Answer:
13
Step-by-step explanation:
let the number be x
how Cindy worked it out :
(x -6) ÷ 3 = 25
x -6 = 75
x = 81
How she should have worked it out:
(x - 3) ÷ 6
(81 - 3) ÷ 6
78 ÷ 6 = 13
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
Which of the following is an arithmetic sequence? A.-2, 4, -6, 8, ... B.2, 4, 8, 16, ... C.-8, -6, -4, -2, ...
Answer:
C. -8, -6, -4, -2, ...
Step-by-step explanation:
An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.
A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.
B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.
C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.
Hope this helps!
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amount of cardboard.
Answer:
2ft by 2ft by 1 ftStep-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
What is the first step in mathematical induction?
Answer:
Show that the statement is true for n=1
Step-by-step explanation:
Hey,
Show that the statement is true for n=1
You can check my other answer there which explains a little bit more the ideas.
https://brainly.com/question/17162256
thank you
In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
[tex]\huge\boxed{y = 8}[/tex]
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
Reset
Next
Answer: A) g(x) = 3x - 14
Step-by-step explanation:
Solve the equation for y and replace y with g(x):
y - 3x = -14
y = 3x - 14
g(x) = 3x - 14
Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two
Answer:
5x^3-2
[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]
Explanation:
The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.
We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.
The coefficient is the number to the left of the variable.
The degree is the largest exponent, which helps form the leading term.
The third degree polynomial written above is considered a cubic binomial. "Cubic" refers to the third degree, while "binomial" means there are 2 terms.
We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.
Find the area of the shaded regions:
area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$
so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$
$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$
abd there are 2 such arcs, so double the area.
[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]
Given:-Radius of the circle = 10 inchesAngle of each sector = 72°Number of sectors = 2To FinD:-Find the area of the shaded regions....?How to solve?For solving this question, Let's know how to find the area of a sector in a circle?
[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]
Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.
Solution:-We have,
No. of sectors = 2Angle of sector = 72°By using formula,
⇛ Area of shaded region = 2 × Area of each sector
⇛ Area of shaded region = 2 × Θ/360° × πr²
⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²
⇛ Area of shaded region = 2/5 × 100 × 22/7
⇛ Area of shaded region = 40 × 22/7
⇛ Area of shaded region = 880/7 inch. sq.
⇛ Area of shaded region = 125.71 inch. sq.
☄ Your Required answer is 125.71 inch. sq(approx.)
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nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?
Answer:
We conclude that no more than 10% of its microwaves need repair during the first five years of use.
Step-by-step explanation:
We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.
In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.
Let p = population proportion of microwaves who need repair during the first five years of use.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10% {means that no more than 10% of its microwaves need repair during the first five years of use}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that more than 10% of its microwaves need repair during the first five years of use}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of microwaves who need repair during the first 5 years of use = 12%
n = sample of microwaves = 50
So, the test statistics = [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]
= 0.471
The value of z-test statistics is 0.471.
Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.
Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.
Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. low Q1 median Q3 high (b) Find the interquartile range.
Answer:
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = 3.5
Step-by-step explanation:
Given that:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14
From the above dataset, the highest value = 14 and the lowest value = 6
The median is the middle number = 11
For Q1, i.e the median of the lower half
we have the ordered data = 6, 9, 9, 10
here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.
i.e
median = [tex]\dfrac{9+9}{2}[/tex]
median = [tex]\dfrac{18}{2}[/tex]
median = 9
Q3, i.e median of the upper half
we have the ordered data = 11 12 13 14
The same use case is applicable here.
Median = [tex]\dfrac{12+13}{2}[/tex]
Median = [tex]\dfrac{25}{2}[/tex]
Median = 12.5
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = Q3 - Q1
The interquartile range = 12.5 - 9
The interquartile range = 3.5
. A discount brokerage selected a random sample of 64 customers and reviewed the value of their accounts. The mean was $32,000 with a population standard deviation of $8,200. What is a 90% confidence interval for the mean account value of the population of customers
Answer:
The 90% confidence interval is [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The sample mean is [tex]\= x = \$ 32, 000[/tex]
The standard deviation is [tex]\sigma= \$ 8, 200[/tex]
Given that the confidence interval is 90% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]
=> [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]
=> [tex]E = 1686.13[/tex]
The 90% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]
=> [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
The range of values for x?
Answer:
x = 32
but
I would say anything from 30 to 33
but truly i have no clue about the range
Step-by-step explanation:
3x-9=87 (because 180 -93 =87)
3x = 96
x = 32
Answer:
it is 32
Step-by-step explanation:
This graph shows the US unemployment rate from August 2010 to November 2011.
Sample Unemployment Rate
Graph
Unemployment Rate
10%
80%
6%
Unemployment Rate
Aug 10
Jan 11
Jun 11
Nov 11
This graph suggests unemployment in the United States
O will continue to fall.
O will continue to rise.
O will remain the same.
O will only change a little.
Answer: Will continue to rise
Step-by-step explanation:
Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.
The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.
This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.
Answer:
EDGE 2021
Step-by-step explanation:
1) 4%
2) Increase
How do you find x when knowing the probability?
Answer:
x
Step-by-step explanation:
probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.
So, to answer the first question, [tex]6^2[/tex] is a perfect square.
(a,b,c) is a Pythagorean triple means the following
[tex]a^2+b^2=c^2[/tex]
Here, it means that
[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]
Thank you.
Answer:
Its B
Step-by-step explanation:
can you please help ?
Answer:
69
Step-by-step explanation:
The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.
We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.
[tex]\frac{5(x)}{2} -6[/tex]
[tex]\frac{5(30)}{2}-6[/tex]
[tex]\frac{150}{2}-6[/tex]
[tex]75-6[/tex]
[tex]69[/tex]
find the value of x? please help
Answer:
49
Step-by-step explanation:
With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!
12-(3-9) 3*3 help please
Step-by-step explanation:
42 is your answer according to bodmas
Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)
Answer:
-7.
Step-by-step explanation:
g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7
= 4 - 12 - 7
= -8 - 7
= -15
f(x) = x + 8
f(-15) = (-15) + 8
= 8 - 15
= -7
Hope this helps!
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
What is the volume of a cube with a side length of
of a unit?
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
