The percent increase in the total number of students on the honor roll is 9.4% .
In the question,
it is given that ,
last year , the number of boys in the honor roll is = 60 boys ,
the number of girls in the honor roll is = 100 girls ,
total number of students last year = 160
percent increase in the number of boys in the honor roll is = 20% ,
so , number of boys become = 60 + (0.20*60) = 72 boys ,
percent increase in the number of girls in the honor roll is = 3% ,
so , number of girls become = 100 + (0.03*100) = 103 girls ,
total number of students this year = 103 + 72 = 175 .
increase in number of students = 175 - 160 = 15
So , percent increase is = (15/160) × 100
= 0.09375 × 100
= 9.375 %
≈ 9.4%
Therefore , the percent increase is 9.4% .
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In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
there are no pictures. Will give brainlest.
Miles is shopping for a new computer. He finds a computer with an original price of $325. 00 but finds that it is 15% off. After paying a 7% sales tax, how much does miles spend on his new computer?.
Miles has to spend $295.3375 on his new computer.
Sales tax is applied to the price after the discount is applied because discounts are typically provided directly by the retailer and lower both the sales price and the money the retailer receives.
So Original price of Computer is $325.00
Discount with computer is 15% off.
15% of $325 is (325*15)/100 = $48.75.
Price of computer after discount = 325-48.75 =$276.25
Now sales tax will be applied on this price.
7% sales tax = 0.07
amount of sales tax = 276.25*0.07 = 19.3375
Price of Computer after sales tax = 276+19.3375 = 295.3375.
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Which decimal is equivalent to 2/27
Answer:
0.07407407
Step-by-step explanation:
divide 2 by 27
Answer:
0.0740
Step-by-step explanation:
just divide 2 by 27
a jar contains 10 blue marbles and 11 red marbles. two marbles are drawn without replacement. what is the probability of getting two red marbles?
0.2620 is the probability of getting two red marbles.
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
a jar contains 10 blue marbles and 11 red marbles.
So, there total 21 marbles are present.
Now among 21 marbles, 11 are red marble. So, odds of a red on the first are 11/21
Next, there are 20 marbles are present and 10 are red. So odds of a red on the second is 10/20.
For, probability both are red, just multiply
= (11/21) x (10/20)
= 0.2620.
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B.
5x + 2 = 2x + 14
WITH SOLUTION
i also need it rn-
Answer:
4
Step-by-step explanation:
5x + 2 = 2x + 14
or, 5x - 2x = 14 - 2
or, 3x = 12
or, x = 12/3
.
. . x = 4
10 post hole that are 3 feet deep and 1 foot across with a pipe down the center that is 3 inches in diameter
The total volume of all 10 holes and pipes is about 24.135 cubic feet.
What is Volume?Generally, To calculate the volume of the holes, you can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
In this case, the radius of the hole is 0.5 feet (since the hole is 1 foot across and the diameter of the pipe is 3 inches, which is 0.25 feet), and the height is 3 feet. Plugging these values into the formula, we get:
Volume = π * 0.5^2 * 3 = 0.785 * 3 = 2.355 cubic feet
So each hole has a volume of about 2.355 cubic feet. To find the total volume of all 10 holes, you can simply multiply this number by 10:
Total volume = 2.355 * 10 = 23.55 cubic feet
This is the volume of the holes themselves, not including the volume of the pipes. To find the volume of the pipes, you can use the same formula, but with the radius of the pipe (which is 1.5 inches, or 0.125 feet) and the length of the pipe (which is 3 feet).
Volume = π * 0.125^2 * 3 = 0.0195 * 3 = 0.0585 cubic feet
So the volume of one pipe is about 0.0585 cubic feet. To find the total volume of all 10 pipes, you can multiply this number by 10:
Total volume = 0.0585 * 10 = 0.585 cubic feet
23.55 + 0.585 = 24.135 cubic feet.
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CQ not found
a fair coin is flipped nultiple times until it lands on heads if the probability of landing on heads is 50% what is the probability of first landing on heads on the fourth attempt
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
what is probability ?There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Since possibility and probability are equivalent, you may define probability as the likelihood that a specific event will occur.
given
A fair coin is repeatedly flipped until it comes up heads.
The coin is impartial.
On the third try, we need to calculate the likelihood of the first landing being on heads.
We are aware that each flip of a fair coin is independent of the others, and that each effort results in P(H) = P(T) = 0.5.
Required probability is the likelihood that the third attempt's first landing will be on heads.
= Chance of (I two trials result in tail and third result in head)
=P(I head) P(II head) P(III tail) (since each trial is independent)
= ( 1 /2 ) (1/2)(1/2) = (1/8 )
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
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Find X round answer to the nearest integer.
mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has
a. rs 11
b. rs 10
c. rs 14
d. rs 9
Answer:
a. 11
Step-by-step explanation:
Mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has:
a. 11
b. 10
c. 14
d. 9
3.5 * 3 = 10.5 cost
She has 11.
suppose there are 6 roads connecting town a to town b and 4 roads connecting town b to town c. in how many ways can a person travel from a to c via b?
Number of ways can a person travels from A to C via B = 24 ways
How it can be calculated that a person can travel in no. of ways?
To calculate the likelihood of an event occurring, we will apply the equation number of favourable outcomes divided by total number of outcomes. We sometimes need to apply a permutation to calculate the overall number of outcomes. A permutation is a method for calculating the number of events that occur when order is important.
Given,
Connection of roads from a = 6
Connection of roads from a = 4
Number of roads from a to b =6
Number of roads from b to c =4
Number of ways can a person travels from a to c via b
= 6*4
= 24 ways
The number of ways a person can go from A to C via B is 24.
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Compare √18 and 23/5 using >, <, or =.
23/5<√18
23/5 = √18
√18 > 23/5
√18<23/5
Answer: Thus, sqrt 18 < 23/5
Step-by-step explanation:
23/5=4.6
4.6x4.6=21.16
18<21.16
Find an equation of the line that has a slope of -1 and a y intercept of 5. Write your answer in the form
y = mx + b.
y =
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Graph the line that has a slope of
1
6
and includes the point (0,0).
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
What is the slope of line?
The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.
Here given thaat the line that has a slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex].
Then,
[tex]y=mx+c\\\\y=\frac{x}{5}+c\\\\x=0,y=0\\\\0=0+c\\\\c=0[/tex]
Thus,
[tex]y=\frac{x}{5}+c\\\\c=0[/tex]
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
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Please help me ASAP. I will give brainliest after 2 people comment.
Answer: x= 18
Step-by-step explanation:
9 divided by 6 = 1.5
That is the rate change
So take 12 times 1.5 = 18
x= 18
If you can please give me a Brainliest, thank you!
Answer:
18
Step-by-step explanation:
See attached worksheet.
A scaled figure will have dirrent dimensions, but with the same proportions. The ratio of the two sides in Figure A is 2/1 (Side/Top). That same ratio will apply to Figure B. So we could write:
x/9 = 2
x = 18
HELP ANYONE PLEASE IT'S DUE TODAY I WAS STUCK ON THIS QUESTION
A line that goes through (0, 0) and (3.6, 14.4).
Wewant a description of the line that describes the same proportional relationship as the points given in the table:
(x, y) = (3.6, 14.4), (12.2, 48.8), (2.1, 8.4)
What is Proportional relation ?The graph of the relation will be a straight line through points with (x, y) values from the table. A graph of a proportional relation also goes through the point (0, 0).
Of the points listed in the answer choices, only (3.6, 14.4) and (12.2, 48.8) are ones that are given in the table. This eliminates all of the answer choices except the correct one:
A line that goes through (0, 0) and (3.6, 14.4).
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What transformations were applied to the parent function k(x)=x| to obtain f(x)= -1/2|x+3/-1.
Answer:
The transformations applied to the parent function k(x)=x| to obtain f(x)= -1/2|x+3/-1 are reflection in the y-axis, vertical stretching by a factor of 1/2, and a horizontal shift of 3 units to the right.
Step-by-step explanation:
To obtain f(x) from k(x), we first reflect k(x) in the y-axis, which changes the sign of the function and flips it over the x-axis. This gives us -k(x). Next, we vertically stretch the graph of -k(x) by a factor of 1/2. This makes the graph of -k(x) taller and narrower. Finally, we shift the graph of -k(x) 3 units to the right. This moves the entire graph 3 units to the right on the x-axis. The resulting function is f(x)=-1/2|x+3/-1.To understand why these transformations were applied, it's helpful to consider the effect of each transformation on the graph of k(x)=x|. Reflecting in the y-axis flips the graph over the x-axis and changes the sign of the function, so it becomes -k(x). Vertical stretching by a factor of 1/2 makes the graph of -k(x) taller and narrower. Finally, shifting the graph of -k(x) 3 units to the right moves the entire graph 3 units to the right on the x-axis. This results in the graph of f(x)=-1/2|x+3/-1.
Answer:
(Assuming it is k(x) = |x| and f(x) = -1/2|x+3| -1
Scale vertically by a factor of -1/2
Shift left 3
Shift down 1
Step-by-step explanation:
The -1/2 is multiplied by everything, so it scales the graph vertically by -1/2. The -1 is again, everything(as opposed to just modifying the x), so it shifts the graph down by 1.
The + 3 is a little more confusing. Basically, x would have to be x-3(which is shifting the graph left) in order to retain the same x-value(to make the equation true) for the same value. This is the same for y, but we usually isolate y so it doesn't come up as often. If we add 1 to both sides, we get [tex]f(x) + 1= -1/2|x+3|[/tex], and for the same reasoning the graph would shift down 1 even though it is f(x) + 1, because for the same x-value the y-value would need to be 1 less to make the equation to hold true.
Feel free to message me/comment on this answer if you would like more clarification/why it is "backwards" or anything else about my answer.
I hope this helps!
What 2 time 200000= because i dont know the question so can i get some help
Answer:
400000
Step-by-step explanation:
sketch the solution to each system of inequalities.
y<=-x-2
y>=-5x+2
Answer:
Where you see the colors overlap is the answer.
Step-by-step explanation:
Desmos is a free graphing calculator.
To qualify for the next marathon, a runner's time must be less than 314 hours. Indicate whether or not each runner will qualify for the next marathon.
who will qualify?
Answer:
(It's weird how I answered this question for someone else 12 minutes ago.)
There was no data provided but due to simple research i have conducted the following data
Qualifiers are in bold, italics and underlined.
Step-by-step explanations:
Chio- 3 1/5
Kevin- 3.2
Ojas- 3 8/30
Sydney- 3 13/60
Qualifiers: Chico, Kevin
let me know if this is incorrect data
Are the polygons similar? If they are, write a similarity statement and give the scale factor.
The image consists of two quadrilaterals PQSN and AGKD. The lengths of the sides PQ = 10, QS = 7.5, SN = 15, NP = 15, AG = 12, GK = 12, KD = 8 and DA = 6. Angle P is congruent to angle K. Angle S is congruent to angle A. Angle N and G are right angles.
A. no
B. yes; POSN ~ KDAG, scale factor: 5 : 4
C. yes; POSN ~ KDAG, scale factor: 4 : 5
The polygons (quadrilaterals) are similar by the congruency of three interior angles and the equal ratios (5 : 4) of a pair of adjacent sides. The correct option is therefore
B. Yes; PQSN ~ AGKD, scale factor; 5 : 4
What are similar polygons?Similar polygons are polygons that have the same interior angle, and proportional dimensions.
The specified parameters indicate that we have;
Polygon PQSN and AGKD are quadrilaterals
Length of sides of polygon PQSN
Length of side PQ = 10, QS = 7.5, SN = 15, NP = 15
Length of sides of polygon AGKD
AG = 12, GK = 12, KD = 8, DA = 6
The measure of the angles are;
∠K ≅∠S
∠S ≅ ∠A
∠N = ∠G = 90°
The angle sum property of a quadrilateral indicates that the measure of the fourth angle of both quadrilateral are congruent
The ratio of two adjacent sides of the quadrilaterals are;
7.5/6 and 10/8
7.5/6 = 1.25
10/8 = 1.25
Therefore;
[tex]\dfrac{7.5}{6} =\dfrac{10}{8} =1.25[/tex]
The ratio of two adjacent sides of the quadrilaterals PQSN and AGKD are therefore the same.
The three interior angles of quadrilateral PQSN are congruent to three interior angles of quadrilateral AGKD, and the ratio of two adjacent sides from each quadrilateral are the same, therefore, quadrilaterals are PQSN is similar to quadrilateral AGKD
The scale factor of dilation from quadrilateral PQSN to AGKD is 7.5 : 6 = 15 : 12 = 5 : 4
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which graph represents the solution of the system of inequalities
2x+6y < 6
x + 3y > 12
Suppose your parents agree to pay you
one cent today, two cents tomorrow (the first day after today), four cents the next day (second day after today), and so forth. Each time they double the amount they pay you. Write an equation expressing amount paid in terms of number of days after today. What kind of function is this? How much will they pay you the 30th day? Surprising?! Show that the amount paid today (0 days after today) agrees with the definition of zero exponents.
They will pay You $5368709.12 on the 30th day
What does the term "compound interest" mean?
Compound interest is when you receive interest on both your interest income and your savings.
You start with a one cent.
You have $0.01 x 2 the following day.
You have $0.01 x 2 x 2 the following day.
and so forth
You will have $0.01 x 2^n-1 on day n.
This means that on the 30th day, you have $0.01 x 2^29 = $5 368 709.12.
That is compound interest at work! It equates to daily payments of 100% interest. It immediately soars to inconceivable heights with even a penny as your initial investment!
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A furniture maker buys foam rubber x times per year. The delivery charge is a flat rate of $400 dollars per purchase regardless of how much is bought. The annual cost of storage is figured as $10,000/x, because the more frequent the purchase, the less it costs for storage. The annual cost is: C = 400x+10,000/x
A. Graph the function.
B. Find the number of purchases per year that minimizes the annual cost of delivery and storage.
Answer:
Should be B
Step-by-step explanation:
If f(x)=2x+1 and g(x)=x−5, find f(x)+g(x) to complete the polynomial
Answer:
[tex]\huge\boxed{\sf 3x -4}[/tex]
Step-by-step explanation:
Given functions:f(x) = 2x + 1g(x) = x - 5Add both equations.
f(x) + g(x):= 2x + 1 + x - 5
Combine like terms
= 2x + x + 1 - 5
= 3x - 4[tex]\rule[225]{225}{2}[/tex]
Answer:
f(x) + g(x) = 3x - 4
Step-by-step explanation:
The problem is,
→ f(x) + g(x)
Let's solve the problem,
→ f(x) + g(x)
→ (2x + 1) + (x - 5)
→ 2x + 1 + x - 5
→ (2x + x) + (1 - 5)
→ 3x +(-4)
→ 3x - 4
Hence, answer is 3x - 4.
Consider all positive integers that are multiples of 10 and are less than or equal to 200. What fraction of those integers are multiples of 15?.
3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.
Algebra: What Is It?Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to as variables because they lack fixed values. We frequently observe certain values that change in our day-to-day problems. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q.
Take into account all positive numbers that are multiples of 10 and have a value lower than or equal to 200.
Let x be the quantity of positive integers that are multiples of 10. The equation then becomes
10x ≤ 200
The value of the x will then be.
x ≤ 20
Below is a list of the numbers.
Set = 20 {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200}
The set that can be divided by 15 is
Set = 6 {30, 6,0 90, 120, 150, 180}
So, the percentage of those integers that are multiples of 15 will be
⇒ 6 / 20
⇒ 3/10
3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.
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At the start of 2014, Jim's house was worth £240,000.
The value of the house increased by 5% every year.
Work out the value of his house at the start of 2017.
Answer: $146,410
Step-by-step explanation:
The life in hours of a battery is known to be approximately normally distributed with standard deviation σ = 1. 25 hours. A random sample of 10 batteries has a mean life of x =40. 5hours. A. Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0. 5. B. What is the P-value for the test in part (a)? c. What is the β-error for the test in part (a) if the true mean life is 42 hours? d. What sample size would be required to ensure that β does not exceed 0. 10 if the true mean life is 44 hours? e. Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life
a)[tex]$z=\frac{40.5-40}{\frac{1.25}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
b) [tex]$p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029$[/tex]
c) [tex]$\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$[/tex]
d) We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_s\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The true mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
e) For this case we can calculate a one sided confidence interval given by:
[tex]$\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)$[/tex]
And if we replace we got:
[tex]$40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152$[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
What is null hypothesis?
In a scientific setting, a hypothesis (plural: hypotheses) is a testable claim about the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.
Part a
We have the following data given:
n=10 represent the sample size
[tex]$\bar{x}=40.5$[/tex] represent the sample mean
[tex]$\sigma=1.25$[/tex]represent the population deviation.
We want to test the following hypothesis:
Null: [tex]$\mu \leq 40$[/tex]
Alternative: [tex]$\mu > 40$[/tex]
The significance level provided was [tex]$\alpha=0.05$[/tex]
The statistic for this case since we have the population deviation is given by:[tex]z=\frac{\bar{x}-\mu}{\frac{-\mu}{\sqrt{n}}}$[/tex]
If we replace the values given we got:
[tex]$z=\frac{40.5-40}{\frac{1.24}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
Part b
The p value on this case is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
Part c
For this case the probability of type II error is defined as the probability of incorrectly retaining the null hypothesis and is defined like this:
[tex]\beta=P\left(Z < z_\alpha-\frac{(x-\mu) \sqrt{n}}{\sigma}\right)[/tex]
Where [tex]$z_\alpha=1.645$[/tex]represent the critical value for the test that accumulates 0.05 of the area on the right tail of the normal standard distribution.
The true mean on this case is assumed [tex]$\mu=42$[/tex], so then we can replace like this:
[tex]\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$$[/tex]
Part d
We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_\beta\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The ture mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
Part e
For this case we can calculate a one sided confidence interval given by:
[tex]\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)[/tex]
And if we replace we got:
[tex]40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
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in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
The American adults who believes in alien as per given 95% of confidence interval and the given sample surveyed is in the range of
( 0.657 , 0.783 ).
As given in the question,
Number of American adults surveyed (sample size) 'n' = 200
Percentage of people who believes in aliens 'p'= 72%
= 0.72
Percentage of people who don't believes in aliens ' 1 - p' = 1 - 72%
= 28%
= 0.28
95% Confidence interval that represents percent of people believes in aliens
Z - score of 95% confidence interval = ± 1.96
Margin of error = (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × 0.28)/ 200
= 1.96 ( 0.032)
= 0.06272
= 0.063
Lower limit = p - Margin of error
= 0.72 - 0.063
= 0.657
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.783
Therefore, for the given 95% confidence interval and sample size the Americans who believes in alien are in range of ( 0.657 , 0.783 ).
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I am very confused on what to do.Can someone help me?
Answer:
739 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
The given scenario can be modelled as an exponential equation.
Let y be the area the fire covers (in meters squared).
Let x by the time (in hours).
If the fire currently covers an area of 32 m² then the initial value, a, is 32.
If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).
Therefore:
a = 32b = 1.17Substitute the values of a and b into the exponential formula:
[tex]y=32(1.17)^x[/tex]
To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:
[tex]\implies y=32(1.17)^{20}[/tex]
[tex]\implies y=32(23.1055991...)[/tex]
[tex]\implies y=739.37917...[/tex]
Therefore, the area the fire will cover in 20 hours' time is 739 m² (nearest 1 m²).
27. Solve and graph
-2n-5≥1 or 5n + 7 > 2
28. S
The solution to the inequality expression -2n - 5 ≥ 1 or 5n + 7 > 2 is -1 > n ≥ -3
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
-2n-5≥1 or 5n + 7 > 2
So, we have
-2n - 5 ≥ 1 or 5n + 7 > 2
Evaluate the like terms
So, we have the following representation
-2n ≥ 6 or 5n > -5
Divide both sides by the coefficient of n
This gives
n ≤ -3 or n > -1
Combine the expression
-1 > n ≥ -3
Hence. the solution is -1 > n ≥ -3
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