Answer:
f(8) = 216
Step-by-step explanation:
f(x) = (2x - 10)³
So f(8) = (2(8) - 10)³
==> f(8) = (16 - 10)³
==> f(8) = (6)³
==> f(8) = 216
Which of the following pairs of equations has exactly the same solution?(1 point)
−3.2x=0.64 and x/4 =−0.05
⅜ x=1 and ⅓ x=⅛
x/3.2 =1.8 and 1.8x=3.2
− 3/4 x=5/2 and 5/2 x=− 3/4
Answer: The first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05, have exactly the same solution. In both of these equations, the value of x comes out as -0.2.
Step-by-step explanation: Simplifying the first set of equations, we get:[tex]-3.2x=0.64[/tex]
[tex]x=0.64/-3.2[/tex]
x=-0.2
[tex]x/4=-0.05[/tex]
[tex]x=-0.05*4[/tex]
x=-0.2
Simplifying the second set of equations, we get:
[tex]3/8x=1[/tex]
[tex]x=8/3[/tex]
x=2.66
[tex]1/3x=1/8[/tex]
[tex]x=1/8*3[/tex]
x=0.375
Simplifying the third set of equations, we get:
[tex]x/3.2=1.8[/tex]
[tex]x=1.8*3.2[/tex]
x=5.76
[tex]1.8x=3.2[/tex]
[tex]x=3.2/1.8[/tex]
x=1.77
Simplifying the fourth set of equations, we get:
[tex]-3/4x=5/2[/tex]
[tex]x=5/2*-4/3[/tex]
x=-3.33
[tex]5/2x=-3/4[/tex]
[tex]x=-3/4*2/5[/tex]
x=-0.3
Therefore, the first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05 have exactly the same solution.
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PLEASE HELP ME WITH THESE 2 QUESTIONS
a sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. assume the population standard deviation is 6.83. what sample size (i.e., how many) would you need to have so that a 95% confidence interval will have a margin of error of 1.0?
Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:
Sample mean of [tex]x = 12.7[/tex]
Population standard deviation of [tex]\sigma = 6.37[/tex]
Sample size of .n = 50
The margin of error is:
[tex]M = z \frac{\sigma }{\sqrt{n} }[/tex]
In which z is the critical value.
We have to find the critical value, which is z with a p-value of [tex]\frac{1+\alpha }{2}[/tex] , in which [tex]\alpha[/tex] is the confidence level.
In this problem, , thus, z with a p-value of , which means that it is z = 1.96.
Then:
[tex]M= 1.96\frac{6.37}{\sqrt{50} } = 1.77[/tex]
The confidence interval is the sample mean plus/minutes the margin of error, hence:
x- M = 12.17 - 1.77 =10.4
x+M = 12.17 + 1.77 = 13.94
The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
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y=-2/7x-7 in standard form
Answer:
Write in standard form.
2x+7y=−49
Step-by-step explanation:
Question 9 Which of the following distributions has a mean that varies? I. The population distribution II. The distribution of sample data III. The sampling distribution of the sample mean
O ll only
O IIl only
O I only
O all three distributions
O II and III
II and III only distributions has a mean that varies
The mean of a distribution is a measure of the central tendency of the data, and it can vary depending on the sample being analyzed.
For the population distribution, the mean is a fixed value that is calculated using all of the data in the population. The mean of the population distribution does not vary.
For the distribution of sample data, the mean is calculated using the data in the sample. If you take different samples from the same population, the mean of each sample will be different, so the mean of the distribution of sample data varies.
For the sampling distribution of the sample mean, the mean is calculated using the means of multiple samples. The mean of the sampling distribution is known as the population mean. As with the distribution of sample data, the mean of the sampling distribution varies depending on the samples that are used to calculate it.
Therefore, the mean of the distribution of sample data and the sampling distribution of the sample mean both vary, while the mean of the population distribution does not vary.
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8 men make 10 cars in a day. How many cars do 20 men complete in day?
Answer: 25 cars
Step-by-step explanation:
Take 10 divided by 8 = 1.25 car per men
Then take 1.25 times 20 = 25 cars
Supply the missing information for each of the right triangles described below. In each example, θ = angle, O = opposite side, A = adjacent side, and H = hypotenuse.
Choice 'A' H = 54.93
Choice 'B' H ≈ 5.493
Choice 'C' H = 5.493
Choice 'D' H ≈ 54.93
Each right triangle has a missing value of 1.9096 where = angle, O = opposing side, A = adjacent side, and H = hypotenuse.
what is right triangle ?A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangle triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
given,
1.9096 is what's lacking.
SOH CAH TOA's identification would appear to be:
The opposite or hypotenuse of sin
Sinθ = O/H
the following being spoken
H = 11 \sin θ = 0.1736
To replace having, use:
0.1736 = O/11
O = 11 * 0.1736
O = 1.9096
the missing value is 1.9096.
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1.45×4
2.65x5
3.77x6
4.89x7
5.52x3
whats are the answers of theses equations
Answer:
1. 45*4 = 180
2. 65*5= 325
3. 77*6=462
4. 89*7= 623
5. 52*3= 156
Answer:
5.8
13.25
22.62
34.23
16.56
Step-by-step explanation:
At what annual percent rate would you need to invest $12,000 and make $2,880 in interest after 8 years?
a. if you add 2 consecutive counting numbers (such as 47, 48), will the resulting sum always, sometimes, or never be divisible by 2? explain why your answer is true. b. if you add 3 consecutive counting numbers (such as 47, 48, 49), will the resulting sum al-ways, sometimes, or never be divisible by 3? ex-plain why your answer is true. c. if you add 4 consecutive counting numbers (such as 47, 48, 49, 50), will the resulting sum always, sometimes, or never be divisible by 4? explain why your answer is true. d. if you add 5 consecutive counting numbers (such as 47, 48, 49, 50, 51), will the resulting sum always, sometimes, or never be divisible by 5? explain why your answer is true. e. if you add n consecutive counting numbers, will the resulting sum always, sometimes, or never be divisible by n? explain why your answer is true.
On solving the provided question we can say that - the answer is 552 and 558, as consecutive integers.
what is consecutive integers?Consecutive integers are those integers in a computation formula that follow one another. No number is lost in a sequence when enumerating successive numbers, hence their spacing is always consistent. Consecutive integers are the next numbers in ascending order. The consecutive integers formula may be used to discover consecutive integers for any number or to determine if a set of numbers is consecutive or not.
First set the 3 numbers to be x-2, x, and x+2. So:
x-2+x+x+2=554
3x=554
There is no solution to this issue since three cannot split equally into 554. In reality
182+184+186=552
184+186+188=558
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the edison electric institute has published figures on the number of kilowatt hours used annually by various home appliances. it is claimed that a vacuum cleaner uses an average of $46$ kilowatt hours per year. if a random sample of $12$ homes included in a planned study indicates that vacuum cleaners use an average of $42$ kilowatt hours per year with a standard deviation of $11.9$ kilowatt hours, do these data suggest that at the $0.05$ significance level the mean annual usage of vacuum cleaners is less than $46$ kilowatt hours? assume the population distribution of usage in kilowatt hours to be normal.
The test statistic is less than - 1.796
Hypothesisi test
H0: μ = 46
Ha: μ < 46
This is a lower tailed test
mean = 42
standard deviation = 11.9
sample size n = 12
The level of significance α = 0.05
degree of freedom df = n - 1 = 12 - 1 = 11
Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164
Test statistic = - 1.164
Using t- table, we can observe that the p - value is between 0.10 and 0.15
Using excel we find p - value = P(t < - 1.796)
p value = 0.1344
H0: μ < 46, rejection rule is
Reject H0 if test statistic < - 1. 796
Therefore, we reject the hypothesis as the test statistic is less than - 1.796
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Each birthday from age 12, You receive $500. You
save the money in an account that pays an annual yield of 6%. How much money will you
have by the time you're 18?
using the points 0, 5 and -2, 2 make an equation in slope intercept form
At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month.
Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate?
A) 10x ((1+0.01)^12)^5
B) 10x(1+0.01^12) ^60
C) 10x (1.01)^5
D) 10x(1.01)^60
E) 10x (0.01)^60
.
g a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland? 1 point radial rectangular lasso pan
You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.
How do they choose the region on the map that Tableau uses to represent Finland? You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.To display only the nations with a World Happiness score of 3.5 or lower, utilize the Filter tool.By tracing a freehand form around several marks with the Lasso tool, you can choose a group of them.When you wish to include only some marks and eliminate others around them, this tool is helpful.Based on the common values, Tableau creates the view of blended data.For instance, Tableau will match data on "Purple" from the main and "Purple" from the secondary if Color is the linking field in both data sources.To learn more about Lasso Selection refer
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9. Given that ypı = 3e27 and Ypz = x2 + 3x are particular solutions of y" – 6y' + 5y = -9222 and y" - 6y' + 5y = 5x2 + 3x – 16 respectively, find the particular solutions of a. Y" – 6y + 5y = 5x2 + 3x – 16 – 9223 b. y" – 6y' + 5y = -10x2 - 6x + 32 +622
Particular solution for the equation a. Y" – 6y + 5y = 5x2 + 3x – 16 – 9223 is
5y = -15e²⁷ - 23/5
Particular solution for b. y" – 6y' + 5y = -10x2 - 6x + 32 +622 is 5y = 8x+ 218
Given:
y= 3e²⁷ (Solution 1)
Y = x² + 3x (Solution 2)
y" - 6y' + 5y = -9222 (Equation 1)
y" - 6y' + 5y = 5x² + 3x – 16 (Equation 2)
Where [tex]y^{"}[/tex] represents the double derivative(d²y) of y and [tex]y^{'}[/tex] represents the first derivative(dy) of the equation y.
Find Solutions for:
a. Y" – 6y + 5y = 5x² + 3x – 16 – 9223
b. y" – 6y' + 5y = -10x² - 6x + 32 +622
y= 3e²⁷ (Solution 1)(Given in the question)
Taking derivative on both sides
by = 3 de²⁷
∵ e²⁷ is constant in comparison to dy the derivative will be 0. Thus, d²y of y is also equal to zero
Then, putting values in the equation 1
- 6y' + 5y + y" = -9222 (Equation 1)
(0) - 6(0) +5(3e²⁷) = -9222
Thus, 15e²⁷ = -9222
5e²⁷ = -3074
e²⁷ = -614.8
Y = x² + 3x (Solution 2)(Given in the question)
Taking derivative on both sides
dY/dx= 2x + 3 -(iii)
taking derivative of y'
d²Y/dx² = 2
∵ 3 is a constant in dy/dx.
Then, putting values in the equation 2
y" -+ 5y - 6y' = 5x² + 3x - 16
(2) - 6(2x + 3) +5y = 5x² + 3x - 16 + 12x - 12x
2 - 12 + 18x + 5y = 5x² +15x - 16 -12x
-10 + 18x - 15x + 5y = 5y -16 -12x
3x + 12x =10 - 16
15x = -6
x= -2/5
Putting values of x, y, dy and d²y in equations (i) & (ii)
a. Y" – 6y + 5y = 5x² + 3x - 16 – 9223
(2) -6(2x+3) + 5y = 5x² + 3x - 16 - 9223 + 12x - 12x
2 - 12x -18 + 5y = 5y - 9223 - 16 - 12x
2 + - 18 + 5y -6/5 -(9222 + 1)
2 + 24-6/5 + 5y + 15e²⁷ - 1 = 0
5y + 15e²⁷ + 18/5 + 1= 0
5y + 15e²⁷ + 23/5= 0
5y = -15e²⁷ - 23/5
b. y" – 6y' + 5y = -10x² - 6x + 32 +622
(0) -6(0) + 5y = -10x² - 6x +654
5y = -10x² - 6x -24x + 24x + 654
5y = -10(x² + 3x) +24x + 654
5y = -10y + 24x + 654
5y +10y = 24x + 654
15y=24x+654
5y = 8x+ 218
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a wodden plnk 15
[tex] \sqrt{3} [/tex]
m long rests on a wall in such a way that it mskes an angel with ground at 15m away from the foot of the wall. find the angle made by the plank with the ground
Step-by-step explanation:
when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is
cos(our angle) × radius
15×sqrt(3) × cos(our angle) = 15
cos(our angle) = 1/ sqrt(3) = 0.577350269...
our angle = 54.73561032...°
Which of the following are the factors of 6x²+5x-6 *?
Answer:There are no choices but i do this type of work on edge so i could proably do it without the choices.
Step-by-step explanation:Answer would be (3x-2)(2x+3)
3x times 2x would be 6x squared 3x times 3 is 9x -2 times 2x is -4x
9x-4x is 5x and -2 times 3 is -6
Hope this helps:)
HAPPY NEW YEARS
if we alternately flip a balanced coin and a coin that is loaded so that the probability of getting heads is 0.45, what are the mean and the standard deviation of the number of heads that we obtain in 10 flips of these coins?
Probability of getting head = 0.45
Probability of getting tail = 1- 0.45
= 0.55
No of flip flops = 10
solve for x please help asap! will give brainlest
Answer:
80+60+3x+4=180
140+3x+4=180
144+3x=180
3x=180-144
3x=36
x=12
Answer:
x = 12
Step-by-step explanation:
All triangles equal to 180 degrees so, we can set up this expression:
180 = (3x + 4) + 80 + 60
All we have to do is solve:
180 = (3x + 4) + 80 + 60
180 = 3x + 4 + 140
180 = 3x + 144
-144 -144
36 = 3x
/3 /3
12 = x
Grocery Store A is selling bananas for $0.75 for 12 pound. Grocery Store B is selling 5 pounds of bananas for $3.75. Which store is offering the best unit rate?
Store B is offering the best unit rate for bananas.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Grocery Store A is selling bananas for $0.75 for 12 pounds.
The unit rate will be = 0.75/12 = 0.06
Grocery Store B is selling 5 pounds of bananas for $3.75.
The unit rate will be = 3.75/5 = 0.75
Hence, Store B is offering the best unit rate for bananas.
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What is the equation of the line that passes through the point (-1,2) and has a slope of -1?
The equation of the line that passes through the point (-1,2) and has a slope of -1, in point-slope form is: y - 2 = -1(x + 1).
What is the Equation of a Line?If we know one point (a, b), that a line passes through and its slope (m), we can write the equation of that line in point-slope form as y - b = m(x - a).
Given the following:
A point (a, b) = (-1, 2)
The slope of the line (m) = -1
To write the equation of the line, substitute m = -1, a = -1, and b = 2 into y - b = m(x - a):
y - 2 = -1(x - (-1))
y - 2 = -1(x + 1).
The answer is: y - 2 = -1(x + 1).
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lost-time accidents occur in a company at a mean rate of 0.3 per day. what is the probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3? assume poisson situation. p(x
The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295
Binomial Distribution
The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.
In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
Mean rate of lost time accident = 0.3 per day
probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.
n = 7
Using binomial distribution formula :
P(x ≤3)
Probability of success (p) = 0.3
1 - p = 1- 0.3 = 0.7
nCx * p^x * (1 - p)^(n-x)
Using the binomial probability distribution calculator to save computation time :
P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668
P(x ≤3) = 0.7295
0.7295
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Find the domain and range of the function by the graph. Is the graph discrete or continuous
Domain is the set of values under which a function is defined.
Range is the outcome of all the values of the domain when put in a function.
graphically, the domain is the set of values under which we get some value in the y-axis for a particular function graph .
while the range is the y-coordinate of all the points lying on the graph .
As the graph is not posted by you.
see this graph of the modulus function for instance:
function IxI is defined for every real possible value of xso, R is the domain.
but the range is only positive values of R in y.
and,
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Which equation has the same solution as 4-2(x-5)=x-19
(A) 2(x+5)= -8.
(B) 3(x-3)=9
(C) x+2=2x-3
(D) 3x-4=2x+7
Answer:
3x-4=2x+7 thus: (D)
x = 11
Step-by-step explanation:
Solve for x:
3 x - 4 = 2 x + 7
Subtract 2 x from both sides:
(3 x - 2 x) - 4 = (2 x - 2 x) + 7
3 x - 2 x = x:
x - 4 = (2 x - 2 x) + 7
2 x - 2 x = 0:
x - 4 = 7
Add 4 to both sides:
x + (4 - 4) = 4 + 7
4 - 4 = 0:
x = 7 + 4
7 + 4 = 11:
Answer: x = 11
___________________________
Solve for x:
4 - 2 (x - 5) = x - 19
-2 (x - 5) = -2 x + 10:
(-2 x + 10) + 4 = x - 19
Add like terms. 4 + 10 = 14:
-2 x + 14 = x - 19
Subtract x from both sides:
(-2 x - x) + 14 = (x - x) - 19
-2 x - x = -3 x:
-3 x + 14 = (x - x) - 19
x - x = 0:
-3 x + 14 = -19
Subtract 14 from both sides:
(14 - 14) - 3 x = -14 - 19
14 - 14 = 0:
-3 x = -14 - 19
-14 - 19 = -33:
-3 x = -33
Divide both sides of -3 x = -33 by -3:
(-3 x)/(-3) = (-33)/(-3)
(-3)/(-3) = 1:
x = (-33)/(-3)
The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:
Answer: x = 11
Answer:3x-4=2x+7
Step-by-step explanation:
first, 4-2x+10=x-19
14+19 =x+2x
33=3x
x=11
A. 2x+10=8
2x= -18
x=-9
B. 3x-9=9
3x=18
x=6
C. x+2=2x-3
3x = 5
x = 5/3
D. 3x-4 = 2x+7
3x-2x=7+4
x=11
Use your calculator to evaluate a¯=−3.7meter/second−13.9meter/second21.4second−7.2second. Part A Average acceleration Use your calculator to evaluate -3.7 meter/second-13.9 meter/second 21.4 second-72…
The average acceleration is - 1.24 m/s². The result is calculated by using calculator. See the picture in the attachment!
What is average acceleration?Average acceleration is the rate of change in velocity per unit time. The formula can be expressed as
[tex]\overline{a} = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex]
Where
v₂ = final velocityv₁ = initial velocityt₂ = final timet₁ = initial timeCalculate this average acceleration using calculator!
[tex]\overline{a} = \frac{-3.7 \: m/s \: - 13.9 \: m/s}{21.4 \: s- 7.2 \: s}[/tex]
See the picture in the attachment!
The average acceleration after rounding is
[tex]\overline{a} = -1.23943661972 \: m/s \: /s[/tex]
[tex]\overline{a} = -1.24 \: m/s^{2}[/tex]
Hence, the average acceleration from the data is - 1.24 m/s².
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A cylindrical wooden column is 3 m high and 28 cm in diameter use value π to calculate the mass in kf of the column if the density of the wood is 0.8g/cm^3
Answer:
1.478 kg
Step-by-step explanation:
Considering density=mass/volume, when we rearrange, we get mass=density*volume. Therefore, as we are given the density, we just need to find the volume to know the mass. The volume of a cylinder is πhr^2, and our radius is 28/2=14, so the volume of the cylinder is π*3*14^2=588π. Then, 588π*0.8=470.4π which is about 1477.8052 g. Then, to convert to kg, we can divide this by 1000 and get about 1.478 kg.
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Complete the relative frequency table, showing all necessary calculations.
By using the tabular data given , the complete relative frequency table has been shown below
What is tabular data?
Data given in the form of rows and columns is known as tabular data.
The relative frequency table has been shown below
Frequency of students who like to like to fly and can drive = 0.32
Total frequency of students who like to fly = 0.70
Frequency of students who like to like to fly cannot drive = 0.70 - 0.32 = 0.38
Frequency of students who can drive = 0.45
Frequency of students who cannot drive = 0.55
Frequency of students who do not like to fly can drive = 0.45 - 0.32 = 0.13
Frequency of students who do not like to fly cannot drive = 0.55 - 0.38 = 0.17
Total frequency of students who do not like to fly = 0.13 + 0.17 = 0.30
The complete relative frequency table is
Can drive Cannot drive Row totals
Like to fly 0.32 0.38 0.70
Do not like to fly 0.13 0.17 0.30
Column totals 0.45 0.55 1
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hadlee spent 1/4 of her money on christmas presents she had 180 remaining . how much did hadlee soend on christmas present
The amount for handle soend on Christmas present will be 240.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Now,
Since, Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Let the amount for handle soend on Christmas present = x
Hence, The amount for handle soend on Christmas present will be;
⇒ x - 1/4x = 180
⇒ 3/4x = 180
⇒ 3x = 180 × 4
⇒ 3x = 720
⇒ x = 240
Thus, The amount for handle soend on Christmas present will be 240.
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What is the equation of the line that passes through the point (-3,-3)(−3,−3) and has a slope of 33?
The required equation of the line having a slope of 33 and passing through (-3, - 3) is y = 33x + 96.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Let the required line be y = mx + b.
∴ - 3 = (33)(-3) + b.
- 3 = - 99 + b.
b = 96.
∴ y = 33x + 96 is the required line.
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