Answer:
Length of shortest side: 57
Length of medium side:59
Length of long side: 119
Step-by-step explanation:
Multiply: (x−5)(x−7) A x2−12x+35 B x2+2x+35 C x2+35 D x2+35x−12
Answer:
x^2 -12x+35
Step-by-step explanation:
(x−5)(x−7)
FOIL
first x*x = x^2
outer -7x
inner -5x
last -7*-5 = 35
Add them together
x^2 -7x-5x +35
x^2 -12x+35
Answer:
Step-by-step explanation:
x*x=2x
x*-7=-7x
-5*x=-5x
-5*-7=+35
2x-12x+35
A
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
A shipping container in the shape of a rectangular prism is 60 feet long, 45 feet wide, and 14 feet tall. What is the volume of the shipping container? *
The amount of money spent on textbooks per year for students is approximately normal.
a. To estimate the population mean, 19 students are randomly selected the sample mean was $390 and the standard deviation was $120. Find a 95% confidence for the population meam.
b. If the confidence level in part a changed from 95% 1to1999%, would the margin of error for the confidence interval (mark one answer): decrease stay the same increase not enough information to answer
c. If the sample size in part a changed from 19 10 22. would the margin of errot for the confidence interval (mark one answer): decrease in stay the same increase in not enough information to answer
d. To estimate the proportion of students who purchase their textbookslused, 500 students were sampled. 210 of these students purchased used textbooks. Find a 99% confidence interval for the proportion of students who purchase used text books.
Answer:a
a
[tex]336.04 < \mu < 443.96[/tex]
b
The margin of error will increase
c
The margin of error will decreases
d
The 99% confidence interval is [tex]0.4107 < p < 0.4293[/tex]
Step-by-step explanation:
From the question we are told that
The sample size [tex]n = 19[/tex]
The sample mean is [tex]\= x = \$\ 390[/tex]
The standard deviation is [tex]\sigma = \$ \ 120[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
So
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]
=> [tex]E = 53.96[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]
=> [tex]336.04 < \mu < 443.96[/tex]
When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider
Generally the sample size mathematically varies with margin of error as follows
[tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]
So if the sample size increases the margin of error decrease
The sample proportion is mathematically represented as
[tex]\r p = \frac{210}{500}[/tex]
[tex]\r p = 0.42[/tex]
Given that the confidence level is 0.99 the level of significance is [tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]
=> [tex]E = 0.0093[/tex]
The 99% confidence interval is
[tex]\r p - E < p < \r p + E[/tex]
[tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]
[tex]0.4107 < p < 0.4293[/tex]
A person collected $700 on a loan of $600 they made 5 years ago. If the person charged simple interest, what was the rate of interest? The interest rate is %. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answer:
Rate= 3 1/3%
Or Rate= 3.33%
Step-by-step explanation:
Final amount collected= $700
Initial amount given out= $600
Interest made= Final amount - initial amount
Interest made= $700-$600
Interest made= $100
Type of interest rate = simple
Number of years = 5
PRT/100= interest
R=(100*interest)/(PT)
R= (100*100)/(600*5)
R= 10000/3000
R= 10/3
R= 3 1/3%
Or R= 3.33%
Define “constant value”
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
show working to this question
Answer:
Step-by-step explanation:
A = {p, q, r}
Subsets: {p,q,r}, {p,q}, {p,r}. {q,r}, {p}, {q}, {r}, ∅
::::
Slope of RT = (-7/2 - 0)/(-3/2 - 0) = 7/3
Point-slope equation for line of slope 7/3 that passes through (0,0):
y = (7/3)x
How would x^3+8 be expressed in factored form
[tex]\it x^3+8=x^3+2^3=(x+2)(x^2-2x+4)\\ \\ \\ a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
Can someone explain and tell me how to go about solving this? Will mark brainliest
Answer:
58 cm
Step-by-step explanation:
Assuming that the squares’s sides are whole numbers, we can find the size of the squares by looking at numbers squared. We find three that equal 153.
10²=10x10=100
7²=7x7=49
2²=2x2=4
100+49+4=153
Now we look at how they are put together to find the perimeter.
The 2x2 has 3 exposed sides totaling 6.
The 7x7 has a top and bottom of 7, and part of a third side of 7-2=5. 7+7+5=19
The 10x10 has 3 exposed sides of 10, and part of a third side of 10-7=3. 10+10+10+3=33
TOTAL Perimeter = 6+19+33=58 cm
An expression is shown below:
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of the f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answer:
Part A:
0 = -16x^2 + 22x + 3
x intercepts = (-0.125, 0) and (1.5, 0)
Part B:
It's going to be a maximum. This is because, the graph opens to the bottom. The coordinates are approximately (0.69, 10.56).
Part C:
I would plug in various x values, then solve for the y value. Repeat the process, and get a good idea of the graph.
Hope this helps!
· f(x)= x2 - 49
Identify the number of zeros of the polynomial function
Answer:
x = -7, x = 7
Step-by-step explanation:
Firstly, you are going to set the equation to 0, and then factor it.
Set equation to 0 -----> f(x)= x^2 - 49 will become x^2 - 49 = 0
Now, you're going to factor the equation.
You'll get (x-7) (x+7) upon factoring.
Thirdly, you will set (x-7)(x+7) equal to 0 and also solve for x.
Keep in mind that you'll be treating them as two separate equations
So, ----> (x-7) = 0 (x+7) = 0
When you solve for the x, you'll find out that x is equal to 7 and -7 ---> these are your zeros.
A loaf of bread costs $1.40 and the markup is 30% of the selling price. Find the selling price.
Answer:
The selling price after the markup is $1.82
Step-by-step explanation:
$1.40 * .30 =
Multiply $1.40 times .30 (which is same as 30%)
$1.40 * .30 = $0.42
Add $1.40 and $0.42
= $1.82
Hope this helps.
By Using 0,2,4,5,6 Write The Smallest Number And the Greatest Number
Answer:
smallest is 0 and greatest is 6
simple
Answer:
0 and 6
Step-by-step explanation:
Because 0 is means nothing.And the highest number is 6
Evaluate a + b for a = 12 and b = 6.
Answer:
Here,
a= 12
b = 6
Then,
a+b
= 12 + 6
= 18
.°. 18 is the solution
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{18}}}}[/tex]
Step-by-step explanation:
If the values of variables of algebraic expressions are given, the value of the term or expression can easily obtained by replacing the variables with numbers.
Given, a = 12 and b = 6
[tex] \sf{a + b}[/tex]
plug the values
⇒[tex] \sf{12 + 6}[/tex]
Add the numbers
⇒[tex] \sf{18}[/tex]
Hope I helped!
Best regards!!
In complete sentences explain how you would factor the numeric expression 34 + 12 + 20.
Answer:
We are asked to determine the correct factorization of the given trinomial which is 5x² - 5x -100. The solution to this problem is shown below:
5x² - 5x - 100 let the problem equal to zero such as:
5x² - 5x - 100 = 0 , factor out 5 from the given trinomial
5(x²-x-20) = 0
5 (x-5)(x+4) = 0
The correct factor is 5(x-5)(x+4).
Step-by-step explanation:
which graph shows the line y-1 = 2(x+2)
Answer:
The graph which shows the line y-1=2(x+2) is shown in the attachment
Business/multivariable calc question
help needed asap!!!!
Answer:
There is a min value of 376 located at (x,y) = (9,7)
============================================================
Explanation:
Solve the second equation for y
x+y = 16
y = 16-x
Then plug it into the first equation
f(x,y) = 3x^2+4y^2 - xy
g(x) = 3x^2+4(16-x)^2 - x(16-x)
g(x) = 3x^2+4(256 - 32x + x^2) - 16x + x^2
g(x) = 3x^2+1024 - 128x + 4x^2 - 16x + x^2
g(x) = 8x^2-144x+1024
The positive leading coefficient 8 tells us we have a parabola that opens upward, and produces a minimum value (aka lowest point) at the vertex.
Let's compute the derivative and set it equal to zero to solve for x.
g(x) = 8x^2-144x+1024
g ' (x) = 16x-144
16x-144 = 0
16x = 144
x = 144/16
x = 9
The min value occurs when x = 9. Let's find its paired y value.
y = 16-x
y = 16-9
y = 7
The min value occurs at (x,y) = (9,7)
Lastly, let's find the actual min value of f(x,y).
f(x,y) = 3x^2+4y^2 - xy
f(9,7) = 3(9)^2+4(7)^2 - 9*7
f(9,7) = 376
The smallest f(x,y) value is 376.
If f(x)=logx, show that f(x+h)-f(x)/h=log[1+h/x]^1/h, h=/=0 (Picture attached, thank you!)
Answer:
Step by step proof shown below.
Step-by-step explanation:
To prove the equation, you need to apply the Logarithm quotient rule and the Logarithm power rule. Here's how the quotient rule looks like.
[tex]log_b(x/y) = log_b(x) - log_b(y)[/tex]
And here's how the power rule looks like
[tex]log_a(x)^n = nlog_a(x)[/tex]
First let's apply the quotient rule.
[tex]\frac{f(x+h)-f(x)}{h} = \frac{log_a(x+h)-log_a(x) }{h} = \frac{log_a(\frac{x+h}{x} )}{h}[/tex]
Now we can do some quick simplification, and apply the power rule.
[tex]\frac{1}{h} log_a(1 + \frac{h}{x} ) = log_a(1+\frac{h}{x} )^\frac{1}{h}[/tex]
HCF of x minus 2 and X square + X - 6
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
Given a right triangle with a hypotenuse of 6 cm and a leg of 4cm, what is the measure of the other leg of the triangle rounded to the tenths?
Answer:
4.5 cm
Step-by-step explanation:
a^2+b^2=c^2
A represents the leg we already know, which has a length of 4 cm. C represents the hypotenuse with a length of 6 cm:
4^2+b^2=6^2, simplified: 16+b^2=36
subtract 16 from both sides:
b^2=20
now find the square root of both sides and that is the length of the other leg.
sqrt20= 4.4721, which can be rounded to 4.5
Answer:
4.5 cm
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
One leg is unknown and the other is 4 cm. The hypotenuse is 6 cm.
[tex]a=a\\b=4\\c=6[/tex]
Substitute the values into the theorem.
[tex]a^2+4^2=6^2[/tex]
Evaluate the exponents first.
4^2= 4*4= 16
[tex]a^2+16=6^2[/tex]
6^2=6*6=36
[tex]a^2+16=36[/tex]
We want to find a, therefore we must get a by itself.
16 is being added on to a^2. The inverse of addition is subtraction. Subtract 16 from both sides of the equation.
[tex]a^2+16-16=36-16\\\\a^2=36-16\\\\a^2=20[/tex]
a is being squared. The inverse of a square is a square root. Take the square root of both sides.
[tex]\sqrt{a^2}=\sqrt{20} \\\\a=\sqrt{20} \\\\a=4.47213595[/tex]
Round to the nearest tenth. The 7 in the hundredth place tells us to round the 4 in the tenth place to a 5.
[tex]a=4.5[/tex]
Add appropriate units. In this case, centimeters.
a= 4.5 cm
The length of the other leg is about 4.5 centimeters.
Sean earned 20 points. Charles earned p more points than Sean. Choose the expression that shows how many points Charles earned.
Answer:
the person above is correct if i did this correct
Step-by-step explanation:
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?
Step-by-step explanation:
Given that,
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.
It means that the total number of outcomes are 17
We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11
So, probability is given by :
[tex]P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}[/tex]
[tex]P(E)=\dfrac{11}{17}[/tex]
So, the probability that the toast lands buttered side down is 11/17.
Use De Moivre's theorem to find the indicated power of the complex number. Write the answer in rectangular form.[2(cos10∘ + i sin10∘)]^3.
Answer:
[tex]\bold{4\sqrt3 + i4}[/tex]
Step-by-step explanation:
Given complex number is:
[tex][2(cos10^\circ + i sin10^\circ)]^3[/tex]
To find:
Answer in rectangular form after using De Moivre's theorem = ?
i.e. the form [tex]a+ib[/tex] (not in forms of angles)
Solution:
De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.
As per De Moivre's theorem:
[tex](cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))[/tex]
So, the given complex number can be written as:
[tex][2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3[/tex]
Now, using De Moivre's theorem:
[tex]\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}[/tex]
So, the answer in rectangular form is:
[tex]\bold{4\sqrt3 + i4}[/tex]
which table shows a proportional relationship between x and y?
Answer:
Table C
Step-by-step explanation:
For x and y to be proportional , then the values of
[tex]\frac{y}{x}[/tex] = constant k
Table B
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{3}[/tex] = 2
[tex]\frac{y}{x}[/tex] = [tex]\frac{24}{6}[/tex] = 4
[tex]\frac{y}{x}[/tex] = [tex]\frac{36}{9}[/tex] = 4
The values are not constant
Table C
[tex]\frac{y}{x}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex]
These values are constant
Then Table C shows a proportional relationship between x and y
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
https://brainly.com/question/11234923?referrer=searchResults
What type of triangle has side lengths 9, 10, and √130? A. obtuse B. not a triangle C. acute D. right
Answer: Option C.
Step-by-step explanation:
The lengths of our triangle are:
9, 10 and √130.
If the triangle is a triangle rectangle, by the Pitagoream's theorem we have:
A^2 + B^2 = H^2
in this case H is the larger side, this must be √130.
then:
A and B must be 9 and 10.
9^2 + 10^2 = (√130)^2
81 + 100 = 130
This is false, so this is NOT a triangle rectangle, the hypotenuse is shorter than it should be.
Now, we have some kind of rule:
if A^2 + B^2 = H^2 then we have one angle of 90° and two smaller ones. (triangle rectangle)
if A^2 + B^2 > H^2 then all the angles are smaller than 90°, this is an acute triangle.
if A^2 + B^2 < H^2 then we have one angle larger than 90°, this is an obtuse angle.
(H is always the larger side, A and B are the two shorter ones).
In this case:
81 + 100 > 130
Then this must be an acute angle.
find the solutions to the equation
-3y(2y+5)=0
Answer:
The solutions are y=0, -5/2
Step-by-step explanation:
-3y(2y+5)=0
We can use the zero product property
-3y =0 2y+5 =0
y =0 2y = -5
y = -5/2
The solutions are y=0, -5/2
pls help ill give you 20 points and only correct answers plsss
Answer:
C) Local Eats
Step-by-step explanation:
So this one is pretty simple in retrospect. Just some proportions
Food Queen) 3.60:6=.60:1 1 pound is 60 cents
Grocery Smart) $1/4:1/2= $1/2:1 $1/2=50 cents 1 pound is 50 cents
Fresh Farm) $3:4=$1.50:2=.75:1 1 pound is 75 cents
Local Eats) .49:1 1 pound is 49 cents
As you can see, the answer is C) Local Eats
Step 1:
First, let's convert all of the numbers on the numerator side to decimals. Food Queen, Fresh Farm, and Local Eats are already in decimals, but Grocery Smart is not. 1/4 is 25%, which is equal to 0.25.
Step 2:
We need to convert all the values to represent the price of one pound. To do that, we just divide as written.
Food Queen: 3.00 ÷ 6 = 0.50
Grocery Smart: 0.25 ÷ 0.5 = 0.50
Fresh Farm: 3.00 ÷ 4 = 0.75
Local Eats: 0.49
Our answer: C. Local Eats. $0.49
a word problem on proportions using a unit rate
Lashonda made $273 for 13 hours of work.
At the same rate, how many hours would she have to work to make $231?
hours
Х
?
eleven hours - 11 hours