a = amount loaned at 8%
b = amount loaned at 18%
How much was loaned at 8 and 18%?Multiply equation 1 by 0.08
0.08a + 0.08b = 880 equation 3
Subtract equation 3 from equation 2
0.10b = 620
b = 620 / .10
b = $6200
a = 11,000 - 6200 = $4800
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The distance between two towns on a
map is 6.25 cm.
The scale on the map is 1 cm = 30 miles.
What is the actual distance between the
two towns?
Answer:
Actual distance=187.5miles
Step-by-step explanation:
1cm=30miles
6.25cm=6.25*30miles
=187.5miles
The distance between the two towns using the map scale is 187.5 miles.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The distance between the towns on map is 1 cm.
And, the scale of map is 1 cm = 30 miles.
As per the problem the actual distance can be found by using the scale of the map as follows,
The distance between two towns is 6.25 × 30 = 187.5 miles.
Hence, the actual distance between the two towns is 187.5 miles.
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How to get T. I have gotten this question wrong multiple times already. It is not simplified it wants it in the complete decimal form.
Answer:
t = 4.0
Step-by-step explanation:
1.) P(t) = 1578
2.) Divide both sides by 1400
3.) Take the natural log of both sides (to remove the "e")
4.) Divide both sides by 0.03
5.) Properly round to the 1st decimal place
Cindy has decided to lease a car. the lease includes a money factor of 0.00354. what interest rate is cindy being charged in her lease? a. 0.85% b. 8.5% c. 1.475% d. 14.75% please select the best answer from the choices provided a b c d
The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.
Given The factor included in lease is 0.00354.
Interest is the amount that a bank or person who gives loan charges from loan taker.
Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.
Money factor=0.00354.
So the interest rate that Cindy will charge is equal to 2400*0.00354
The interest rate Cindy will be charged =8.496%
=8.5%
Hence the interest rate charged is approximately 8.5%.
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Mila plants 820 hectares of potatoes and corn. To maximise his profit he plants 140 hectares more of potatoes than of corn. How many hectares of each does he plant?
Answer:
480 Hectares potatoes, 340 Hectares corn
Step-by-step explanation:
Let x be the land used to plant potatoes in hectares.
Let y be the land used to plant corn in hectares.
Given the information from the question, we know that:
x + y = 820 - Equation 1
and
x - y = 140 - Equation 2
as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.
We will use Equation 1 - Equation 2.
x-x+y-(-y)=820-140
2y = 680
y = 680 ÷ 2 = 340 hectares
We substiture y into equation 1 to find x
x + 340 = 820
x = 820 - 340
= 480 hectares
Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.
Answer:
p=x+140whilec=x x+140+x=820ans=340 Answer=corn 340. while potatoes 480Solve this system using the substitution method. -3x + 4y = 1 -4x + 5y = -2
Answer:
the x value is 13 and the y value is 10. x=13 and y=10
What is the value of f(4) in the function below? f(x) = -1/1·2x A. 16 OB. 8 C. 2 OD. 4
Answer: 4
Step-by-step explanation:
[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
The transformation was a 180° rotation about the origin.
We can solve this question by plotting the points R (1, 1)
S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.
As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.
Hence, the transformation was a 180° rotation about the origin.
Your question was incomplete. Please check below for full content.
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)
Which best describes the transformation?
The transformation was a 90° rotation about the origin.
The transformation was a 180° rotation about the origin.
The transformation was a 270° rotation about the origin.
The transformation was a 360° rotation about the origin.
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if there are 24 sushi pieces in 6 packages of sushi how many pieces of sushi are in 2 packages of sushi HURRY!!!!
Answer: 8 pieces
Step-by-step explanation:
- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package
- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8
- so there’s 8 pieces of sushi in 2 packages
hope this helps :)
Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
Distance formula: √(x₂-x₁)² + (V2 - V₁)²
O(x-4)² + y² = 100
O(x-4)2 + y² = 10
O x² + (y-4)² = 10
O x² + (y-4)² = 100
Answer:
(x-4)² + y² = 100
Step-by-step explanation:
The only circles that have a center at (4 , 0) are :
(x-4)² + y² = 100
(x-4)² + y² = 10
……………………
• (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10
Then
The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)
• (-2 - 4)² + 8² = 100
Then
The circle (x-4)² + y² = 100 contains the point (-2, 8)
The graph of the exponential function with base, e, has a_______ at _______ Its domain is _______ Its range is _____
The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.
What is the description of the graph of an exponential functions whose base is e?It follows from the task content that the function in discuss can be written as;
y = e^x.
Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).
The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.
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The common _____ of two rays that make an angle is called the vertex.
your answer goes here
What is the next whole number after 3355 in the base six system
Answer:
Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6
Given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what percent of the data points are above 76?
According to the empirical rule, the percent of the data points that are above 76 is; 2.28%
How to use Empirical Rule in Statistics?We are given;
Mean; μ = 88
Standard deviation; σ = 6
Sample mean; x' = 76
Formula for z-score is;
z = (x' - μ)/σ
z = (76 - 88)/6
z = -2
Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%
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0.2 was divided into a particular number. this quotient was the multiplied by 7, and 2.8 was taken from that product. if the previous operation resulted in -499.8 find the initial number
Answer:
(x/0.2)(7)-2.8=-499.8
x=-14.2
Step-by-step explanation:
(x/0.2)(7)-2.8=-499.8
7x/0.2 -2.8 = -499.8
35x -2.8 = -499.8
35x = -499.8 +2.8
35x = -497
35x/35 = -497/35
x = -14.2
you probably already got it solved, but at least this can help anyone else!
Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4 ? (2 points) graph of 2 x plus 4, with discontinuity at negative 2, 0 graph of 2 x plus 4, with discontinuity at 2, 8 graph of 2 x minus 4, with discontinuity at negative 2, negative 8 graph of 2 x minus 4, with discontinuity at 2, 0
We can simplify the given rational function into a linear one, the graph is below.
Which graph represents the function?
Here we have the rational function:
[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]
Factorization the numerator, we get:
4x² - 16 = 0
4x² = 16
x² = 16/4 = 4
x = ±√4 = ±2
Then the numerator can be written as:
4*(x - 2)*(x + 2)
And the denominator can be rewritten as:
2x - 4 = 2*(x - 2)
Then the function becomes:
[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]
So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.
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Please help!
If a student (represented by initials) was chosen at random, find P(HH|C).
P(HH|C)=2/5
P(HH|C)= 13/16
P(HH|C)=9/16
P(HH|C)=3/5
Answer:
a.) P(HH|C)=2/5
Explanation:
Given following:
P(HH) = 7P(C) = 10P(HH ∩ C) = 4P(HH ∪ C) = 13Solving steps:
[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]
[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]
[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]
Im trying to figure out the answer
Step-by-step explanation:
[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]
all the details are in the attachment.
I need help with this question I got 1 as an answer but it’s saying it’s wrong
log 4 (x³ +255) = 4
Answer:
see image
Step-by-step explanation:
I did two different problems depending on whether the 4 beside the log is a base or not.
If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.
For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.
Find the real numbers x and y.
27+yi= 11-x + 4i
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -16 [/tex]
[tex]\qquad \tt \rightarrow \: y =4 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]
[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]
[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]
By equating both equations we get :
[tex]\qquad \tt \rightarrow \: x = - 16[/tex]
[tex]\qquad \tt \rightarrow \: y = 4[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
(1 point) The matrix
6 4
-7 k
is invertible if and only if k is not equal to
Answer:
k ≠ -14/3
Step-by-step explanation:
A square matrix is invertible if and only if its determinant is not zero.
DeterminantThe determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:
det = (6)(k) -(-7)(4) = 6k +28
Restriction on kThe requirement that the determinant is not zero places a restriction on k.
6k +28 ≠ 0
k +14/3 ≠ 0 . . . . . . divide by 6
k ≠ -14/3 . . . . . . . . subtract 14/3
For the matrix to be invertible, the value of k must not be -14/3.
what is the range of f(x)=3^x
Answer: [tex]f(x) > 0[/tex]
Step-by-step explanation:
The range of all exponential functions without a vertical shift is the set of positive real numbers.
Find the first three terms of the sequence, Classify the sequence as arithmetic ( give d value ), geometric ( give r value ), both, or neither..... Sn = 10n
The first three terms of the sequence are 10, 20, and 30.
How to depict the sequence?The function given is 10n. In this case, the terms will be:
First term = 10n = 10 × 1 = 10
Second term = 10 × 2 = 40
Third term = 10 × 3 = 30
In this case, the first three terms of the sequence are 10, 20, and 30.
It an arithmetic sequence as there is a common difference of 10.
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point H represent in this context?
CORRECT (SELECTED)
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Explanation: Point HHH is on line aaa, so it represents Josiah's distance at a certain time. Point HHH is also on line bbb, so it represents the same distance and time for Chana.
The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.
How to solve for the point H.At the point H, there is an intersection between the distance covered by both of these individuals.
This point is the point where we are shown that Chana has caught up with Josiah as they are skating.
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