The scarf is $20 without tax.
The scarf is 20% off of 25, 5 is 20% of 25 so all you have to do is 25 - 5 to get your answer.
25 - 5 = 20
The sale price of the scarf , not including the tax is $20.00.
What is sale price?A sale price is the discounted price at which goods or services are being sold.
Formula for finding the sale pricesale price = original price - discount price
According to the given question,
the original price of the scarf is $25.00
discount price = 20%of original price
⇒ discount price =[tex]\frac{20}{100}[/tex]×[tex]25[/tex]
⇒discount price = $5.00
Therefore,
sale price of scarf = $25.00-$5.00
Sale price of scarf = $20.00
Hence, the sale price of the scarf, not including tax is $20.00
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Convert 30 to radians. Leave answer as a reduced fraction in terms of pi
Answer:
[tex]\frac{\pi }{6}[/tex]
Step-by-step explanation:
[tex]\frac{\pi}{180}[/tex] = [tex]\frac{x}{30}[/tex]
180x = 30π
x = [tex]\frac{30\pi }{180}[/tex]
x = [tex]\frac{3\pi }{18}[/tex]
x= [tex]\frac{\pi}{6}[/tex]
Toby wants a paintbrush that costs $2.70, a set of paints that costs $15.45, and an easel that costs $22.90. Toby already has $1.00. How much more money does Toby need?
Answer:
$40.05
Step-by-step explanation:
You would add up 2.70+15.45+22.90 then, subtract the total by 1.00
Answer:
40.05
Step-by-step explanation:
you basically add up all the prices then subtract the 1 dollar the he has and u get ur answer
The scale on a map reads 1/2 inch = 75 miles. If the distance between two cities on the map is 3 and 1/4 inches, find the actual distance between the cities
Answer:
487.5 miles
Step-by-step explanation:
The actual distance between the cities is 487.5 miles.
What is Proportion?Two or more ratios made to be equivalent to each other is termed as the method of proportion.
That is, if 'a' related to 'b' is proportional to 'p' related to 'q', then,
a : b : : p : q
⇒ a/b = p/q
⇒ aq = bp
Here we have the scale on a map reads 1/2 inch as 75 miles.
We have to find the actual distance of two cities if the distance between the cities in the map is 3 and 1/4 inches.
3 and 1/4 inches = (3 × 4 + 1) / 4 = 13/4 inches.
Let x be the actual distance between the cities.
Using proportion,
1/2 : 75 : : 13/4 : x
[tex]\frac{1/2}{75}[/tex] = [tex]\frac{13/4}{x}[/tex]
1/2 × x = 13/4 × 75
1/2 × x = 243.75
x = 487.5
Hence the actual distance between the cities is 487.5 miles.
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Country A has a growth rate of 4.9% per year. The population is currently 4 comma 151,000, and the land area of Country A is 14,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answer:
There will be one person on 1 square yard of land after 1,892,147.588 years.
Step-by-step explanation:
Continuous exponential growth formula:
[tex]P(t)=Pe^{rt}[/tex]
P(t)= Population after t years.
P= Initial population
r=rate of growth.
t= time in year
Given that,
Growth rate of country A (r)= 4.9% per year=0.049 per year.
Initial population (P)= 151,000.
Land area of country area= 14,000,000,000 square yards.
There will be one person on one square yard of land.
So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.
P(t)=14,000,000,000 person
[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]
[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]
[tex]\Rightarrow t}=1,892,147.588[/tex] years
There will be one person for every square yard of land after 1,892,147.588 years.
Find the volume of this prism
Answer:
840cm cubed
Step-by-step explanation:
720+120
The table displays the scores of students on a recent exam. Find
the mean of the scores to the nearest 10th.
Score Number of Students
80
85
6
90
95
100
6
8
Summary:
pls I need a summary asap
The mean is 59
Add all the scores together, then divide by the number of test scores
The mean of the scores to the nearest 10th Score Number of Students is 59.
We have given a data,
80,85,6,90,95,100,6,8
What is the meaning of mean?
Mean is the adding all the scores together, then divide by the number of test scores.
So we have given a data,
80,85,6,90,95,100,6,8
80+85+6+90+95+100+6+8=470
The number of of test scores=8
[tex]mean=\frac{470}{8}=58.75[/tex]
Mean≈59
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A tree grows 6 feet per year. Which rates are equivalent to 6 feet per year? Select all that apply. A. 2 inches per year B. 18 inches per year C. 12 feet in 4 years D. 72 inches per year E. 2 yards per year F.18 feet in 3 years
Answer:
D is correct E is correct F is correct
Step-by-step explanation:
72/12=6 ft per year
2 yards= 6 ft per year
18/3=6 ft per year
The equivalent rates to 6 feet per year are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
Explanation:The student is asking about equivalent rates. To determine which rates are equivalent to 6 feet per year, we need to compare each option against the given rate. The conversion factors needed for this problem are:
1 foot = 12 inches1 yard = 3 feetOption A: 2 inches per year is not equivalent to 6 feet per year.
Option B: 18 inches per year is equivalent to 6 feet per year because 18 inches is 1.5 feet, and thus, 1.5 feet multiplied by 4 would give us 6 feet in 4 years.
Option C: 12 feet in 4 years is equivalent to 6 feet per year because dividing 12 feet by 4 years gives us 3 feet per year, which is half of the given rate.
Option D: 72 inches per year is equivalent to 6 feet per year because 72 divided by 12 is 6.
Option E: 2 yards per year is equivalent to 6 feet per year because 2 multiplied by 3 is 6.
Option F: 18 feet in 3 years is equivalent to 6 feet per year because dividing 18 feet by 3 years gives us 6 feet per year.
Thus, the equivalent rates to 6 feet per year from the options given are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.
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Given that segment US and segment RU are equidistant from the center, determine the value of m in the circle below.
Leave your answer in fraction form.
m = _____
Answer:
7/4
Step-by-step explanation:
We know that US = RU, so we can just set those expressions equal to each other.
US = 3m + 2
RU = -m + 9
US = RU ⇒ 3m + 2 = -m + 9 ⇒ 4m = 7 ⇒ m = 7/4
Hope this helps!
Answer:
7/4 or 1¾
Step-by-step explanation:
Since US = UR
3m + 2 = -m + 9
4m = 7
m = 7/4
m = 1¾
Two cards are selected from a deck of cards numbered from 1 to 10. Once a card is selected, it is not replaced. What is P(two even numbers)? Write the answer as a fraction in simplest form.
Include Explanation please
10 cards would have 5 even cards.
First pick would be 5/10 = 1/2 probability of getting an even card.
Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9
The probability of both happening would be Found by multiplying the two probability’s together:
1/2 x 4/9 = 4/18 = 2/9
Two cards are selected from a deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] and once a card is selected, it is not replaced, then Probability of two even numbers is [tex]\frac{2}{9}[/tex] .
What is Probability ?Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
We have,
Let [tex]E[/tex] be event of drawing cards.
A deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] .
i.e. total number of possible outcomes [tex]=10[/tex]
And,
Even numbers from [tex]1[/tex] to [tex]10[/tex] are [tex]2,4,6,8,10[/tex]
[tex]=10[/tex]
Total even numbers are [tex]5[/tex].
So,
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
Probability[tex](E)[/tex] [tex]=\frac{5}{10}*\frac{4}{9}[/tex]
[tex]=\frac{2}{9}[/tex]
So, the Probability of two even numbers is [tex]\frac{2}{9}[/tex] , as there are total [tex]10[/tex] cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only [tex]9[/tex] cards, so when next time we select a card then Probability will be from those [tex]9[/tex] cards.
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7. A travel website wants to gauge the perceived quality of a major airport. The maximum possible rating is 10, and the results of a random sample of 50 travelers can be found in the Airport.xlsx file. Develop a 95% confidence interval estimate of the population mean rating for the airport based upon this data.
Answer:
The 95% confidence interval has Minimum = 6.053 and Maximum = 7.467
Step-by-step explanation:
Here we have
Data as
1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10
The sum is 338
∴ Mean, [tex]\bar x[/tex] = 6.76, Standard Deviation, s = 2.55
Sample size, n = 50
For a 95% confidence interval, we have
[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Where z is;
z at 95% z = [tex]\pm[/tex]1.96
Therefore, we have
95% confidence interval as Minimum = 6.053 to Maximum = 7.467.
A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Which statement is true?
Both data sets have a gap.
Both data sets have the same median.
Both plots have the same mode.
Both data sets have the same number of data points.
Answer:
D. Both data sets have the same number of data points.
Step-by-step explanation:
Answer:
itd d on egeunity
Step-by-step explanation:
If anyone could answer these
help pls!!!!!!!!!!! i don't know how to attempt
Answer:16
Step-by-step explanation:AC is half of ED
A fountain in the park has two circular pools that are the same size. What is the total area of the pools if the radius is 3 yards? Use 3.14 for Pi and round the approximate area to the nearest tenth, if necessary. Check all that apply.
Answer:
56.6 square yards.
Step-by-step explanation:
Given:
A fountain in the park has two circular pools that are the same size.
Question asked:
What is the total area of the pools if the radius is 3 yards ?
Solution:
First of all we will calculate the area of a circular pool.
As we know:
[tex]Area\ of\ circle=\pi r^{2}[/tex]
[tex]=\frac{22}{7} \times(3)^{2} \\ \\ =\frac{22}{7}\times9\\ \\ =\frac{198}{7} \\ \\ =28.28\ square\ yards[/tex]
Area of circular pool nearest tenth = 28.3 square yards
Now, as given that both pools are of same size.
Total area of the pools = 28.3 square yards + 28.3 square yards
= 56.6 square yards.
Thus, the total area of the pools are 56.6 square yards.
Answer:
ur answer is 56.5 and 18
Step-by-step explanation:
vlad a economiit o suma de bani.A cheltuit 20 lei pentru felicitari apoi tatal i-a dublat suma. A cheltuit 40 lei pe martioare apoi bunicul i-a mai dat 50 lei. A cumparat un buchet de flori pentru mama lui pe care a dat 30 lei apoi tatal i-a dublat suma.La final, vlad a contatat ca mai are 280 lei
He had saved 320 initially
Step-by-step explanation:
Let the amount he saved be 'a'
Amount spent = 20 + 40 + 30
= 90
His grand father gave 50
At the end he has 280
280 = a - 90 +50
a = 280 -50 +90
= 320
He had saved 320 initially
I will give you all my points and mark you the brainliest! Please help
Answer and Step-by-step explanation:
Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:
A/B = 5/3 ⇒ 90/B = 5/3 ⇒ 5B = 270 ⇒ B = 54
So, we know that angle B is 54 degrees.
Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:
90 + 54 + X + Y = 360
X + Y = 216 degrees
We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:
X/Y = 1/3 ⇒ Y = 3X
Substitute 3X in for Y in X + Y = 216:
X + 3X = 216
4X = 216
X = 54
Thus, we see that both angles B and X equal 54, so B = X.
Hope this helps!
Answer:
[tex]\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b\\[/tex]
Consider the graph below.
Which of the following is the function represented
by the graph?
y=(x+3)-5
2
*5
*
x
+
5
DONE
ONANODOTTI
Answer:
y=−259x+8
Step-by-step explanation:
i think this might be the answer but not sure
Answer:D
Step-by-step explanation:
READ CAREFULLY! :)
John is putting a fence around his garden that is shaped like a half circle and a rectangle
Answer:
46 feet
Step-by-step explanation:
Perimeter of rectangle needed =
[tex]14+14+7= 35\\[/tex]
Half of the circumference of a circle needed =
[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]
Total perimeter needed =
[tex]35 + 11=46[/tex]
Answer:
46 ft
Step-by-step explanation:
John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft
He also needs to put a fence along the half circle:
C (circumference) = 2×π×r = π×d
⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft
Together: 14 + 7 + 14 + 11 = 46 ft
Find the slope of the line through (–9, –10) and (–2, –5). A. –five-sevenths B. seven-fifths C. five-sevenths D. –negative seven-fifths (please help much aprecciated)
Answer:
C 5/7
Step-by-step explanation:
We can find the slope of a line using
m = (y2-y1)/(x2-x1)
= (-5 - -10) /(-2 - -9)
= (-5 +10)/(-2+9)
5/7
An isosceles triangle has an angle that measures 70°. Which other angles could be in that isosceles triangle? Choose all that apply. 40 55 70 1-
Answer:
This depends on the way the triangle
Step-by-step explanation:
Anyway angles that apply includes: 55 and 70
Select the expression that represents the additive inverse of 6. A. 1/6 B. -1/6 C. -(-6) D. -6
Answer:
D. -6.
Step-by-step explanation:
The inverse is the number when added to 6 results in 0.
So it is 0 - 6 = -6. (6 + -6 = 0)
Answer:
C
Step-by-step explanation: I big brain
Write in slope-intercept form an equation of the line that passes through the given points.
(6,8),(3,−9)
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptSlope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points that fall on the lineSolving the Question
We're given:
The line passes through (6,8), (3,-9)1) First, find the slope using the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{8-(-9)}{6-3}\\\\m=\dfrac{8+9}{6-3}\\\\m=\dfrac{17}{3}[/tex]
Therefore, the slope of this line (m) is [tex]\dfrac{17}{3}[/tex]. Plug this into slope-intercept form:
[tex]y=\dfrac{17}{3}x+b[/tex]
2) Now, find the y-intercept by using one of the given points:
[tex]y=\dfrac{17}{3}x+b[/tex]
Plug in one of the given points as (x,y):
[tex]8=\dfrac{17}{3}(6)+b\\\\8=34+b\\b=8-34\\b=-26[/tex]
Therefore, the y-intercept of the line is -26. Plug this into our original equation:
[tex]y=\dfrac{17}{3}x+b\\\\y=\dfrac{17}{3}x-26[/tex]
Answer[tex]y=\dfrac{17}{3}x-26[/tex]
To write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to determine the slope first and then use one of the points to find the y-intercept.
Step 1: Find the slope (m)
The slope of a line passing through two points, (x1, y1) and (x2, y2), can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given our points (6, 8) and (3, -9), we can substitute them into our formula:
x1 = 6, y1 = 8
x2 = 3, y2 = -9
m = (-9 - 8) / (3 - 6)
m = (-17) / (-3)
m = 17/3
m = 5.666666666666667 (rounded to 5.67 for simplicity)
Step 2: Find the y-intercept (b) using one of the points
Next, we can use the point-slope form of a line equation, which is:
y - y1 = m(x - x1)
We will use the first point (6, 8) and the slope m = 5.67 that we calculated.
Substitute the point and the slope into the point-slope form equation:
8 - y1 = 5.67(6 - x1)
Since we know that (x1, y1) is (6, 8), this simplifies to:
8 - 8 = 5.67(6 - 6)
b = 8 - 5.67(6)
Now, we do the multiplication and subtraction:
b = 8 - 34.02
b = -26
So now we have our y-intercept, which is b = -26.
Step 3: Write the equation in slope-intercept form
Now that we have both m and b, we can write the equation of the line:
y = mx + b
Substitute m and b into the equation:
y = 5.67x - 26
This is the equation of the line in slope-intercept form that passes through the points (6, 8) and (3, -9). For exact calculations, you may want to use the more precise value of the slope (5.666666666666667) in the equation:
y = 5.666666666666667x - 26
By doing so, we obtain a more accurate representation of the line's equation.
In a recent survey of monetary donations made by 489 college graduates, the following information was obtained. 95 has donated to a political campaign, 76 had donated to assist medical research, 133 had donated to preserve the environment, 25 had donated to all three, 38 had donated to a political campaign and to medical research, 46 had donated to medical research and to preserve the environment, and 54 donated to a political campaign and to preserve the environment.
(a) How many college graduates donated to none of the listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?
Answer:
Step-by-step explanation:
The Venn diagram representing this situation is shown in the attached photo.
P represents the set of college graduates that donated to a political campaign.
M represents the set of college graduates that donated to assist medical research.
E represents the set of college graduates that donated to preserve the environment.
From the diagram,
The number of college graduates that donated to all three is 25
The number of college graduates that donated to a political campaign and medical research only is
38 - 25 = 13
The number of college graduates that donated to a political campaign and preserve the environment only is
54 - 25 = 29
The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21
The number of college graduates that donated to a political campaign only is
95 - (29 + 25 + 13) = 28
The number of college graduates that donated to medical research only is
76 - (13 + 25 + 21) = 17
The number of college graduates that donated to preserve the environment only is
133 - (29 + 25 + 21) = 58
a) the number of college graduates that donated to none is
489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)
= 298 college graduates
b) the number of college graduates that donated to exactly one of the three listed causes is
28 + 17 + 58 = 103
The percentage would be
103/489 × 100 = 21.1%
This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
Answer:
Δπ Min = -0.0709
Δπ Max = -0.0535
Step-by-step explanation:
Here we have
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Where:
[tex]{\hat{p_{1}}[/tex] = 13% = 0.13
[tex]\hat p_{2}[/tex] = 14% = 0.14
n₁ = 163
n₂ = 160
Therefore, we have;
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Plugging the values gives
z = -0.263
CI 90% = critical z = [tex]\pm[/tex]1.644
The minimum difference in true proportion = -0.0709
The maximum difference in true proportion = 0.0535.
A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees. What is the measure of Arc A U? 44° 50° 64° 92
The angle subtended by an arc [tex]\widehat{AU}[/tex] is given by the angle ∠UOA.
Response:
[tex]\widehat{AU}[/tex] is 50°Which methods can be used to find [tex]\widehat{AU}[/tex] ?According to circle theorem, we have;
Angle at the center = 2 × Angle at the circumference∠QUA = 111°
Therefore;
[tex]m\widehat{QDA}[/tex] = 2 × ∠QUA
[tex]m\widehat{QDA}[/tex] = 2 × 111° = 222°
Which gives;
Angle ∠QOA = [tex]m\widehat{QUA}[/tex] = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA by angle addition property
Which gives;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
[tex]\widehat{AU}[/tex] = ∠UOA = 50°Learn more about more circle theorems here:
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Evaluate 4 - 2f when f = 1.
Answer:
2
Step-by-step explanation:
4 -2f
Let f =1
4 - 2(1)
Multiply and divide first
4 -2
2
What is the next term of the geometric sequence?
72,36, 18,
Answer:
9
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first
36/72 = 1/2
To find the next term, take the last term and multiply by the common ratio
18*1/2 = 9
Answer:
9.
Step-by-step explanation:
The common ratio = 36/72 = 18/36 = 1/2.
So the next term is 18 * 1/2 = 9.
y= 0.216 x + 32.575
what is the slope
Given:
The given equation of the line is [tex]y=0.216x+32.575[/tex]
We need to determine the slope of the equation.
Slope:
Let us determine the slope of the equation.
The general form of the equation of the line is given by
[tex]y=mx+b[/tex]
where m is the slope of the equation and b is the y - intercept.
Now, we shall compare the general form of the equation of the line with the given equation, we have;
[tex]m= 0.216[/tex] and [tex]b=32.575[/tex]
Thus, the slope of the equation of the line is [tex]m= 0.216[/tex]
the slope is 0.216
And just in case you need it the y-intercept is 32.575
I hope this was helpful :)
Complete the division. The remainder is 0. The quotient is
X^2 - X - 12
-X^2 + x + 12
12x^2 - X-1
12x^2 + x + 1
Answer:
The first option....x^2-x-12
Step-by-step explanation:
Answer: x^2-x-12
Step-by-step explanation: correct answer
A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the width, find the dimensions of the pool.
Answer:
[tex]x \approx 21.080\,ft[/tex], [tex]y = 29.080\,ft[/tex]
Step-by-step explanation:
The total area of the pool and the walkway is:
[tex](x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}[/tex]
[tex](x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}[/tex]
[tex]x^{2} + 20\cdot x - 866\,ft^{2} = 0[/tex]
The roots of the second-order polynomial is:
[tex]x_{1} \approx 21.080\,ft[/tex] and [tex]x_{2} \approx -41.081\,ft[/tex]
The only possible root is:
[tex]x \approx 21.080\,ft[/tex]
The other dimension of the pool is:
[tex]y = x + 8\,ft[/tex]
[tex]y = 21.080\,ft + 8\,ft[/tex]
[tex]y = 29.080\,ft[/tex]