The exponential equation used to represent the population of the town is given by y = 5655(1.026)ˣ
An exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population remaining after x years.
The population grow at the rate of 2.6% annually. Hence:
b = 100% + 2.6% = 1.026
There are initially 5655 people, hence a = 5655.
The equation becomes:
y = 5655(1.026)ˣ
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Help I will give brainliest
the inequality is 8 (w+18) ≤ 19
Answer: -15.625
Step-by-step explanation:
Let w represent the number:
8 (w + 18) ≤ 19
[tex]\frac{8\left(w+18\right)}{8}\le \frac{19}{8}[/tex]
[tex]w+18\le \frac{19}{8}[/tex]
[tex]w+18-18\le \frac{19}{8}-18[/tex]
[tex]w\le \:-\frac{125}{8}[/tex]
-125/8 or -15.625
Check:
[tex]8\left(-15.625+18\right)\le \:19[/tex]
[tex]8\cdot \:2.375 \leq 19[/tex]
[tex]19 \leq 19[/tex]
Therefore, the number is -15.625
Can someone help me please
Answer:
31.25
Step-by-step explanation:
Divide 250 by 8=31.25
pls help!ill give brainlest to the smartest!
(5 + 13 + 21 + ......... + 18) = ?
Correction:
5+13+21+...+181
First term = 5
Common difference = 13-5 = 8
Last term = an = 181
⇛a+(n-1)d = 181
⇛5+(n-1)(8) = 181
⇛ 5+8n-8 = 181
⇛ 8n-3 = 181
⇛ 8n = 181+3
⇛ 8n = 184
⇛n = 184/8
⇛ n = 23
Sum of the first n terms = Sn = (n/2)(a+an)
Sum of 23 terms = S 23
⇛(23/2)(5+181)
⇛ (23/2)(186)
⇛23×93
⇛2139
A pine tree measured 40 1 / 2 feet tall. Over the next 7 1 / 2 years, it grew to a height of 57 feet. During the 7 1/2 years, what was the average yearly growth rate of the height of the tree?
The average yearly growth rate of the height of the tree is 2 1/3 feet
Given:
original height of the pine tree = 40 1/2 feet
Height in next 7 1/2 years = 57 feet
Change in height = Height in next 7 1/2 years - original height of the pine tree
= 57 height - 40 1/2 feet
= 17 1/2 feet
Average growth rate yearly = Change in height / number of years
= 17 1/2 feet ÷ 7 1/2 years
= 35/2 ÷ 15/2
= 35/2 × 2/15
= (35 × 2) / (2 × 15)
= 70/30
= 2 10/30
= 2 1/3 feet
Therefore, the average yearly growth rate of the height of the tree is 2 1/3 feet
Learn more about fraction:
https://brainly.com/question/1622425
6x + 3 > 26
How do I solve the math problem above
Answer:
x > 23/6
Step-by-step explanation:
Solve this one the same way you would a 2-step linear equation.
6x +3 > 26 . . . . . given
6x > 23 . . . . . . . . subtract the unwanted constant from both sides (step 1)
x > 23/6 . . . . . . . .divide both sides by the coefficient of x (step 2)
__
Additional comment
If the coefficient of the variable in a 2-step linear inequality is negative, then the inequality symbol must be reversed when dividing by that negative number.
Find an angle betwwen 0 and 2pie that is coterminal with -19pie/10
Answer:
π/10
Step-by-step explanation:
α=-19π/10=-19π/10+2π=(-19π+20π)/10=π/10
What is 26% as a fraction in simplest form?
A. 26/100
B. 26/10
C. 6/25
D. 13/50
Answer:
it'd be d: 13/50 !!
Answer:
D. 13/50
Step-by-step explanation:
0.26 ⇔ 26/100 ⇔ 13/50
A swim teacher sells lesson packages. The best deal has the highest ratio of lessons to total cost.
Swim Lesson Packages
Number of Total Cost
Lessons
1
$10
5
$40
10
$80
15
$80
Which package is the best deal?
0 1 lesson for $10
O 5 lessons for $40
ОООО
10 lessons for $80
O 15 lessons for $80
Answer:
15 lessons for $ 80
Step-by-step explanation:
In case 1
Cost of 1 lesson = $10
In case 2
Cost of 1 lesson = 40/5 = $8
In case 3
Cost of 1 lesson = 80/10 = $8
In case 4
Cost of 1 lesson = 80/15 = $ 5.33
Hence,
The best deal is case 4 i.e 15 lessons for $ 80
12/14 , 15/, 19/24 which one is greater?
Step-by-step explanation:
12/14= 85.7143% 19/24= 79.1667%
Solve for x in the following inequality: 3(-2x - 4) > 18
Answer:
x < -5
Step-by-step explanation:
3 ( -2x - 4 ) > 18
→ Expand the brackets
-6x - 12 > 18
→ Add 12 to both sides
-6x > 30
→ Divide both sides by -6
x < -5
Answer:
[tex]\boxed {\boxed {\sf x< -5}}[/tex]
Step-by-step explanation:
We are asked to solve the following inequality for x.
[tex]3(-2x-4) > 18[/tex]
Solve for x by isolating it and performing the inverse operations.
3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.
[tex]\frac {3(-2x-4)}{3} > \frac{18}{3}[/tex]
[tex](-2x-4) > \frac{18}{3}[/tex]
[tex]-2x-4 > 6[/tex]
4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.
[tex]-2x-4+4 > 6+4 \\[/tex]
[tex]-2x > 10[/tex]
x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.
[tex]\frac {-2x}{-2} > \frac {10}{-2}[/tex]
[tex]x> \frac {10}{-2}[/tex]
Since we divided by a negative number, the inequality sign must be flipped.
[tex]x< \frac{10}{-2}[/tex]
[tex]x < -5[/tex]
What is the equation of this line?
y=6x−14
y=14x−6
y=6x−4
y=4x−6
Hope it helps.
Don't forget to click the Brainliest button if you like my answer and if you have any query, feel free to ask in the comment section.
What's The Interest Rate?
I = $200
P = $800
T = 24 months
Which of the following is most likely the next step in the series?
Answer:
The answer is C
Step-by-step explanation:
(I'm not completely sure)
Plz Help 100 points and brainlyest if correct
Use the chart to answer the questions.
Which triangle has vertices (–3, –5), (7, 4), (0, 4)?
Answer:
see attached
Step-by-step explanation:
The one that matches the triangle shown in the attachment has the given vertices.
The length of the opposite side of a right triangle is 2cm longer than the length of the adjacent side. The hypotenuse is 4cm longer than the adjacent side. Use a quadratic equation to determine the perimeter of the triangle.
PLEASE HELP
Answer:
Step-by-step explanation:
Let x be the adjacent side length in cm
opposite side is x + 2 cm
hypotenuse is x + 4 cm
x² + (x + 2)² = (x + 4)²
x² + (x² + 4x + 4) = (x² + 8x + 16)
x² - 4x - 12 = 0
(x - 6)(x + 2) = 0
so either
x - 6 = 0 x = 6
or
x + 2 = 0 x = -2
positive answer is x = 6 as negative length does not make sense
opposite side is 6 + 2 = 8
hypotenuse is 6 + 4 = 10
perimeter is 6 + 8 + 10 = 24 cm
1. A FoodPanda rider believes that his tips from various customers has a slightly right skewness with a mean of RM10 and a standard deviation of RM2.50. a. Calculate the mean and standard deviation of the sampling distribution of this tips for a sample of 25 customers. Describe the shape of its sampling distribution. [4 marks]
Using the Central Limit Theorem, it is found that:
The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, if the sample size is at least 30, the shape is approximately normal, otherwise it still is skewed.In this problem, the mean is of 10 and the standard deviation is of 2.50, hence [tex]\mu = 10, \sigma = 2.5[/tex]
Sample of 25, hence [tex]n = 25, s = \frac{2.5}{\sqrt{25}} = 0.5[/tex]
Since the underlying distribution is skewed and the sample size is less than 30, the shape of the sampling distribution is slightly right skewed.
The sampling distribution is slightly right skewed, with mean of RM 10 and standard deviation of RM 0.5.
A similar problem is given at https://brainly.com/question/25817309
A pipe that is 165 feet long is cut into three parts whose lengths are in the ratio 2 : 5 : 8. Find the length of the longest piece. Longest piece: 2 feet
Answer:
88 ft
Step-by-step explanation:
Let's say the shortest piece has length 2x, so the medium piece has length 5x and the longest piece has length 8x. Added together, they equal 165, so
2x + 5x + 8x = 165
15x = 165
divide both sides by 15 to isolate x
x = 11
8x = longest piece = 88 ft
3. The length of a rectangle is 20 meters long and the width is 15 meters. Find the
ratio of the length to the width of the rectangle. Then simplify the ratio.
Answer:
4/3 1.333 1 1/3
Step-by-step explanation:
How many days are in 52 weeks?
Answer:
A year but -1.
Step-by-step explanation:
52x7=364.
Hope this helps!
Answer:
there are 364 days in 52 weeks.
Step-by-step explanation:
To find out how many days are in 52 weeks you have to multiply the amount of days there are in a week by 52, there are 7 days in a week and 7 times 52 is 364 so the answer is 364
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answer:
Step-by-step explanation:
When it's clear, the easiest way to do the problem is to used the x and y intercepts.
This question is one of the clear one.
The x intercept is 2,0
The y intercept is 0,1
You want the slope.
m = (y2 - y1)/(x2 - x1)
y2 = 1
y1 = 0
x2 = 0
x1 = 2
m = (1 - 0)/(0 - 2)
m = 1 / -2
m = -1/2
In this case the slope and gradient have the same value -- - 1/2 or - 0.5
how do i solve for this?
Step-by-step explanation:
1. KOL = 90
2.KLO = 25
3.NL= 30
4.KL = 17
workings
1.for angle
KOL =90 : the diagonals of rhombus are perpendicular to each other
2. angle LKO + angle KLO + angle KOL =180 : angles of triangle are supplementary(add to 180)
65+ KLO + 90 =180
KLO +155
KLO = 180 - 155
KLO = 25
3. NL = NO + LO: diagonals of the rhombus bisect each other
NL = 15 +15
NL = 30
4. Cos 25 = 15/KL
multiply by KL on both sides
KL × Cos 25 =15
divide by cos 25 on both sides
KL = 17
hi so my teacher gave me this and i am not sure if i did it right, this is what i put for the first Question
degree = 3
leading coefficient = 1
and the it is the arrows are going up/down so its a odd degree
and i put that the answer is d i did the rest like this please tell me where i went wrong/if i did
Answer:
First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:❤
How can you simplify this expression?
Answer:
add the exponents
Step-by-step explanation:
PLEASE HELP I WILL MARK YOU BRAINLEST!!!
please read the question on the photo and these are the choices bellow!!
A-translation, reflection
B- rotation, reflection
C-reflection, rotation
D-rotation, translation
Two handymen can do a home repair in 2 hours if they work together. One of the men takes 3 hours more than the other man to finish the job by himself. How long does it take for each handyman to do the home repair individually?
Using the together rate, it is found that:
It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.The together rate is the sum of each separate rate.
In this problem, we have that:
The together rate is of [tex]\frac{1}{2}[/tex].The first man takes x hours, hence his rate is of [tex]\frac{1}{x}[/tex]The second man takes x + 3 hours, hence his rate is of [tex]\frac{1}{x + 3}[/tex]Applying the together rate:
[tex]\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}[/tex]
[tex]\frac{x + 3 + x}{x(x + 3)} = \frac{1}{2}[/tex]
[tex]4x + 6 = x^2 + 3x[/tex]
[tex]x^2 - x - 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -1, c = -6[/tex], hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-6) = 25[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{25}}{2} = 3[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{25}}{2} = -2[/tex]
We are interested into the positive root, then [tex]x = 3[/tex], [tex]x + 3 = 6[/tex], which means that:
It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.You can learn more about the together rate at https://brainly.com/question/25159431
. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers (based on data from the highway Loss Data Institute). Using a 0.01 significance level, you need to test the claim that the air-bag hospitalization rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts. What conclusion should you make
Answer:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
0.00885... < 0.01
The test statistic of 46 is significant
There is sufficient evidence to reject H₀ and accept H₁
Air bags are more effective as protection than safety belts
Step-by-step explanation:
821 crashes
46 hospitalisations where car has air bags
7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts
α = 0.01 or 1% ← level of significance
One-tailed test
We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;
The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;
So we are testing if hospitalisations in cars with air bags is less than 0.078;
So, firstly:
Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags
X~B(821, 0.078)
Null hypothesis (H₀): p = 0.078
Alternative hypothesis (H₁): p < 0.078
According to the information, we reject H₀ if:
P(X ≤ 46 | X~B(821, 0.078)) < 0.01
To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;
If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:
[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]
You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
Now, we need to consider if the condition for rejecting H₀ is met and recognise that:
0.00885... < 0.01
There is sufficient evidence to reject H₀ and accept H₁.
To explain what this means:
The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;
In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.
Find the slope of the line that passes through (19, 72) and (20, -1).
Step-by-step explanation:
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Evaluating Expressions with Real Numbers - Item 8069
Which statement best explains why this expression is equal to 1?
0.54 +0.27
0.24 + 0.57
Answer:
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. For example 0.54+0.27 and 0.24 +0.57, If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
hope this helps.