Answer:
x = 10/243
Step-by-step explanation:
3^5x = 10
243x = 10
Divide 243 on both sides
10/243
Nikolai Bell was recently hired at a new company. The Bells need to choose between two different health plans for their family’s primary insurance: Option 1: the Deluxe Plan or Option 2: the Basic Plan.
Step 2: Identify Variables and Assumptions
Identify the key variables in the Bell’s situation. (Select all that apply)
The cost of each plan.
The benefits paid by each plan.
The health of the Bell family.
The location of the nearest fast food restaurant.
The number of hours that Nikolai works each week.
The Bell’s monthly income.
To help make a decision Nikolai looked at all of the family’s medical expenses from the last year. He used mathematical tools to calculate what the total costs would have been if they had Option 1: the Deluxe Plan and what the total costs would have been if they had Option 2: the Basic Plan.
Identify the assumptions that Nikolai is using to make his decision.
The Bell’s medical costs will remain about the same as last year.
If Nikolai works hard, he can get a raise.
If the Bells are careful, they will not need any medical insurance.
If the Bell’s have health insurance they do not need to have an emergency savings account.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs for each plan using last year’s medical expenses as an estimate.
Option 1: The Deluxe Plan
(You pay . . .)
Option 2: The Basic Plan
(You pay . . .)
Co-payment for Office Visit = $
20
Co-payment for Office Visit = $
30
Prescription Drugs at 30%
Prescription Drugs at 50%
Emergency Room Visit = first $
75 plus 10% of remaining charge
Emergency Room visit = first $
75 plus 30% of remaining charge
Hospital stay or procedures at 10%
Hospital stay or procedures at 30%
Other approved expenses at 10%
Other approved expenses at 30%
Monthly premium = $
425
Monthly premium = $
150
The Bell Family’s medical expenses from last year are summarized in the table below:
Month
The Bell Family’s Medical Expenses
January
1 office visit(s) & $
95 prescription
February
1 Emergency room visit (charged $
400)
March
2 office visit(s)
July
1 office visit(s)
August
Hospital stay for surgery (hospital/doctor charged $
9,000) and $
85 prescription
September
2 office visit(s)
Key variables in the Bell's situation include the cost of each plan, the benefits paid by each plan, and the health of the Bell family.
What assumption can we make?The assumptions Nikolai is using are that the Bell's medical costs will remain about the same as last year.
Calculating total costs for each plan using last year's medical expenses:
Option 1: The Deluxe Plan
Monthly Premium: $425 * 12 = $5100
Office Visits: 6 * $20 = $120
Prescriptions: 0.3 * ($95 + $85) = $54
Emergency Room: $75 + 0.1 * ($400 - $75) = $107.50
Hospital Stay: 0.1 * $9000 = $900
Total: $6,281.50
Option 2: The Basic Plan
Monthly Premium: $150 * 12 = $1800
Office Visits: 6 * $30 = $180
Prescriptions: 0.5 * ($95 + $85) = $90
Emergency Room: $75 + 0.3 * ($400 - $75) = $172.50
Hospital Stay: 0.3 * $9000 = $2700
Total: $4,942.50
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WILL MARK BRAINLIEST
Jamelia observes that is f(x)=2^x, then the graphs of 4f(x) and f(x) +3 both have a y-intercept of 1. Does this mean that multiplying f(x) by 4 and adding 3 to f(x) transform the graph the same way?
No, multiplying the function f(x) by 4 and adding 3 to f(x) do not transform the graph the same way.
Although both transformations result in a y-intercept of 1, they have different effects on the shape and direction of the graph.
Multiplying f(x) by 4 stretches the graph vertically, making it four times as tall. This also makes the function grow much more quickly for positive values of x and decay much more quickly for negative values of x.
Adding 3 to f(x) shifts the graph vertically upward by 3 units. This transformation does not change the shape of the graph, but simply moves it up or down on the y-axis.
Therefore, the two transformations have different effects on the graph and cannot be considered the same.
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When ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams per kilogram of body weight when the fever is under 102.5 degrees Fahrenheit.How much medicine would be usual dose for a 18 month old weighing 29 pounds?
The usual dose of ibuprofen for an 18-month-old child weighing 29 pounds would be approximately 65.772 milligrams.
To calculate the usual dose of ibuprofen for a 18-month-old child weighing 29 pounds, we need to convert the weight from pounds to kilograms. Since 1 pound is approximately 0.4536 kilograms, we can use this conversion factor.
Weight of the child: 29 pounds
Weight in kilograms: 29 pounds × 0.4536 kilograms/pound = 13.1544 kilograms (rounded to four decimal places)
Now that we have the weight of the child in kilograms, we can calculate the usual dose of ibuprofen.
Usual dose of ibuprofen: 5 milligrams/kilogram
Dose for the 18-month-old child: 5 milligrams/kilogram × 13.1544 kilograms = 65.772 milligrams (rounded to three decimal places)
Therefore, the usual dose of ibuprofen for an 18-month-old child weighing 29 pounds would be approximately 65.772 milligrams. It's important to note that this is a general calculation, and it's always best to consult a healthcare professional for accurate dosing instructions based on the specific circumstances of the child.
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Daniel is thinking of a 2-digit number that is less than 50. When it is divided by 2, there is no remainder. When it is divided by 3, there is a remainder of 1 When it is divided by 5, there is a remainder of 3 What number is Daniel thinking of?
Answer:
28
Step-by-step explanation:
The two digit numbers less than 50 that when divided by 5 have a remainder of three are: 13, 18, 23, 28, 33, 38, 43, and 38.
Since the number must be evenly divisible by 2, you can remove the odd answers which leaves you with 18, 28, 38, and 48.
The only one that has a remainder of 1 when divided by 3 is 28.
ANSWER:
28
28÷2=14
28÷3=9 with remainder of 1
28÷5=5 with a remainder of 3
In a triangle ABC, AB = 6 cm, BC = 10 cm and CBA 70°
(a) Find the area of the triangle.
(b) Find AC.
Check the picture below.
well, let's move like the crab, backwards, let's first find AC and then its area using Heron's Area formula.
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ b = \sqrt{10^2+6^2~-~2(10)(6)\cos(70^o)} \implies b = \sqrt{ 136 - 7200 \cos(70^o) } \\\\\\ b \approx \sqrt{ 136 - (41.0424) } \implies b \approx \sqrt{ 94.9576 } \implies b \approx 9.74[/tex]
now that we have all three sides, let's plug them in
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 10\\ b \approx 9.74\\ c = 6\\ s\approx\frac{10+9.74+6}{2}\\ \qquad 12.87 \end{cases} \\\\\\ A\approx\sqrt{12.87(12.87-10)(12.87-9.74)(12.87-6)} \\\\\\ A\approx\sqrt{12.87(2.87)(3.13)(6.87)} \implies A\approx\sqrt{794.258}\implies A\approx 28.18[/tex]
what is the surface area
The surface area of the cylinder with a base diameter of 23 yd and a height of 28 yd is 908.5π yd².
What is the surace area of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The surface area of a cylinder is expressed as;
Surface area = 2πr² + 2πrh
Where r is radius of the circular base, h is height and π is constant.
From the image, the diameter is 23 yd and the height is 38 yd.
Radius r = diameter/2
Radius r = 23/2
Radius r = 11.5 yd
We can plug these values into the above formula:
Surface area = 2πr² + 2πrh
Surface area = ( 2 × π ( 11.5 )² ) + ( 2 × π × 11.5 × 28 )
Surface area = ( 2 × π 132.25 ) + ( 2 × π × 11.5 × 28 )
Surface area = 264.5π + 644π
Surface area = 908.5π yd²
Therefore, the surface area is 908.5π yd².
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Boy bacar is older than Aria. Their ages are consecutive integers. Find Boubacar’s age if the sum of the square of Bounacars age and 2 times Aria’s age is 193.
(i’ll give brainlist)
Answer:
Boubacar is 13 years old
Step-by-step explanation:
Boubacar is a year older than Aria.
We can represent Aria's age with x, and Boubacar's as x+1
We can now write the equation:
(x+1)²+2x=193
(x²+2x+1)+2x=193 (Use the binomial formula)
x²+4x+1=193 (Collect like terms
x²+4x-192=0 (Move 193 to the other side)
Again, we can solve this by the quadratic equation:
[tex]x = \frac{ - 4 + - \sqrt{ {4}^{2} - 4 \times 1 \times ( - 192) } }{2 \times1 } \\ x = \frac{ - 4 + - \sqrt{16 + 768} }{2} \\ x = \frac{ - 4 + - \sqrt{784} }{2} \\ x = \frac{ - 4 + - 28}{2} [/tex]
And again, we have 2 real solutions because of the ± symbol.
x1=-4+28/2
x1=24/2
x1=12
x2=-4-28/2
x2=-32/2
x2=-16
Since their age can't be negative, Boubacar's age is x1+1, which is 12+1, or 13.
I need help asap please answer this for me.
Answer:
6
Step-by-step explanation:
The median is the middle number. In this case, it is 6.
Pls hurry!
simplify: [tex]\frac{6!}{3!}[/tex]
(A) 90
(B) 24
(C) 30
(D) 120
Answer:
D
Step-by-step explanation:
n! ( factorial ) is defined as
n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1
then
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
3! = 3 × 2 × 1 = 6
[tex]\frac{6!}{3!}[/tex]
= [tex]\frac{720}{6}[/tex]
= 120
A joke is being spread by a group of students. Each day,
any student who has heard the joke tells it to 1 student
who has not already heard it. If 2 students knew the
joke at the end of the first day and 4 students knew it at
the end of the second day, how many students knew
the joke at the end of the third day? How many knew it
at the end of the fourth day?
At the end of the third day, there will be 40 students who know the joke and at the end of the fourth day, there will be 80 students who know the joke.
At the end of the first day, 2 students knew the joke.
This means that these 2 students have told the joke to 2 different students who had not heard it before.
So, by the end of the first day, there are 2 + 2 = 4 students who know the joke.
At the end of the second day, 4 students knew the joke.
This means that these 4 students have each told the joke to 4 different students who had not heard it before.
So, by the end of the second day, there are 4 + (4× 4) = 20 students who know the joke.
Now let's determine the number of students who know the joke at the end of the third day.
Following the same pattern as before, each of the 20 students who know the joke at the end of the second day will tell it to 1 student who hasn't heard it.
So, at the end of the third day, there will be 20 + (20× 1) = 40 students who know the joke.
In the same sequence, at the end of the fourth day, there will be 40 + (40 × 1) = 80 students who know the joke.
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5/2 pounds to ounces
Answer:
40
Step-by-step explanation:
1LB = 16 Ounces
5/2= 2.5
So
16+16 = 32
16/2 = 8
32+8=40
Answer:
40
Step-by-step explanation:
1 pound is equal to 16 ounces
so 5/2 x 16 is 40
20POINTS TO WHOEVER ANSWERS
Answer:
Step-by-step explanation
convert 1 2/3 = 5/3
3/4 / 5/3
3/4 x 3/5
9/20 ?
A 1-day movie rental at Red Box cost $2.00. For each additional day there is a fee of $0.59. How much will it cost to rent a movie 7 days?
The population of a town increased from 3800 in 2007 to 6100 in 2010 find the absolute and relative (percent) increase.
The requried population increased by approximately 60.53%.
To find the absolute increase, we subtract the initial population from the final population:
Absolute increase = Final population - Initial population
Absolute increase = 6100 - 3800
Absolute increase = 2300
Therefore, the population increased by 2300 people.
To find the relative increase, we first calculate the percent change:
Percent change = (New value - Old value) / Old value x 100%
Percent change = (6100 - 3800) / 3800 x 100%
Percent change = 2300 / 3800 x 100%
Percent change = 60.53%
Therefore, the population increased by approximately 60.53%.
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A 3 kg bag of rice lasts exactly 30 days for Mrs. and Mr. Pestonjee when both consume equal amounts. If Mr. Pestonjee cuts down his rice intake by half on his doctor's advice, how many days would a 3 kg bag last them? A 35 B 40 C 42 D 45
Answer:
40
Step-by-step explanation:
they both consume equal amounts.
let's call his intake M and hers F.
1.5M + 1.5F = 3(kg)
if he reduces his intake by half, he now only has 1.5/2 = 0.75 in exactly 30 days.
their collective intake is now 0.75M + 1.5F
1.5 + 0.75 = 2.25.
3/2.25 = 4/3.
4/3 is one third more than 3/3 (1).
so a 3kg bag will last one third longer than 30 days. 30 X 4/3 = 120/3 = 40 (days).
Find the area of the following triangle:
5 cm, 10 cm and hyp= unknown
A=[?] cm^2
Enter as exact answer with decimal.
[tex]Answer=[/tex]
[tex]25[/tex]
[tex]Because:[/tex]
[tex]a=\frac{1}{2} bh[/tex]
[tex]a=\frac{1}{2} (5)(10)[/tex]
[tex]a=\frac{1}{2} (50)[/tex]
[tex]a=25[/tex]
Suppose that an individual has a body fat percentage of 18.8% and weighs 184 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answer:
34.6 pounds
Step-by-step explanation:
18.8% = 0.188
0.188 X 184 = 34.592 = 34.6 pounds (to nearest one tenth)
NO LINKS!! URGENT HELP PLEASE!!
Find the measure of one interior angle and one exterior angle in each regular polygon. Round your answer to the nearest tenth if necessary 3aa and 4aa
Answer:
3.
one interior angle: 90°
one exterior angle: 90°
4.
one interior angle: 140°
one exterior angle: 40°
Step-by-step explanation:
Note:
For interior angle:
The sum of the interior angles of a polygon is [tex]\boxed{\bold{(n-2)*180}}[/tex], so the measure of one interior angle[tex]\boxed{\bold{\frac{(n-2)*180}{n}}}[/tex] .where n is the number of sides. A regular polygon has all of its interior angles equal.
For exterior angle:
The sum of the exterior angles of a polygon is 360°, so the measure of one exterior angle is [tex]\boxed{\bold{\frac{360}{n}}}[/tex].
The exterior angle of a polygon is supplementary to its interior angle, meaning that the two angles add up to 180 degrees.
Now for the question:
3.
no. of side (n)=4
one Interior angle: by substituting the value of n
we get,
[tex]\boxed{\bold{\frac{(n-2)*180}{n}=\frac{(4-2)*180}{4}=90^o}}[/tex]
one exterior angle: by substituting the value of n
we get,
[tex]\boxed{\bold{\frac{360}{4}=90^o}}[/tex]
4.
no. of side (n)=9
one Interior angle: by substituting the value of n
we get,
[tex]\boxed{\bold{\frac{(n-2)*180}{n}=\frac{(9-2)*180}{9}=140^o}}[/tex]
one exterior angle: by substituting the value of n
we get,
[tex]\boxed{\bold{\frac{360}{9}=40^o}}[/tex]
Answer:
3) Interior Angle = 90°
Exterior Angle = 90°
4) Interior Angle = 140°
Exterior Angle = 40°
Step-by-step explanation:
A regular polygon is a polygon that has all sides of equal length and all angles of equal measure.
The interior angle of a regular polygon is the angle formed by two adjacent sides within the polygon.
The formula for the interior angle of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Interior Angle of a Regular Polygon}\\\\Interior Angle $=\dfrac{(n-2)\cdot 180^{\circ}}{n}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \end{minipage}}[/tex]
The exterior angle of a regular polygon is the angle formed by one side of the polygon and the extension of the adjacent side.
The sum of the exterior angles of any polygon is 360°.
Therefore, the formula for the exterior angle of a regular polygon is:
[tex]\boxed{\begin{minipage}{6cm}\underline{Exterior Angle of a Regular Polygon}\\\\Exterior Angle $=\dfrac{360^{\circ}}{n}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \end{minipage}}[/tex]
Question 3The given regular polygon has 4 sides.
Therefore substitute n = 4 into the formulas to find the measure of one interior angle and one exterior angle.
[tex]\boxed{\begin{aligned}\textsf{Interior Angle}&=\dfrac{(4-2)\cdot 180^{\circ}}{4}\\\\&=\dfrac{2\cdot 180^{\circ}}{4}\\\\&=\dfrac{360^{\circ}}{4}\\\\&=90^{\circ}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\textsf{Exterior Angle}&=\dfrac{360^{\circ}}{4}\\\\&=90^{\circ}\end{aligned}}[/tex]
Question 4The given regular polygon has 9 sides.
Therefore substitute n = 9 into the formulas to find the measure of one interior angle and one exterior angle.
[tex]\boxed{\begin{aligned}\textsf{Interior Angle}&=\dfrac{(9-2)\cdot 180^{\circ}}{9}\\\\&=\dfrac{7\cdot 180^{\circ}}{9}\\\\&=\dfrac{1260^{\circ}}{9}\\\\&=140^{\circ}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\textsf{Exterior Angle}&=\dfrac{360^{\circ}}{9}\\\\&=40^{\circ}\end{aligned}}[/tex]
Functions f(x) and g(x) are shown:
f(x) = x2 g(x) = x2 + 8x + 16
In which direction and by how many units should f(x) be shifted to match g(x)?
A. Left by 4 units
B. Right by 4 units
C. Left by 8 units
D. Right by 8 units
The transformation of the function is left by 4 units
Given data ,
Let the parent function be represented as f ( x )
Now , f ( x ) = x²
Let the transformed function be represented as g ( x )
where g ( x ) = x² + 8x + 16
On factorizing , we get
g ( x ) = ( x + 4 )²
Therefore , Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
So , the transformation is left by 4 units
Hence , the transformed function is g ( x ) = ( x + 4 )²
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Rewrite the expressions without the absolute value sign. |x+12| , if x>−11
Answer: The absolute value of a number is its distance from 0 on the number line. For any real number x, the absolute value of x is defined as:
|x| = x if x >= 0 |x| = -x if x < 0
In the given expression, |x+12|, we need to consider the condition that x > -11. If x > -11, then x+12 > 1. Since x+12 is positive, we can remove the absolute value sign and the expression becomes x+12.
So, the given expression |x+12| can be rewritten without the absolute value sign as x+12 when x > -11.
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cube and then spin a spinner with two equal-sized sections
What is the probability of rolling a number greater than 2 and spinning red?
1
2
3
4
5
6
Red (R)
1R
2R
3F
4R
5R
6R
Yellow (Y)
1Y
2Y
3Y
4Y
5Y
6Y
A1/3
B1/2
C1/4
D1/6
The probability of rolling a number greater than 2 and spinning red is 1/3. Option A
How to determine the the probability of rolling a number greater than 2 and spinning redThe probability of rolling a number greater than 2 is 4 out of 6 since there are four numbers (3, 4, 5, and 6) that meet the condition out of the six possible outcomes.
To find the probability of both events occurring, we multiply the individual probabilities:
P(rolling a number greater than 2 and spinning red) = P(rolling a number greater than 2) * P(spinning red)
P(rolling a number greater than 2 and spinning red) = (4/6) * (1/2)
Simplifying the fraction:
P(rolling a number greater than 2 and spinning red) = 2/3 * 1/2
P(rolling a number greater than 2 and spinning red) = 1/3
Therefore, the probability of rolling a number greater than 2 and spinning red is 1/3.
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Could someone help me with this question? Thank you
For the profits of a fruit grower, the matrixes are:
A = [tex]\left[\begin{array}{ccc}125&100&75\\100&175&125\end{array}\right][/tex]B = [tex]\left[\begin{array}{ccc}3.50&3.50&3.50\\6.00&6.00&6.00\end{array}\right][/tex]BA =[tex]\left[\begin{array}{ccc}125&100&75\\100&175&125\end{array}\right] \left[\begin{array}{ccc}3.50&3.50&3.50\\6.00&6.00&6.00\end{array}\right] = \left[\begin{array}{ccc}437.50&437.50&437.50\\1175.00&1575.00&1375.00\end{array}\right][/tex]How to write matrix?(a) The matrix A representing the number of bushels of each crop i that are shipped to each outlet j is:
A = [tex]\left[\begin{array}{ccc}125&100&75\\100&175&125\end{array}\right][/tex]
Each entry aij of the matrix represents the number of bushels of crop i (apples or peaches) sent to outlet j (The Farmer's Market, The Fruit Stand, or The Fruit Farm).
(b) The matrix B representing the profit per bushel of each fruit is:
B = [tex]\left[\begin{array}{ccc}3.50&3.50&3.50\\6.00&6.00&6.00\end{array}\right][/tex]
Each entry bij of the matrix represents the profit per bushel of crop i (apples or peaches) sent to outlet j (The Farmer's Market, The Fruit Stand, or The Fruit Farm).
(c) The product BA is:
BA = [tex]\left[\begin{array}{ccc}125&100&75\\100&175&125\end{array}\right] \left[\begin{array}{ccc}3.50&3.50&3.50\\6.00&6.00&6.00\end{array}\right] = \left[\begin{array}{ccc}437.50&437.50&437.50\\1175.00&1575.00&1375.00\end{array}\right][/tex]
Each entry bij of the product matrix represents the total profit earned from selling the bushels of crop i (apples or peaches) to outlet j (The Farmer's Market, The Fruit Stand, or The Fruit Farm). For example, the entry in the first row and first column represents the total profit earned from selling 125 bushels of apples to The Farmer's Market, which is $437.50.
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Factor. x 2 + 3 x − 70 x 2 +3x−70
The factored form of the expression [tex]x^2 + 3x - 70[/tex] is (x + 10)(x - 7).
How to factor the expressionTo factor the expression [tex]x^2 + 3x - 70[/tex], we look for two numbers whose product is -70 and whose sum is 3.
After examining the factors of 70, we find that 10 and -7 satisfy these conditions.
So, we can factor the expression as follows:
[tex]x^2 + 3x - 70[/tex] = (x + 10)(x - 7)
Therefore, the factored form of the expression [tex]x^2 + 3x - 70[/tex] is (x + 10)(x - 7).
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Describe the transformations of the following equation:
Captionless Image
reflect over x-axis, left 2, up 2
reflect over y-axis, left 2, up 2
left 2, up 2
reflect over x-axis, right 2, up 2
The true statement for the function p(x) is p(-2) and p(0) cannot be compared as p(0) is undefined. Option D is correct.
The given function is a logarithmic function and it is undefined at x = 0.
First, let us understand the logarithmic function:
A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.
We are given:
p(x) = log 5x
substitute x = 0 in the above equation, we will get;
p(0) = log 5 × 0
p(0) = log 0
p(0) = undefined
Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.
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Using the equation of the function p(x) below, determine which of the statements below is true. Show your work.
Captionless Image
p(-2) > p(0)
p(-2) < p(0)
p(-2) and p(0) cannot be compared because p(-2) is undefined.
p(-2) and p(0) cannot be compared because p(0) is undefined.
If San Jose’s coordinates
are (76, -12), where the
coordinates represent
miles, find the distance
between San Jose and San
Francisco to the nearest
mile.
The distance between San Jose and San Francisco to the nearest mile is
37 miles
How to find the distanceWe can use the distance formula to find the distance between the two points
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
where
(x1, y1) and (x2, y2) are the coordinates of the two points
Plugging in the given coordinates we get
distance = √((53 - 76)² + (17 - (-12))²)
distance = √(23² + 29²)
distance = √(1370)
distance ≈ 37.01 miles
distance ≈ 37 miles
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complete question
If San Jose's coordinates are (76,-12), where the coordinates represent miles, find the distance between San Jose and San Francisco (53,17) to the nearest mile.
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A community sports league is raising money by making custom shirts to sell at league games. They plan to sell the shirts for $15. Each shirt costs $8 to make. They spent $55 for advertising.
Use n to represent the number of shirts they sell. Multiply this by the money they make for each shirt, then subtract the advertising cost.
Which expression represents the money that the league raises?
There are 40 centipedes in an area of rainforest. The number of centipedes is expected to increase by 64% every year compared to the year before. a) How many centipedes are expected to be in the area of rainforest in 5 years' time? b) How many centipedes are expected to be in the area of rainforest in 20 years' time? Round your answers to the nearest 100.
There are expected to be 700 centipedes in the area of rainforest in 5 years' time.
There are expected to be 129,800 centipedes in the area of rainforest in 20 years' time.
We have,
a)
To calculate the number of centipedes in 5 years, we can use the equation:
N = N0 × (1 + r)^t
where:
N0 = initial number of centipedes (40)
r = annual growth rate (64% or 0.64)
t = time in years (5)
N = final number of centipedes after 5 years
Plugging in the values, we get:
N = 40 × (1 + 0.64)^5
N ≈ 666.23
Rounding to the nearest hundred, we get:
N ≈ 700
b)
To calculate the number of centipedes in 20 years, we can use the same equation:
N = N0 × (1 + r)^t
where:
N0 = initial number of centipedes (40)
r = annual growth rate (64% or 0.64)
t = time in years (20)
N = final number of centipedes after 20 years
Plugging in the values, we get:
N = 40 × (1 + 0.64)^20
N ≈ 129,834.26
Rounding to the nearest hundred, we get:
N ≈ 129,800
Therefore,
There are expected to be 700 centipedes in the area of rainforest in 5 years' time.
There are expected to be 129,800 centipedes in the area of rainforest in 20 years' time.
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Graph $\triangle ABC$△ABC with vertices cap A times open paren negative 1 comma negative 2 close paren$A\left(-1,\ -2\right)$A(−1, −2) , cap b times open paren 1 comma negative 1 close paren$B\left(1,\ -1\right)$B(1, −1) , and cap c times open paren 2 comma negative 2 close paren$C\left(2,\ -2\right)$C(2, −2) and its image after a dilation centered at the origin with a scale factor of 2$2$2 .
A graph of the triangle and its image after a dilation centered at the origin with a scale factor 2 is shown below.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 2 that is centered at the origin as follows:
Ordered pair A (-1, -2) → Ordered pair A' (-1 × 2, -2 × 2) = Ordered pair A' (-2, -4).
Ordered pair B (1, -1) → Ordered pair B' (1 × 2, -1 × 2) = Ordered pair B' (2, -2).
Ordered pair C (2, -2) → Ordered pair C' (2 × 2, -2 × 2) = Ordered pair C' (4, -4).
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List the zeros of .
If you have more than one solution, separate them with commas.
We discover that the zeros of the function y = x(2x - 1) are x = 0 and x = 1/2.
We must identify the x values for which y equals zero in order to identify the zeros of the function y = x(2x - 1). In other words, we're searching for the x-intercepts of this function's graph.
We set y equal to zero and work on x while solving for the zeros. This equation can only be true if either x = 0 or 2x – 1 = 0. We obtain x = 1/2 by solving for x in the second equation. These are the locations where the function's graph crosses over the x-axis.
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Complete question - List the zeros of y = x(2x-1).
If you have more than one solution, separate them with commas.
ii) y = 4√x-x, 0≤x≤8 find the absolute maxima and minima
The absolute maximum value is 0 and it occurs at x = 0 and x = 8, while the absolute minimum value is also 0 and it occurs at the same points.
To find the absolute maxima and minima of the function y = 4√(x - x), where 0 ≤ x ≤ 8, we need to evaluate the function at its critical points and endpoints within the given interval.
First, let's find the critical points by taking the derivative of the function y with respect to x and setting it equal to zero:
y = 4√(x - x)
[tex]dy/dx = (4/2\sqrt{(x - x)} ) \times (1) = 2/\sqrt{(x - x) }[/tex]
To find the critical points, we set dy/dx = 0:
2/√(x - x) = 0
The denominator cannot be zero, so there are no critical points within the given interval (0 ≤ x ≤ 8).
Next, we evaluate the function at the endpoints of the interval:
For x = 0:
y = 4√(0 - 0) = 4√0 = 0
For x = 8:
y = 4√(8 - 8) = 4√0 = 0
Hence, the function has minimum values of 0 at both endpoints of the interval.
Therefore, the absolute maximum value is 0 and it occurs at x = 0 and x = 8, while the absolute minimum value is also 0 and it occurs at the same points.
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