9514 1404 393
Answer:
large: 15.5 kgsmall 6.5 kgStep-by-step explanation:
Let x and y represent the weights of the large and small boxes, respectively. Then the two delivery weights give rise to the equations ...
3x +5y -79 = 0
12x +2y -199 = 0
Using the "cross multiplication method" of solving these equations, we find ...
d1 = (3)(2) -(12)(5) = 6 -60 = -54
d2 = 5(-199) -(2)(-79) = -995 +158 = -837
d3 = -79(12) -(-199)(3) = -948 +597 = -351
1/d1 = x/d2 = y/d3
x = d2/d1 = -837/-54 = 15.5
y = d3/d1 = -351/-54 = 6.5
The large boxes weigh 15.5 kg; the small boxes weigh 6.5 kg.
_____
Additional comment
My preferred quick and easy way to solve equations like this is using a graphing calculator. In addition to that, an algebraic method is shown.
The "cross-multiplication method" shown here is what I consider to be a simplified version of what you would find in videos. It is a variation of Cramer's rule and the Vedic maths methods of solving pairs of linear equations. I find it useful when "elimination" or "substitution" methods would result in annoying numbers. In such cases, it uses fewer arithmetic operations than would be required by other methods.
Short description: writing the coefficients of the general form equations in 4 columns, where the last column is the same as the first, a "cross multiplication" is computed for each of the three pairs of columns. Those computations are of the form ...
[tex]\text{column pair: }\begin{array}{cc}a&b\\c&d\end{array}\ \Rightarrow\ d_n=ad-cb[/tex]
The relationship between the differences d₁, d₂, and d₃ and the variable values is shown above.
A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.
How many miles per hour is the superhero flying?
Work Shown:
30 min = 30/60 = 0.5 hours
distance = rate*time
rate = distance/time
rate = (2450 miles)/(0.5 hours)
rate = (2450/0.5) mph
rate = 4900 mph
For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.
A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *
Answer:
12.6 ft
Step-by-step explanation:
1/10 + 3/5
ANSWER QUICK PLS FIRST ANSWER GETS BRAINLIEST
what is the absolute value of |9|?
Answer:
9
Step-by-step explanation:
it's as simple as that 9 is 9 away from 0
Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
Algebra 2, please help! thank you
The function y = 2 cos 3(x + 2π∕3) +1 has a phase shift (or horizontal shift) of
A) –2π∕3
B) 3
C) 1
D) 2
Answer:
-2pi/3
Step-by-step explanation:
y = 2 cos 3(x + 2π∕3) +1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
We have a shift to the left of 2 pi /3
Answer:
A
Step-by-step explanation:
The standard cosine function has the form:
[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]
Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]
We can rewrite this as:
[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]
Therefore, a = 2, b = 3, c = -2π/3, and d = 1.
Our phase shift is represented by c. Thus, the phase shift is -2π/3.
Our answer is A.
a store sign reads "Take 75% of the original price when you take an additional 15% off the sale price, which is 60% off the original price." Is the stores sign accurate?
Answer:
The new price is 66% off the original not 75% off
Step-by-step explanation:
Let x be the original price
First take 60 percent off
x - x*60% = new price
x- .60x = .40x
The new price is .40x
Then take 15 % off
(.40x) - (.40x)*15%
.40x - .40x*.15
.40x - .06x
.34x
100 -.34 =.66
The new price is 66% off the original not 75% off
In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment
Answer:
The answer is "Specific treatment levels".
Step-by-step explanation:
When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.
T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
Read more about equations at:
https://brainly.com/question/2396830
Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
What is the product of 2/5 × 3/4?
Answer:
3/10
Step-by-step explanation:
2/5*3*4
=6/20
=3/10
CHứng minh rằng trong hệ g - phân với 2
Simplify: −4(b+6)−2b(1−4b
Step-by-step explanation:
-4b-24-2b+8b2
8b2-6b-24=0
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?
Answer:
The standard error of the estimated difference is of 0.0313.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Brand A:
33 out of 197, so:
[tex]p_A = \frac{33}{197} = 0.1675[/tex]
[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]
Brand B:
25 out of 290, so:
[tex]p_B = \frac{25}{290} = 0.0862[/tex]
[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]
What would be the standard error of the estimated difference?
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]
The standard error of the estimated difference is of 0.0313.
What is the formula for the volume of a pyramid?
V = πr2h
V = 3/4πr2h
V = 1/3πr2h
V = 1/3Bh
write any five sentences of fraction?
Step-by-step explanation:
Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
a fraction has 2 parts
The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.
There are different types of fraction
unit fractionimproper fractionproper fractionmixed fractionWhat is distributive property???
A number multiplied by a sum is the same as the sum of the number multiplied by each addend; a(b + c) = ab + ac
Answer:
the distributive property of binary operations generalizes the distributive law from elementary algebra, which asserts that one has always For example, one has One says that multiplication distributes over addition.
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
56 x 10^-4)
Group of answer choices
2.37 x 10^-16
4.21 x 10^15
2.4 x 10^-16
4.2 x 10^15
9514 1404 393
Answer:
(d) 4.2×10^15
Step-by-step explanation:
Your calculator will tell you the quotient is about ...
4.21348...×10^15
The least precise number in the division is 1.5, which has 2 significant digits. Therefore, the result should be rounded to 2 significant digits:
4.2×10^15
The whole number 23 is an example of a ____ number.
prime or composite?
The answer is prime! I hope this helps you out!
Answer:
23 is a prime number. Reason: Prime number are those numbers which are divisible by 1 and itself. Example: 5 is divisible by 1 and 5 only.
helpppp asap pleaseee
Answer:
29/3 is your answer
Step-by-step explanation:
pls mark as brainliest
Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
Wayne has a rectangular painting. The width of the painting is
5/6
of a foot, and the length is
3/4
of a foot. What is the area of the painting?
Answer:
5/8 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
A = 5/6 * 3/4
A = 3/6 * 5/4
A = 1/2 * 5/4
A = 5/8 ft^2
What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms? (5 points)
Answer:
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
Step-by-step explanation:
There's a handy formula we can use to find the sum of a geometric sequence, and here it is
[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]
The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.
First lets visualize this sequence
[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]
Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.
[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]
Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.
[tex]S_n = \sum{a*r^{n-1}}[/tex]
To finish up lets plug these coefficients in and get our sum after 10 terms.
[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]
What is the discriminat of 2x+5x^=1
Answer:
don't know...........
Write an explicit formula for the sequence.
-4,7,-10,13,-16
Step-by-step explanation:
Sequence is
4
,
7
,
10
,
13
,
16
,
.
.
.
a
1
=
4
,
a
2
=
7
,
a
3
=
10
,
.
.
.
If it is Arithmetic sequence,
a
2
−
a
1
=
a
3
−
a
2
=
a
4
−
a
3
& so on
In the given sum,
a
2
−
a
1
=
7
−
4
=
3
a
3
−
a
2
=
10
−
7
=
3
a
4
−
a
3
=
13
−
10
=
3
Since the difference between the successive terms is same and
hence
common difference
d
=
3
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
Question 6 of 10
Which situation shows a constant rate of change?
A. The number of tickets sold compared with the number of minutes
before a football game
B. The height of a bird over time
C. The cost of a bunch of grapes compared with its weight
D. The outside temperature compared with the time of day
SUBMI
a) the cost of a bunch of grapes compared with its weight
GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
