Answer:
total amount paid = 32.5 + 28.9 + 24.95 = 86.35
20% of the total amount paid = 0.2 * 86.35 = 17.27
you tip 17.25$
The perimeter of a rectangle is 80 cm. Find the lengths of the sides of the rectangle giving the maximum area.Enter the answers for the lengths of the sides in increasing order.
Answer:
The lengths of the sides are 20 cm and 20 cm
Step-by-step explanation:
Given
Perimeter, P = 80cm
Represent the length and width with L and W, respectively;
[tex]P= 2*(L + B)[/tex]
Substitute 80 for P
[tex]80 = 2 * (L + B)[/tex]
Divide through by 2
[tex]40 = L + B[/tex]
[tex]L + B = 40[/tex]
Make L the subject of formula
[tex]L = 40 - B[/tex]
Area of a rectangle is calculated as thus;
[tex]Area = L * B[/tex]
Substitute 40 - B for L
[tex]Area = (40 - B) * B[/tex]
Express this as a function
[tex]A(B) = (40 - B)* B[/tex]
[tex](40 - B)* B = A(B)[/tex]
Set A(B) = 0 to determine the roots
Hence;
[tex](40 - B)* B = 0[/tex]
[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]
[tex]40 = B[/tex] or [tex]B = 0[/tex]
[tex]B = 40[/tex] or [tex]B = 0[/tex]
The maximum area of a rectangle occurs at half the sum of the roots;
So;
[tex]B= \frac{B_1 + B_2}{2}[/tex]
[tex]B= \frac{40+0}{2}[/tex]
[tex]B= \frac{40}{2}[/tex]
[tex]B = 20[/tex]
Recall that [tex]L = 40 - B[/tex]
[tex]L = 40 - 20[/tex]
[tex]L = 20[/tex]
Hence the lengths of the sides are 20 cm and 20 cm
What is the approximate area of a circle enclosed by a piece of rope 50.24 inches long? (Use the fact that π ≈ 3.14 to make your calculations.)
Answer:
the approximate area of this circle is 200.96 inches long.
Step-by-step explanation:
To answer this problem we need to remember that the area of a circle is given by the formula:
Area = π[tex]r^2[/tex] where r is the radius.
and the perimeter is:
Perimeter = 2πr
Now, the problem tells us that the circle is enclosed by a piece of rope that's 50.24 inches long. So the perimeter of the circle is 50.24 inches.
Since we have the value of the perimeter and the value of pi, we are going to substitute these values in the perimeter formula to find r.
Perimeter = 2πr
50.24=2(3.14)r
50.24= 6.28r
50.24/6.28= r
8= r
Thus, the radius of the circle is 8 inches long.
Now, we can use this value to find the area of the circle:
Area = π[tex]r^2[/tex]
Area = π[tex]8^2[/tex]
Area = 3.14 (64)
Area = 200.96
Therefore, the approximate area of this circle is 200.96 inches long.
The approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
The length of rope by which a circle is made, is known as circumference of circle.
Circumference of circle = [tex]2\pi r[/tex] , where r is radius of circle.
Since, length of rope is 50.24 inches.
[tex]2\pi r=50.24\\\\r=\frac{50.24}{2*3.14}=8 inch[/tex]
Area of circle = [tex]\pi r^{2}[/tex]
= [tex]3.14 *(8)^{2}=200.96[/tex] square inch
Thus, the approximate area of a circle enclosed by a piece of rope is 200.96 square inch.
Learn more:
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In a study of pain relievers, 50 people were given product A, and 35 experienced relief. In the same study, 25 people were given product B, and 19 experienced relief. Fill in the blanks of the statement below to make the statement the most reasonable possible. Product __ performed better in the study because __% got relief with this product, whereas only __% got relief from product __
Answer:
Product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
Step-by-step explanation:
Product A
Total number of people tested = 50
Total number o who experienced relief using product A
= 35
% of people who got relief using product A
= 35/50 x 100%
= 70%
Product B
Total number of people tested = 25
Total number of people who experienced releif using product B
= 19
% of peope who got relief using product B
= 19/25 x 100%
= 76%
From the above:
76% of people got relieved whilst using product B
70% who got relieved using product A.
Therefore, product B performed better in the study because 76% got relief with this product, whereas only 70% got relief from product A
What is the product of 2p + q and -39 - 6p + 1?
0 -12p2 - 6pq – 4p - 32 + 1
O-12p2- 12pq + 2p – 392 +9
- gp² q² + 12pq - 2p + 9
12p2 + 12pq +2p + 302 + 9
Answer:
Option (2)
Step-by-step explanation:
In this question we have to find the multiplication of the two expressions.
(2p + q)(-3q - 6p + 1)
= 2p(-3q - 6p + 1) + q(-3q - 6p + 1) [By distributive property]
= -6pq - 12p²+ 2p - 3q² - 6pq + q
= -12p² - (6pq + 6pq) - 3q² + 2p + q
= -12p² - 12pq + 2p - 3q² + q
Therefore, Option (2) will be the correct option.
x+3y-Z=0
2x+y+Z=1
3X-y+Z=3
Evaluate the polynomial when x = 3 and y = - 8
x2 + y2 + xy
Work Shown:
Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.
x^2 + y^2 + x*y
3^2 + (-8)^2 + 3*(-8)
9 + 64 - 24
73 - 24
49
Answer:
49
Step-by-step explanation:
We are given the polynomial:
[tex]x^2+y^2+xy[/tex]
We want to evaluate when x=3 and y= -8. Therefore, we must substitute 3 for each x and -8 for each y.
[tex](3)^2+(-8)^2+(3*-8)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Solve the parentheses first. Multiply 3 and -9.
3*-8=-24
[tex](3)^2+(-8)^2 + -24[/tex]
[tex](3)^2+(-8)^2-24[/tex]
Now, solve the exponents.
3^2= 3*3 =9
[tex]9+ (-8)^2 -24[/tex]
-8^2= -8*-8= 64
[tex]9+64-24[/tex]
Add 9 and 64
[tex]73-24[/tex]
Subtract 24 from 73
[tex]49[/tex]
The polynomial evaluated for x=3 and y= -8 is 49.
Drag the ruler over each side of the triangle to find its length. The length of AB is . The length of BC is . ASAP Drag the protractor over each angle to find its measure. The measure of angle C is . The measure of angle B is .
Answer:
Drag the ruler over each side of the triangle to find its length.
The length of AB is
✔ 5
.
The length of BC is
✔ 4
.
Drag the protractor over each angle to find its measure.
The measure of angle C is
✔ 90°
.
The measure of angle B is
✔ 36.9°
.
Step-by-step explanation:
The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Drag the ruler over each side of the triangle to find its length.
The length of side AB of the triangle is 5 units.
The length of side BC of the triangle is 4 units.
Drag the protractor over each angle to find its measure.
The measure of angle C of the triangle is 90°.
The measure of angle B of the triangle is 37°.
The length of sides AB and BC of the triangle will be 5 units and 4 units.
And the measure of angle C and angle B of the triangle will be 90° and 37°.
More about the right-angle triangle link is given below.
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An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented 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{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
Please answer this correctly without making mistakes
Answer:
17/16 OR [tex]1\frac{1}{16}[/tex] minutes
Step-by-step explanation:
Since Jayla spent 1/16 of a minute AND one whole minute watching a millipede crawl, we'd need to first add the two numbers.
Since the given minute is out of 16, we can convert the one minute to 16/16. This means we can add the other 1/16 of a minute.
This leaves us with Jayla watching the millipede for 17/16 OR [tex]1\frac{1}{16}[/tex] minutes.
Hope this helps!! <3 :)
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )
Question 2 of 10
What is the slope of the line x = 3?
Answer:
[tex]\boxed{\mathrm{U n d e f i n e d \ slope }}[/tex]
Step-by-step explanation:
x = 3 is a vertical line.
The slope of a vertical line is undefined.
5 STARS IF CORRECT! Can you find the value of an expression when values for x and y are given? Explain.
If the expression has only two variables [tex] x[/tex] and $y$, or if there's just one variable out of these two, then the answer is yes.
If the expression has more variables (other than X and y), then the answer is no.
The radius of a circle measures 5 inches A central angle of the circle measuring 12 radians cuts off a sector
What is the area of the sector?
Enter your answer as a simplified fraction in the box
area =
inches squared
Answer:
25/4 square inches
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = (1/2)r²θ
where r is the radius and θ is the central angle in radians.
For your sector, the area is ...
A = (1/2)(5 in)²(1/2) = 25/4 in²
Nan lives 13 miles from the airport. Felipe lives 6 miles from the airport.
How many more miles does Nan live from the airport than Felipe?
Answer:
7
Step-by-step explanation:
it's simply 13 - 6
7 it the answer, that was easy
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
Find the midpoint of the segment connecting (−1.8, 1.9) and (1.2, 2.7).
Answer:
(-0.3, 2.3)
Step-by-step explanation:
(-1.8+1.2)/2 = -0.3
(1.9+2.7)/2 = 2.3
Answer:
( - 0.3 , 2.3 )Step-by-step explanation:
Let the points be A and B
A ( - 1.8 , 1.9 ) ⇒( x₁ , y₁ )
B ( 1.2 , 2.7 )⇒ ( x₂ , y₂ )
Now, let's find the midpoint:
[tex] \mathsf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} )}[/tex]
Plug the values
[tex] \mathsf{ = (\frac{ - 1.8 + 1.2}{2} \: , \frac{1.9 + 2.7}{2} )}[/tex]
Calculate
[tex] \mathsf{ = ( \frac{ - 0.6}{2} \: , \frac{4.6}{2} )}[/tex]
[tex] \mathsf{ = (- 0.3 \:, 2.3)}[/tex]
Hope I helped!
Best regards!
The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2
Answer: [tex]4x^2-21x-2[/tex] .
Step-by-step explanation:
Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].
Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])
[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]
Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .
ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
Diabetic patients have normally distributed cholesterol with mean 200 and standard deviation=10.
Find the percentage of patients whose cholesterol is between 198 mg/dL and
207 mg/dL ?
Answer:
The percentage of patients whose cholesterol is between 198 mg/dL and 207 mg/dL is 33.73%
Step-by-step explanation:
To calculate this proportion, we follow the probability route, using the z-score statistics
Mathematically;
z-score = (x-mean)/SD
from the question, mean = 200 and SD = 10
So for 198
z-score = (198-200)/10 = -2/10 = -0.2
For 207
z-score = (207-200)/10 = 7/10 = 0.7
So the probability we want to calculate is;
P(-0.2<z<0.7)
Mathematically this can be calculated as;
P(z<0.7) - P(z<-0.2)
We can calculate the required probability using the standard normal distribution table
P(-0.2<x<0.7) = 0.3373 from the standard distribution table
So it is this 0.3373 that we now convert to percentage and that is 33.73%
You are investing $5,000 and can invest for 2 years or 3 years at 1.75% and 1.25% interest rates, respectively. Which earns more interest
Answer:
The 3 years investment earns more interest
Step-by-step explanation:
Given
Principal, P = $5,000
Required
Determine which earns more interest
When Rate = 1.75% and Year = 2
Interest is as follows;
[tex]I = \frac{PRT}{100}[/tex]
Substitute 1.75 for R, 5000 for P and 2 for T
[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]
[tex]I = \frac{17500}{100}[/tex]
[tex]I = \$175[/tex]
When Rate = 1.25% and Year = 3
Interest is as follows;
[tex]I = \frac{PRT}{100}[/tex]
Substitute 1.25 for R, 5000 for P and 3 for T
[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]
[tex]I = \frac{18750}{100}[/tex]
[tex]I = \$187.5[/tex]
Comparing the interest of both investments, the 3 years investment earns more interest
Lauren bought 4 bags of popcorn for $3.00. What is the unit rate per bag of popcorn."?
Answer:
$0.75
Step-by-step explanation:
Given that
Number of bags of popcorn bought = 4
Total money spent = $3.00
To find:
Unit rate per bag of popcorn = ?
i.e. price of one bag of popcorn is to be find out.
Solution:
We can use ratio here to find the rate of one bag of popcorn.
4 bags bought at $3
4 bags : $3
Let us divide both the sides with 4.
[tex]\frac{4}4[/tex] bags : $ [tex]\frac{3}4[/tex]
OR
1 bag bought at $ 0.75
We can alternatively use unitary method.
4 bags are bought at $ 3
1 bag is bought at $ [tex]\frac{3}{4}[/tex]
1 bag is bought at $0.75.
So, unit rate per bag of popcorn is $0.75.
Найдите наибольшее значение функции y=8ln(x+7)-8x+3 на отрезке [-6,5;0]
Answer:
Maximum at (-6,51), or value of f(-6) = 51
Step-by-step explanation:
f(x) = 8*log(x+7)-8*x+3
differentiate with respect to x
f'(x) = 8/(x+7) -8
To find maximum, set f'(x) = 0
f'(x) = 8/(x+7) -8 = 0
solver for x
x= -6
evaluate f(x) at x=-6
f(-6) = 8log(-6+7) - 8(-6) + 3
= 0 +48 +3
= 51
Note: next time please post only in English. This post will soon be deleted.
If you move from zero to 15 on the number line, you are representing all of the following exce
the opposite of -15
the opposite of 15
the absolute value of 15
the distance between zero and 15
Answer: the opposite of 15
Step-by-step explanation:
Every number 'a' on number line is exactly opposite of '-a'.
So, 15 is the opposite of '-15'
Also absolute value for any number gives its positive value, soabsolute value of 15 = 15
Moving 0 to 15 gives the distance between zero and 15.
So all statements are true except "the opposite of 15".
Hence, the required statement is "the opposite of 15".
Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft
Answer:
Height = 4 feet
Step-by-step explanation:
To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree
But the tree is 32 feet tall but on shadow it's 160
So lemme determine how long I'll be in my shadow first
Distance away from tree= 140 feet
Length of shadow cast by tree
= 160 feet
Length of shadow= 160-140
Length if shadow= 20 feet
My height= x
X/20= 32/160
X= 20*32/260
X = 4 feet
Height = 4 feet
Help please I need help as soon as possible!all answers are appreciated! Keisha tried to evaluate an expression step by step. 3+(−4)−7
Answer:
D no mistakes
Step-by-step explanation:
3+(-4)-7 is equal to 3-4-7=-8
Answer:0
Step-by-step explanation:
3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0
Find usubscript10 in the sequence -23, -18, -13, -8, -3, ...
Step-by-step explanation:
utilise the formula a+(n-1)d
a is the first number while d is common difference
Answer:
22
Step-by-step explanation:
Using the formular, Un = a + (n - 1)d
Where n = 10; a = -23; d = 5
U10 = -23 + (9)* 5
U10 = -23 + 45 = 22
Using only the confidence interval approach, at LaTeX: \alpha α = 0.05, the conclusion about the LaTeX: \beta β1 hypothesis test is:
Answer:
Reject the null hypothesis because the value of null is outside the interval.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
if Israel spends the most time on social media with an average of 11.1 and peru spends a total time of 8.3 how much more time does israel spend on social media than peru
Answer:
israel spends 2.8 more (units) than peru.
Step-by-step explanation:
11.1 - 8.3 = 2.8, so israel spends 2.8 (units), more on social media.
If Discriminant > 0 :
What is "m" in ( 2x^2 + 4x + 1 - 3m=0) ?
The given equation is in the form ax^2+bx+c = 0 with
a = 2b = 4c = 1-3mD = discriminant
D = b^2 - 4ac
D = 4^2 - 4(2)(1-3m)
D = 16 - 8(1-3m)
D = 16 - 8 + 24m
D = 24m + 8
D > 0
24m + 8 > 0
24m > -8
m > -8/24
m > -1/3
As long as m is larger than -1/3, then the discriminant is positive. There are infinitely many solutions to pick from.
