Answer:
1. 766,536cm^3
2. 29,680,948cm^3
3. 41,620.8cm^3
Step-by-step explanation:
1. 123×82 = 10,086 10,086×76 = 766,536
2. 422×278 = 117,316 117,316×253 = 29,680,948
3. 87×2.3 = 200.1 200.1×208 = 41,620.8
Hope this helps! :)
Which would result in a lower price to first discount an item by 10% and then by a further 15%, OR to first discount an item by 15% and then by a further 10%. Justify your reasoning.
Answer:
Neither one. They will both result in the same price.
Step-by-step explanation:
To discount an item 10%, you charge 90% of the price of the item. To find 90% of a price, you multiply the price by 0.9.
To discount an item 15%, you charge 85% of the price of the item. To find 85% of a price, you multiply the price by 0.85.
Since multiplication is commutative, multiplying a number by 0.9 and then by 0.85 is the same as multiplying the number by 0.85 first and then by 0.9.
Let's say the item costs x.
Take off the 10% discount first: 0.9x
Now take off the 15% discount: 0.85 * (0.9x)
Now do it the other way.
Take off the 15% discount first: 0.85x
Now take off the 10% discount: 0.9 * (0.85x)
Since 0.85 * 0.9 * x = 0.9 * 0.85 * x, the results are the same.
Answer: neither
Please help how to do this
Answer:
Frumpyton
Step-by-step explanation:
Since the standard deviation of Frumpyton is a lower number, this means a higher percentage of outcomes (job salaries) will be within a closer range to the mean salary. Since Frumpyton's standard deviation is $2,000 and the window your looking for is $32,000 to $36,000, if you go one interval up or down from the mean of $34,000, it falls in that range. Whereas, Dirtballville's standard deviation is $3,000 so it's more likely to fall outside of that range.
01:55:07
The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y – 3 = {(x - 1). What is the
slope-intercept form of the equation for this line?
O y = 3x+2
O y= 2x-4
O y=+*+
O y = 3x - 2
Answer
y = 3x - 2
Step-by-step explanation
The slope-intercept form of the equation for this line is,
⇒ y = x + 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point-slope form of the equation of the line that passes through points (-9, -2) and (1, 3) is,
⇒ y - 3 = (x - 1)
Now, We can simplify as;
⇒ y - 3 = (x - 1)
⇒ y - 3 + 3 = (x - 1) + 3
⇒ y = x + 2
Thus, The slope-intercept form of the equation for this line is,
⇒ y = x + 2
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Please help NO LINKS
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
Given the following formula, solve for r.
Find, correct to the nearest degree, the three angles of the triangle with the given ven
A(1, 0, -1), B(4, -3,0), C(1, 2, 3)
o
CAB =
O
LABC =
O
LBCA =
9514 1404 393
Answer:
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
Step-by-step explanation:
This can be done a couple of different ways (as with most math problems). We can use the distance formula to find the side lengths, then the law of cosines to find the angles. Or, we could use the dot product. In the end, the math is about the same.
The lengths of the sides are given by the distance formula.
AB² = (4-1)² +(-3-0)² +(0-(-1)) = 16 +9 +1 = 26
BC² = (1-4)² +(2-(-3))³ +(3-0)² = 9 +25 +9 = 43
CA² = (1-1)² +(0-2)² +(-1-3)² = 4 +16 = 20
From the law of cosines, ...
∠A = arccos((AB² +CA² -BC²)/(2·AB·CA)) = arccos((26 +20 -43)/(2√(26·20)))
∠A = arccos(3/(4√130)) ≈ 86°
∠B = arccos((AB² +BC² -AC²)/(2·AB·BC)) = arccos((26 +43 -20)/(2√(26·43)))
∠B = arccos(49/(2√1118)) ≈ 43°
∠C = arccos((BC² +CA² -AB²)/(2·BC·CA)) = arccos((43 +20 -26)/(2√(43·20)))
∠C = arccos(37/(4√215)) ≈ 51°
The three angles are ...
∠CAB = 86°
∠ABC = 43°
∠BCA = 51°
_____
Additional comment
This sort of repetitive arithmetic is nicely done by a spreadsheet.
The population of a colony of 300 bacteria grows exponentially. After 2 hours, the population reaches 500. How much time will it take for the population to reach 9,600
Answer:
t = 13.56915448 hrs.
Step-by-step explanation:
500 = 300 [tex]e^{2k}[/tex]
5/3 = [tex]e^{2k}[/tex]
ln(5/3) = 2k ln(e)
k = ln(5/3)/2
k= 0.255412812
~~~~~~~~~~~~
9600 = 300 [tex]e^{0.255412812 t}[/tex]
32= [tex]e^{0.255412812 t}[/tex]
ln(32) = [tex]0.255412812 t[/tex] ln(e)
t = ln(32)/0.255412812
t = 13.56915448 hrs.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
See attachment showing the rise and run
Slope = 1
Step-by-step explanation:
In the diagram attached below, the rise is represented by the blue line, while the run is represented by the red line.
Rise = 4 units
Run = 4 units
It's a positive slope because the line slopes upwards from left to right
Slope = rise/run = 4/4
Slope = 1
Write a compound inequality to represent all of the numbers between -4 and 6.
Answer:
-4 < x < 6
Step-by-step explanation:
Find the value for x
Answer:
[tex]180 - 2x + 180 - 4x + x = 180 \\ 360 - 5x = 180 \\ 180 = 5x \\ x = 36[/tex]
The heights (in inches) of a sample of eight mother/daughter pairs of subjects were measured. Using a spreadsheet with the paired mother/daughter heights, the linear correlation coefficient is found to be 0.693. Find the critical value, assuming a 0.05 significance level. Is there sufficient evidence to support the claim that there is a linear correlation between the heights of mothers and the heights of their daughters?
A. Critical value = ± 0.666; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
B. Critical value = ± 0.707; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
C. Critical value =± 0.666; there is sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Answer:
D. Critical value =± 0.707; there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Step-by-step explanation:
Given that :
Correlation Coefficient, r = 0.693
The sample size, n = 8
The degree of freedom used for linear correlation :
df = n - 2
df = 8 - 2 = 6
Using a critical value calculator for correlation Coefficient at α = 0.05
The critical value obtained is : 0.707
The test statistic :
T = r / √(1 - r²) / (n - 2)
T = 0.693 / √(1 - 0.693²) / (8 - 2)
T = 0.693 / 0.2943215
T = 2.354
Since ;
Test statistic < Critical value ; we fail to reject the null and conclude that there is not sufficient evidence to support the claim of a linear correlation between heights of mothers and heights of their daughters.
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
Help please somebody ASAP
Answer:
[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]
Step-by-step explanation:
I don't think we can factor this so we'll have to multiply to make the denominators the same
[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 41 and 53? Do not enter the percent symbol.
Find the factors of function f, and use them to complete this statement. f(x)=2x^(4)-x^(3)-18x^(2)+9x
From left to right, function f has zeros at
Hello,
[tex]f(x)=2x^4-x^3-18x+9x\\\\=x(2x^3-x^2-18x+9)\\\\=x(x^2(2x-1)-9(2x-1))\\\\=x(2x-1)(x^2-9)\\=x(2x-1)(x-3)(x+3)\\[/tex]
Zeros are : 0; 1/2; -3; 3.
The zeros of the function are -3, 0, 1/2 and 3.
The given function is [tex]f(x)=2x^{4} -x^{3} -18x^{2} +9x[/tex].
What are the zeros of a function?Zeros of a function are the points where the graph of the function meets the X-axis i.e., at the solutions of f(x) = 0.
Now, factorise the given function, that is f(x)=x(2x³-x²-18x+9).
=x[x²(2x-1)-9x(2x-1)]
=x(2x-1)(x²-9)
=x(2x-1)(x+3)(x-3)
= -3, 0, 1/2, 3
Therefore, the zeros of the function are -3, 0, 1/2 and 3.
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Can someone just check my answers please? Please let me know which questions are wrong. Thank you for your time.
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
PLEASE BE RIGHT FILL IN THE BLANKS
Answer:
3 units to the right and 2 units up
Step-by-step explanation:
Help please!!!!!!!!!!!
Answer:
y = 14
Step-by-step explanation:
[tex] \frac{15}{21} = \frac{5}{7} [/tex]
[tex] \frac{10}{x} = \frac{5}{7} [/tex]
[tex]x = 14[/tex]
Now,
10/15 = y/21
15y = 10*21
y = 210/15
y = 14
This is a Right answer...
I hope you understand..
Mark me as brainliest...
Given: CD is an altitude of triangle ABC.
Prove: a^2 = b^2 +c^2 = 2bccos A
Answer:
Step-by-step explanation:
Statements Reasons
1). CD is an altitude of ΔABC 1). Given
2). ΔACD and ΔBCD are right 2). Definition of right triangles.
triangles.
3). a² = (c - x)² + h² 3). Pythagoras theorem
4). a² = c² + x² - 2cx + h² 4). Square the binomial.
5). b² = x² + h² 5). Pythagoras theorem.
6). cos(x) = [tex]\frac{x}{a}[/tex] 6). definition of cosine ratio for an angle
7). bcos(A) = x 7). Multiplication property of equality.
8). a² = c² - 2c(bcosA) + b² 8). Substitution property
9). a² = b² + c² - 2bc(cosA) 9). Commutative properties of
addition and multiplication.
1. Nikita invests 6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to ? 6,720
plzzzz tell me
Answer:
Hope it is helpful and useful
6. What are the coordinates of W? (0,t) W 0 (,0) Rhombus (0, -1) o (-r, o) (0,r). (t,0)
Answer:
B. (-r, 0)
Step-by-step explanation:
W is on the x axis, so the y coordinate is 0.
It is also r away from the origin, so the x coordinate is -r
Hope this helps!
48. What is the volume of the cuboid below? 3cm 2cm 2cm
Answer:
Cuboid = width*height*length
Cuboid = 24 cm^2
sec x tanx( 1- sin^2 x) = __x
Answer:
sin(x)
Step-by-step explanation:
sec x tanx(1 - sin^2 x)
1 - sin^2 x = cos^2 x
sec(x)tan(x)cos^2(x)
[tex]\frac{1}{cos(x)}[/tex] * [tex]\frac{sin(x)}{cos(x)}[/tex] * cos^2(x)
[tex]\frac{sin(x)cos^2(x)}{cos^2(x)}[/tex]
sin(x)
what is the complete factorization of 8x^2-8x+2
Answer:
2x(4x-4+1)
Step-by-step explanation:
i hope it will help you
Answer:
x=1/2
Step-by-step explanation:
press the calculator
8x²-8x+2=0
x=1/2
min,x=1/2
min,y=0
For the problem I tried dividing but my answers were not correct. How can I solve this problem then? Can someone help me out here please?
Answer:
8
Step-by-step explanation:
5 = 40
1 = x
Then we multiply by the rule of crisscrossing
5 x X = 40 x 1
5x = 40 then divide both by 5
X = 8
The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 107 and a standard deviation of 60, but does not necessarily follow a normal distribution.The probability that a daily average over a given month is greater than x is 2.5%. Calculate x. You may find standard normal table useful. Give your answer to 3 decimal places.x =
Answer:
x = 128.472
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
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, the Central Limit Theorem can also be applied, as long as n is at least 30.
The number of diners each day has a mean of 107 and a standard deviation of 60.
This means that [tex]\mu = 107, \sigma = 60[/tex]
Distribution of the daily average:
Over a month of 30 days, so [tex]n = 30, s = \frac{60}{\sqrt{30}} = 10.955[/tex]
The probability that a daily average over a given month is greater than x is 2.5%. Calculate x.
This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 107}{10.955}[/tex]
[tex]X - 107 = 1.96*10.955[/tex]
[tex]X = 128.472[/tex]
So x = 128.472
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answer:
It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Step-by-step explanation:
Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:
1/3 = 0.333
1/2 = 0.5
0.333 = 2
2.5 = X
2.5 x 2 / 0.333 = X
15 = X
Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?Complete the table below. Use the minimum data entry as the lower limit of the first class.Class Frequency, f Relative frequencyx-x x xx-x x xx-x x xx-x x xx-x x x sumf= X?(Type integers or decimals. Round to the nearest thousandth as needed.)DATA:Triglyceride levels of 26 patients (in milligrams per deciliter of blood)138 199 240 143 294 175 240 216 223180 138 266 161 175 402 172 459 147391 152 199 294 188 320 421 161
Answer:
[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
Step-by-step explanation:
Solving (a): The frequency distribution
Given that:
[tex]Lowest = 138[/tex] --- i.e. the lowest class value
[tex]Class = 5[/tex] --- Number of classes
From the given dataset is:
[tex]Highest = 459[/tex]
So, the range is:
[tex]Range = Highest - Lowest[/tex]
[tex]Range = 459 - 138[/tex]
[tex]Range = 321[/tex]
Divide by the number of class (5) to get the class width
[tex]Width = 321 \div 5[/tex]
[tex]Width = 64.2[/tex]
Approximate
[tex]Width = 64[/tex]
So, we have a class width of 64 in each class;
The frequency table is as follows:
[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]
Solving (b) The relative frequency histogram
First, we calculate the relative frequency by dividing the frequency of each class by the total frequency
So, we have:
[tex]\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}[/tex]
See attachment for histogram
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
PLEASE HELP
The function in the table is quadratic:
TRUE
FALSE
Answer:
False
Step-by-step explanation:
Each f(x) increases by 8 therefore this equation is a linear function. If you where to graph it would be a straight line
Hope this helped :)
Answer:
False
Step-by-step explanation:
The slope is the same between all pounts which means the function is linear.
Hope this helps!