Answer:
13
Step-by-step explanation:
The range of the data set can be defined as: max-min, and in a sorted data set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.
With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.
This means the range is defined as: 30 - 17 = 13
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]
[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]
[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{30}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{17}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\rm{30 - 17}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]There are three novels on Sam's reading table: Light, Zami, and Money.
. On his next trip, he can choose to take some, none, or all of these novels. In the braces below, list all the possible sets of novels that Sam can take.
Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø.
The subsets of the set of novels is given as follows:
{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.
How to find the subsets of a set?Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.
In this problem, the novels are given as follows:
Light, Zami, and Money.
Hence the possible subsets are given as follows:
{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.
With is the list that is asked for this problem, which are the subsets of the set of novels.
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Please help me this is due Monday!
Answer:
1.
2. Additive Identity
3. Associative Property
4. Multiplication Inverse Property
5. Multiplication Property of 0
6. Commutative Property
7.
8.
Step-by-step explanation:
A customers monthly bill is $50 including taxes. You mom ’ll offer a 30% discount applicable towards the $50 on a monthly basis. The discount started being applied to his account on June 16. Therefore for the month of June the customer will receive a discount on a prorated basis on the monthly bill. The customers billing cycle begins on the first the month. What is the total billed amount for the month of June?
Using proportions, the billed amount for the month of June is:
D. $42.50
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The discount will be applied only for the second half of the month, from June 16 to June 30, hence instead of a discount of 30%, it will count as a discount of 15%, meaning that 85% of the bill will be paid, hence the amount paid will be of:
A = 0.85 x $50 = $42.50.
Hence option D is correct.
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For the equation:
y=−x^2+10x−24, the x-intercepts are already given on the graph. Now, using the parabola tool, graph rest of the equation.
The graph of the parabola can be seen in the image below.
How to graph the parabola?
We need to find some points on the parabola, and then draw a curve that connects them.
On the graph you already have the x-intercepts, so you already have two points.
Now let's get another point which is the vertex.
For our parabola:
[tex]y = -x^2 + 10x - 24[/tex]
The vertex is at:
[tex]x = -10/(2*-1) = 5[/tex]
Evaluating in x = 5 we get:
[tex]y = -5^2 + 10*5 - 24 = 1[/tex]
So we also have the point (5, 1), now we can just connect the points and get the parabola:
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Find the slope and reduce.
P=(2, 3) Q=(9, 7)
Slope =
Answer: 4/7
Step-by-step explanation:
Slope = Rise/Run = (7-3)/(9-2) = 4/7
Answer:
4/7
Step-by-step explanation:
The formula to find the slope is: (change in y)/(change in x)
Or also: Rise/Run
The change in y is: 3 --> 7 which is +4
The change in x is: 2 --> 9 which is +7
So the (change in y)/(change in x) will be 4/7.
Since 4/7 cannot be simplified further, that is our final answer.
Dominique from "Dominique's Pizza" bakes p pizzas every day. Currently, it costs her $8 dollar sign, 8 per day to use the oven and $1.50 per pizza for the ingredients
Tomorrow, the price for the ingredients will increase from $1.50 per pizza to $2 per pizza. The oven costs will stay the same at $8 per day.
Dominique did some calculations and found that she should bake 8 more pizzas each day in order for the total expenses per pizza (including ingredient and shared oven costs) to remain the same.
Write an equation in terms of p to model the situation.
The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.
What is an equation?
Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.
How do we form the above equation?Everyday pizza production is equal to p.Brick oven use fees are $10 per day.Ingredients for brick oven pizza cost $2 per pizza.$20 a day is the cost of using an electric oven.Pizzas baked in an electric oven cost $0.8 per pizza in ingredients.If an electric oven is used, the total cost of making a pizza falls by $1, including the cost of the ingredients.Total cost of baking p pizzas with brick oven = A = p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).
Total cost of baking p pizzas with electric oven = B = p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).
B = A - 1 (as using electric oven saves $1 per day, as given)
Thus, we get:
2p + 10 = 0.8p + 20
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I have to be at work at 4 am it takes 34 mins to walk to work from my house what time would i have to leave my house to be at work on time at 4 am
Answer:
3:26 to be on time!
Step-by-step explanation:
If you leave your house at 3:26 am and then walk 34 minutes it will be 4 am
once you get to work.
What are the quartiles of the data
The quartiles of the data are: 60.5,64,66
Option(b) is correct.
The quartile divides the distribution into four groups and calculates the range of values above and below the mean.
A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.
Similar to how the median divides the data in half, with 50% of the measurements falling below it and 50% falling above it, the quartile divides the data into fourths, with 25% of the measurements falling below the lower quartile, 50% falling below the median, and 75% falling below the upper quartile.
The interquartile range, a measurement of variation around the median, is calculated using quartiles.
For the given data set: 58,60,60,61,62,64,64,64,66,70,72
Median = 64
Lower quartile = Median of the lower half = 60.5
Upper quartile = Median of the upper half = 66
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Can I just get the answer for this I feel like it’s wrong.
The initial membership fee for Club A is; $2.5.
The initial membership fee for Club B is; $3.
Hence, Club A has a lower initial membership fee.
What is the initial membership fee for each Club?It follows from the concepts of linear graphs that the interpretation of the initial membership fee is the y-intercept of the graphs given.
This is so because, it corresponds to the total cost at a point when the number of movies watched is; 0. That is, before any movie is watched.
Consequently, the graph calibrations (including the missing Club A graph) allow the determination of the initial membership fee (y-intercept) as declared above.
Ultimately, Club A has a lower initial membership fee.
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Ivan bought two magazines for $4.95 each. If the sales tax was 6.75% what was the total amount that he paid for the magazines?
Step-by-step explanation:
the total sale price for the magazines were
2×4.95 = $9.90
so,
100% = 9.9
1% = 100%/100 = 9.9/100 = 0.099
6.75% = 6.75×1% = 6.75×0.099 = 0.66825 ≈ $0.67
so, he paid in total
$9.90 + $0.67 = $10.57
8. If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker. (a) 145 /281 (b) 617 /1124 (c) 1031 /1124 (d) 37 /1124
The probability that the person is a man or heavy smoker is 621 / 1124.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that the respondent is a man or heavy smoker can be determined by adding the probability that the respondent is a man and the probability that the respondent is a heavy smoker together.
The probability that the person is a man or heavy smoker = (number of men / total number of respondents) + (number of heavy smokers / total number of respondents)
(531 / 1124) + (90 / 1124) = 621 / 1124
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last week you worked the following hours monday 5 1/2 wednesday 6 3/4 friday 4 1/2 how many hour did you work in all week
Answer:
Step-by-step explanation:
You worked 16 hours and 45 minutes
5 1/2 = 5 hours and 30 minutes
6 3/4 = 6 hours and 45 minutes
4 1/2 = 4 hours and 30 minutes
Add the hour and minutes.
5 hours 30 min + 4 hours 30 min = 10 hours
10 hours + 6 hours 45 min = 16 hours and 45 minutes
Show all work to write the expression in simplified rational exponent form:
[tex]\sqrt[4]{17x^{2}}[/tex]
(Fourth root of 17 x squared)
Answer:
[tex](17x)^{\frac{2}{4}}[/tex]
Step-by-step explanation:
There's not much work to show for this problem, but I'll explain it for you
Use the exponent rule for roots to combine the 4 and the 2 like a fraction
2 on the top and 4 on the bottom
[tex](17x)^{\frac{2}{4} }[/tex]
That's it! Pretty easy
Good Luck!
pls mark brainliest
. Last weekend, Michael
drove to his friend's house.
When he left, he noticed
that the fuel gauge in his
car indicated that his gas
tank was 4 full. When he
returned home, the fuel
gauge in his car indicated
that his gas tank was ½ full.
If the gas tank holds 24
gallons, how many gallons
did Michael use on his
drive?
It can be said that the total amount of fuel that was used by Michael when he was away to his friends was 12 gallons.
How to solve for the quantity.The question said that the tank was full before he left to his friends. This was after he checked the gauge of the gas tank.
The question says that the required quantity needed to fill up this tank is 24 gallon. Hence if it is full, then the total gallon it had before he made this trip was 24 gallon.
Then we are told that he went ahead to check the gauge when he finished and was at home. The quantity of fuel he had at this time was 1/2 of what was there.
This would be 1/2 * 24
12
Hence he made use of 12 gallons when he was away.
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P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen que queda entre la esfera y el cubo es: 30.49cm^3
¿Como calcular el volume sobrante?
El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.
Para el cubo que tiene una arista de 4cm, el volumen es:
V = (4cm)^3 = 64 cm^3
Para la esfera con un diametro de 4cm, el radio es:
R = 4cm/2 = 2cm
Y el volumen será:
V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3
El volumen que queda entre la esfera y el cubo es:
V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3
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Help!
which of the following functions are graphed below
The wall, shown above in Figure 105.1401, has an overall length that is 37’ and 8 1/4" . Three receptacle outlets are to be installed in this wall. L2 is twice as long as L1 . L1 should be _____' _____''.
Since L₂ is twice as long as L₁, the length of L₁ should be 12' and 6 3/4".
How to calculate the length (L₁)?First of all, we would convert the value of the overall length in feet to inches as follows:
1 feet = 12 inches
37 × 8 1/4 feet = X inches
Cross-multiplying, we have:
X = 1809/4 inches.
Since L₂ is twice as long as L₁, we have:
L₂ = 2L₁
Also, the overall length is given by:
T = 2L₁ + 2L₂
T = L₂ + 2L₂
T = 3L₂
1809/4 = 3L₂
L₂ = 1809/4 × 1/3
L₂ = 1809/12
L₂ = 150.75''
L₂ = 12' and 6 3/4".
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Find a potential function for the vector field
The answers to the question are given as x²y + 24x +16y and 87
How to solve for the potential function of the vector field
(2xy + 24, x² + 16)
We have to check in order to be sure that the vector that we have here is a gradient field
we have fx = 2xy + 24 and fy = x² + 16
Such that we would have x²y + 24x +g(y)
for f(y) g' = 16 = 16 + c
Given that there is no lose of generality, we are going to have the following where
x²y + 24x +16y
b. We have to solve this oart by making use of the fundamental theory of integrals
f2,4 = 4*4 + 24*2 + 16*4
= 16 + 48 + 64
= 128
f1,1 = 1*1 + 24*1 + 16*1
= 1 + 24 + 16
= 41
128 - 41 = 87
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Please help, need for hw and cant find the fourth degreee
The quartic equation behind the graph is y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8.
How to derive the expression for a quartic function
Quartic functions are fourth grade polynomials and according to the fundamental theorem of algebra, such kind of expressions have at least two real roots and at most four real roots. The graph of the picture shows a polynomial with two roots of multiplicity 2: x₁ = - 1, x₂ = 2.
y = a · (x + 1)² · (x - 2)² (1)
Where a is the leading coefficient.
If we know that (x, y) = (0, 4), then the leading coefficient of the polynomial is:
4 = a · (0 + 1) · (0 - 2)
4 = - 2 · a
a = - 2
Then, the quartic equation is equal to:
y = - 2 · (x + 1)² · (x - 2)²
y = - 2 · (x² + 2 · x + 1) · (x² - 4 · x + 4)
y = - 2 · [(x² + 2 · x + 1) · x² + (x² + 2 · x + 1) · (- 4 · x) + (x² + 2 · x + 1) · 4]
y = - 2 · (x⁴ + 2 · x³ + x² - 4 · x³ - 8 · x² - 4 · x + 4 · x² + 8 · x + 4)
y = - 2 · (x⁴ - 2 · x³ - 3 · x² + 4 · x + 4)
y = - 2 · x⁴ + 4 · x³ + 6 · x² - 8 · x - 8
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if tan theta = 1/√5 then verify the identity sin²theta + cos²theta = 1
The identity of sin²Ф + cos²Ф = 1 is verified below
How to evaluate Trigonometry Ratio ?Trigonometry ratio can be evaluated by following the laid down rules with the the use of table and calculator
Given that tan Ф = 1/√5
Where Tan Ф = Opposite / adjacent
We can calculate the hypotenuse by using Pythagoras theorem
Hyp² = 1² + (√5)²
Hyp² = 1 + 5
Hyp = √6
sin Ф = opp / hyp
sin Ф = 1/√6
sin²Ф = 1/6
cos Ф = adj / hyp
cosФ = √5 / √6
cos²Ф = 5/6
sin²Ф + cos²Ф = 1/6 + 5/6
sin²Ф + cos²Ф = 6/6
sin²Ф + cos²Ф = 1
Therefore, the identity of sin²Ф + cos²Ф = 1 is verified.
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Will mark brainliest
A table of values of an increasing function f is shown.
x 10 14 18 22 26 30
f(x)
−14
−8
−1
1
4
7
The upper estimate and lower estimate become R5 = 16 and L5 = −64
According to the statement
we have given that the some values of the increasing function f and we have to find the lower estimate and upper estimate values.
So, For this purpose, we know that the
the values of x is 10 14 18 22 26 30
And the values of f(x) is −14 −8 −1 1 4 7
So,
Δx = 4 because
L5 = 4(−12 − 6 − 2 + 1 + 3) = −64,
And
R5 = 4(−6 − 2 + 1 + 3 + 8) = 16.
And from these functions we see that the
The function being increasing, the Riemann sum with left endpoint L5 = −64 is a lower estimate,
And while the sum with right endpoints R5 = 16 is an upper estimate.
So, The upper estimate and lower estimate become R5 = 16 and L5 = −64
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Calculus HW , will someone please teach me how to do this problem. I'm struggling, thanks! 10 Points
Compute the first two derivative.
[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]
[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]
[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]
Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so
[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]
and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].
Intercepts
Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since
[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]
The first intercept you listed is not a valid intercept. One or both coordinates must be 0.
Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).
[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]
The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).
Relative minima/maxima
Find the critical points. We have [tex]f'(x) = 0[/tex] when
[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]
and [tex]f'(x)[/tex] is undefined when
[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]
Check the sign of the second derivative at the first two critical points.
[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at } f(-2\sqrt2) = -8[/tex]
[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]
For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.
[tex]f(-4) = f(4) = 0[/tex]
So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).
Inflection points
We have [tex]f''(x) = 0[/tex] for
[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]
The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).
If Emery has $1,400 to invest at 5% per year compounded monthly, how long will it be before he has $2,400? If the compounding is
continuous, how long will it be? (Round your answers to three decimal places.)
Answer:
Step-by-step explanation:
(1400x14.5x5%) + 1400 =2415
Answer: 14.5 months
Divide. Write your answer in simplest form.
3/14 divided by 7/10???
Answer:
[tex]\frac{15}{49}[/tex]
Step-by-step explanation:
[tex]\frac{3}{14} /\frac{7}{10} =\frac{3}{14} *\frac{10}{7} = \frac{3}{7} *\frac{5}{7} =\frac{15}{49}[/tex]
What must be true for line EF to not intersect plane L?
Answer:
If line EF is parallel to line CD, it will not intersect plane L.
We will start with a string which is pulled tight enough to vibrate at 288 Hertz when
plucked. Let the length of the string be 1 unit. We can find additional nice sounding
notes by using a string of a smaller length with the same amount of tension. To find
the string lengths, we need to use fractions whose numerators are powers of 2 and
whose denominators are powers of 3 (which are larger than ½, but smaller than 1).
The first few fractions are given below. Determine the remaining fractions:
The series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
The string lengths are fractions whose numerators are powers of 2 and denominators are powers of 3, and the fractions are larger than 1/2 but smaller than 1.
Some powers of 2 are:
2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024, 2¹¹ = 2048, 2¹² = 4096, 2¹³ = 8192, 2¹⁴ = 16384, 2¹⁵ = 32768, 2¹⁶ = 65536, and 2¹⁷ = 131072.
Some powers of 3 are:
3⁰ = 1, 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729, 3⁷ = 2187, 2⁸ = 6561, 3⁹ = 19683, 3¹⁰ = 59049, and 3¹¹ = 177147.
The fractions, for which the numerator is a power of 2, the denominator is a power of 3, and the value is between 1/2 and 1 are:
2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
Thus, the series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
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write each number as a logarithm with base 2:-3
The number -3 written as a logarithm with a base of 2 is log₂(0.125) or log₂(1/8)
What are logarithms?As a general rule, logarithms are mathematical expressions that are written in the form log(x) or ln(x), for natural logarithms
How to rewrite the number as a logarithm?The number is given as:
x = -3
The base of the logarithm is given as:
Base = 2
To rewrite the given number as a base of 2, we take the exponent of the number where the base is 2
This is represented as:
Number =2^-3
Apply the power rule of indices
Number =1/2^3
Evaluate the exponent
Number = 1/8
Evaluate the quotient
Number = 0.125
Hence, when the number -3 is rewritten as a logarithm with base 2, the equivalent logarithm expression is log₂(0.125) or log₂(1/8)
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A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?
A: The coordinates of the point R' are (- 6, 21).
B: The coordinates of the point T' are (1, 3).
How to generate new points by definition of dilation
In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of dilationk - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointPart A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:
R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]
R'(x, y) = (- 6, 21)
Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:
T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]
T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)
T'(x, y) = (- 2, 7) + (3, - 4)
T'(x, y) = (1, 3)
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Sarah, Tony, and Megan are helping their parents plan the layout of the backyard. The patio is as wide as the fire pit, and 5 feet long. The pool is enlarged to yield the following layout:
If the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
Given that the patio is as wide as the fire pit, and 5 feet long.
We are required to form an equation which can describe the area of the backyard.
Equation is relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or many more depending on the powers of the variable.
If we see the figure carefully then we can find that the length of the backyard is 2x+6 and the breadth of the backyard is 5+x and backyard is in shape of rectangle.
Area of rectangle =Length *breadth
=(2x+6)*(5+x)
=30+10x+6x+2[tex]x^{2}[/tex].
Hence if the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
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Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to four decimal places.)
16
0
sin
x
dx, n = 4
Split up [0, 16] into 4 equally-spaced subintervals of length [tex]\frac{16-0}4=4[/tex],
[0, 16] = [0, 4] U [4, 8] U [8, 12] U [12, 16]
with midpoints 2, 6, 10, and 14, respectively.
Then with the midpoint rule, we approximate the integral to be about
[tex]\displaystyle \int_0^{16} \sin(\sqrt x) \, dx \approx 4 \left(\sin(\sqrt2) + \sin(\sqrt6) + \sin(\sqrt{10}) + \sin(\sqrt{14})\right) \approx \boxed{4.1622}[/tex]