Applying the negative exponent, the equivalent expression [tex]3^{-3}[/tex] is 1/27.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator.
Hence, the equivalent expression is:
[tex]3^{-3} = \dfrac{1}{3^3} = \dfrac{1}{27}[/tex]
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Which of the following is NOT a rational expression?
The expression that is not rational is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
Which of the given expressions is not rational?A rational expression is something of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.
This means that we need to have the variable "x" on the denominator.
Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:
[tex]f(x) = \frac{6x}{4}[/tex]
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Answer: B
Step-by-step explanation:
I took the test and this was the correct answer
How do I find the domain and range in this graph?
Answer:
Domain: [tex]-4 < x \leq 4[/tex]Range: [tex]0 \leq y \leq 4[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
What is the remainder of x^5+2x^4+9x^3-6x^2+3x+3165 divided by x-5
Answer:
8530
Step-by-step explanation:
The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530
3. Find how many numbers between 232 and 252.
Answer:
252-232=20-1=19
Step-by-step explanation:
the question said in between so you don't count the first and the last numbers
How would five billion, eighteen million, two hundred sixteen thousand, forty be written in standard form?
A. 5,018,216,004
B. 5,018,210,014
C. 5,018,216,040
D. 5,180,216,040
Answer:
c
Step-by-step explanation:
answer is C . First last digits are forty you will have down 2 answers
Answer:
the answer to the question is C
find x and y please please help
L1 and L2 are parallel
so the interior alternate angles are equal
4y - 40 = 3y ( interior alternate angles)
4y - 40 = x + 15 ( vertically opposite angles).
solving the first equation, we get
4y - 3y = 40
y = 40°
putting values of y= 40° in eq. 2, we get
4y - 40= x + 15
4(40) - 40 = x + 15
160 -40 = x + 15
120 - 15 = x
105° = x
X = 105° , Y = 40°A rental car agency charges $230 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $415?
The number of miles you can travel in one week for $415 is
Answer:
740 miles
Step-by-step explanation:
$415-$230=$185
$185÷0.25 per miles =740 miles
Luis created the graph below to show the temperature from 8:00 a.m. (8 hours after midnight) until 8:00 p.m.
On this graph, 4:00 p.m. occurs at 16 hours after midnight, and 6:00 p.m. occurs at 18 hours after midnight. Which statements are true about the temperatures Luis recorded on the graph? Select THREE answers.
The temperature increased until 4:00 p.m.
The temperature was not recorded between 4:00 p.m. and 6:00 p.m.
The temperature decreased after 6:00 p.m.
The temperature increased and then decreased before holding constant.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.
A slope also known as the gradient of a line is a number. The correct option is A, C, and D.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
For the given question,
The temperature increased until 4:00 p.m.This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.
The temperature decreased after 6:00 p.m.This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.
Hence, the correct option is A, C, and D.
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Answer:
ACD
Step-by-step explanation:
Figure M and it’s congruent image, figure N, are graphed on the coordinate plane below.
Describe a sequence of transformations that will take figure M onto its congruent image, figure N.
EXPLAIN THE ANSWER!!
The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
As we can see in the graph there are two shapes are shown.
Figure M and Figure N
The sequence of transformations that will take figure M onto its congruent image, figure N is:
First, we need to draw a line that passes through (3, 0) and (0, -3)
The equation of the line is:
[tex]\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)[/tex]
y + 3 = x
y = x - 3
The reflection over the above line will take figure M onto its congruent image, figure N.
Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.
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As a unit price, a half-dozen for
$6.00 is
a. $36.00 each
b. $6.00 each
c. $0.50 each
d. $1.00 each
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe
the population proportion is approximately p 37%. You would like to be 99.5% confident that your
esimate is within 2.5% of the true population proportion. How large of a sample size is required?
H
n=
The sample size required is 2938.645
What is Probability ?Probability is the likeliness of an event to happen.
It is given that
p = .37
∈ = 0.025
∝ = 1 - 0.995 = 0.005
∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex] (From z table)
Sample size n is given by
[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]
Therefore the sample size required is 2938.645
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Round to the nearest ten thousandths 15.76548908 *
The price of a cup of coffee was 2.40 yesterday. Today, the price rose to
2.75. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
≈ 14.6%
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = 2.75 - 2.40 = 0.35 , then
percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )
Can u help me with this I don’t understand
Answer:
D -6, 15
Step-by-step explanation:
Because 3,11 is the middle, and 12,7 is the other end, you can do
12 - 3 = 9
3 - 9 = 6
then
11 - 7 = 4
11 + 4 = 15
so
6 is you x and 15 is your y
find the area for this pls
Answer:
Area = 3.36 in²
Step-by-step explanation:
[tex]Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h[/tex] ,
where a and b are the two parallel sides, and h is the height.
[tex]Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}[/tex]
NEED HELP ASAP PLEASEE
Answer:
2nd one is the correct
March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar. I need help with this question.
[tex] \huge \tt \underline {\green{Answer}}[/tex]
If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees
ie. $1 = Rs 66.79
$ 1 = 66.79 × 1
$ ? = 110.66
$ = New / old
$ = 110.66 / 66.79
$ = 1.65683485552
or
$1.66 = 110.66
Suppose that the number of a certain type of computer that can be sold when its price is P (in dollars) is given by a linear function N(P).
(a) Determine N(P) if N(1000) = 10000 and N(1700) = 6500. (Use symbolic notation and fractions where needed.)
N(P) =?
(b) Select the statement that gives the slope of the graph of N(P), including units and describes what the slope represents.
●5 computers per dollar
● -1/5computers per dollar
● -5 computers per dollar
● -5 dollars per computer
(c) What is the change N in the number of computers sold if the price is increased by AP = 110 dollars? (Give your answer as a whole number.)
AN = ?
Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6
Step-by-step explanation:
Bret is planning a long hike. He figures that he will need at least 0.75 liters of water for each hour on the trail. He also wants to have 1.8 liters of water in reserve at all times. If he can only carry 9 liters of water maximum, how many hours can he hike?
The number of hours that Bret can hike with 9 liters of water is 9.6 hours.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Water needed = 0.75 liters per hour
For x number of hours = 0.75x liters
Reserved water = 1.8 liters.
Total water needs for x hours = (0.75x + 1.8)
The number of hours that can be hiked with 9 liters will be as,
(0.75x + 1.8) = 9
x = 9.6 hours.
Hence "The number of hours that Bret can hike with 9 liters of water is 9.6 hours".
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or
Soda is often packaged in cans that are supposed to contain 12 ounces. However, no
manufacturing plant is perfect and so there might be slight errors. For example, Sam's Splendid
Soda company has verified that the amount of soda in their cans has a normal distribution with
a mean of 12 ounces and a standard deviation of 0.7 ounces. Although this is made up, it's not
completely divorced from the truth.
1. You open a can of Sam's and realize there are only 11.6 oz in the can. What is the
probability that a single can will contain 11.6 ounces or less of soda? (2 points)
2. Troubled by the under-filled soda, you decide to empty out all the cans in a six pack of Sam's
Soda and find that the mean amount of soda in all the cans is 11.6 ounces. What is the
probability that six pack will have a mean of 11.6 ounces or less of soda? (2 points)
3. Not satisfied with the information you figured out in #2, you take a case (36 cans) and
empty out all the cans of Sam's Soda and find that the mean amount of soda in all the cans is
11.6 ounces. What is the probability that case will have a mean of 11.6 ounces or less of soda?
(2 points)
4. Draw three normal distributions on the same set of axes or with the same scale to show
how the probabilities decrease from one can to six cans to 36 cans even though we're looking
at "less than 11.6 ounces." (2 points)
5. Use the graphs and your own understanding of the Central Limit Theorem to write a few
sentences explaining what is happening here. (2)
The probability that a single can will contain 11.6 ounces or less of soda is 0.2843
Probability that a can contains 11.6 ounces or lessThe given parameters are:
x = 11.6
Mean = 12
Standard deviation = 0.7
Calculate the z value using:
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
This gives
[tex]z = \frac{11.6-12}{0.7}[/tex]
z = -0.57
The probability is then calculated as:
P(x ≤ 11.6) = P(z ≤ -0.57)
Using the z table of probabilities, we have:
P(x ≤ 11.6) = 0.2843
Probability that a pack contains 11.6 ounces or lessIn (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a pack contains 11.6 ounces or less is
P(6) = 0.2843^6
P(6) = 0.00053
Probability that a case contains 11.6 ounces or lessIn (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a case contains 11.6 ounces or less is
P(36) = 0.2843^36
P(36) ≈ 0
Draw three normal distributionsSee attachment for the normal distributions
The happening on the graphThe summary of the graph is that, as the sample size increases the probability decreases
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Which equation represents a circle with a center at (-5,5) and a radius of 3 units?
Answer:
[tex] {(x + 5)}^{2} + {(y - 5)}^{2} = 9 [/tex]
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. xxx yyy -12−12minus, 12 141414 -2−2minus, 2 212121 888 282828 What is the xxx-intercept of the line? ((left parenthesis ,,comma ))
Answer:
(-32, 0)
Step-by-step explanation:
Answer:
(-32,0)
Step-by-step explanation:
A couple decides that Sophia will drive the first 3/5 of a trip and Toby the last 2/5. The entire trip is A couple decides that Sophia will drive the first 3/5 of a trip and Toby the last 2/5. The entire trip is 500 miles long. How far will Sophia drive?500 miles long. How far will Sophia drive?
Answer:
60 miles
Step-by-step explanation:
miles that Sophia drove = 3/5 x 100 = 60 miles
A fraction is a way to describe a part of a whole. The distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
A fraction can also be described in the form of a percentages, to represent the part of the whole.
Given that the length of the entire trip is 500 miles. Also, the first 3/5 of the trip are covered by Sophia and the last 2/5 of the trip are covered by Toby.
Now, the distance covered by Sophia and Toby will be,
Distance covered by Sophia = (3/5) × 500 miles = 300 miles
Distance covered by Toby = (2/5) × 500 miles = 200 miles
Hence, the distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
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What is the area of a rectangle with vertices at (6, −3), (3, −6) , (−1, −2), and (2, 1)? Enter your answer in the box. units²
The area of triangle is 24 sq. units
What is Area of rectangle?Area of rectangle is product of its length to its breadth.
i.e., Area of rectangle = length* breadth
let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)
Using distance formula
AB = √(3-6)²+ (-6 +3)²
AB= √9 + 9
AB= √18
AB= 3√2
now,
BC= √(-1-3)²+ (-2 +6)²
BC = √16 +16
BC = √32
BC =4 √2
Now, Area of rectangle
= AB* BC
= 3√2 *4 √2
= 12*2
= 24 square units
Hence, area of rectangle is 24 sq. units
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Consider the following data concerning the demand (y) and price (x) of a consumer product the least squares line is found to be y= 306,619-27.71.x
A) Interpret b1
B) find a point prediction of the demand corresponding to be price 2.10
C) Find %95 confidence interval for b1 and interpret it
The value of B1 shows a fall in demand as price rises by a unit. The point prediction is given as y = 306,560.8
How to solve the question using the interceptThe regression equation shows that y= 306,619-27.71.x
b1 = -27.71
The interpretation for b1 is that if the price of this good is increased by 1, then the demand for the good would fall by about 27.71.
The point prediction for demandThe regression line equation is given as
y= 306,619-27.71.x
when x which is price is = 2.10
Then the value of y would be:
y = 306,619 - 27.71*2.10
y = 306,560.8
c. a 95% C1 for B1 is given as:
1.96 * 27.71.
= 54.31
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A 13 -ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving away at the rate of 15 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
Write the inequality shown by the shaded region in the graph with the boundary line y=−4x+1.
Answer:
5 is the answer
Step-by-step explanation:
because it is
How many pounds of candy that sells for $0.82 per lb must be mixed with candy that sells for $1.36 per lb to obtain 9 lb of a mixture that should sell for $0.91 per lb?
7.5 pounds of the $0.82 per lb candy must be used in the mixture.
How many pounds of each candy should we use?First, let's define the variables:
x = pounds of the $0.82 candy used.y = pounds of the $1.36 candy used.We want to make 9 lb of mixture, then:
x + y = 9.
And the price of these 9 pounds must be $0.91, then we can write:
x*$0.82 + y*$1.36 = 9*$0.91 = $8.19
Then we have a system of equations:
x + y = 9.
x*$0.82 + y*$1.36 = $8.19
We can isolate y on the first equation so we get:
y = 9 - x
Now we can replace that on the other equation:
x*$0.82 + (9 - x)*$1.36 = $8.19
And now we can solve this for x.
x*($0.82 - $1.36) = $8.19 - 9*$1.36
-x*$0.54 = -$4.05
x = (4.05/0.54) = 7.5
So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.
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PLEASE HELP ASAP! Consider the scatter plot. Complete the equation that models the curve of best fit for this data.
curve of best fit: f(x)
The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Consider the scatter plot.
Then the equation that models the curve of best fit for this data will be
At (1.2, 3), then we have
[tex]\rm 3 =ab^{1.2}[/tex] ..........1
At (4, 16), then we have
16 = ab⁴ ..........2
By solving the equations 1 and 2, we have
a = 1.4646 and b = 1.818
Then the equation will be
y = 1.4646·(1.818)ˣ
Then the graph is drawn.
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What u
Is 2(x+3) / 4(x+1)
Answer:
Step-by-step explanation:
2 ( x + 3 ) / 4 ( x + 1 )
2 (x + 3) ÷4 (x + 1)
2 (x + 3) ÷ 2×2(x+1)
cancel out the 2 in the numerator with the 2 in the denominator
(x + 3) ÷ 2(x + 1)
x+3 / 2(x+1)
