The area of the given rectangle is 1200 square units.
Given that, width = 30 units and length = 40 units.
What is the area of a rectangle?The formula of the area of a rectangle is used to find the area occupied by the rectangle within its boundary. The area of a rectangle is obtained by multiplying its length and width. Thus, the formula for the area, 'A' of a rectangle whose length and width are 'l' and 'w' respectively is the product "l × w".
Now, the area of a rectangle = 40 × 30
= 1200 square units
Therefore, the area of the given rectangle is 1200 square units.
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Jesse and three friends buy snacks for a hike. They buy trail mix for $5.42, apples for $2.55, and granola bars for $3.39. If the four friends split the cost of the snacks equally, how much should each friend pay?
Answer:
$2.84 is your answer
Catherine walks her dog 3/4 mile everyday how far does she walk each week
need this solved (3x+2y)(5x-6y)
tina wants to save money for school. tina invests 1100 in an account that pays an interest of 7.25%. how many years will it take the account to reach 6600?
It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.
Explanation:This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.
In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).
Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.
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A student got 34 pencils for school. If she sharpen 16 of the pencils before school what is her ratio of unsharpened pencils to sharpened pencils
34-16 = 18
so 18 are unsharpened
ratio is 18/16 reduced to 9/8
Mr. Small, the store manager for Jay's Appliance, is having a difficult time placing a selling price on a refrigerator that cost $410. Mr. Small knows his boss would like to have a 45% markup based on cost. The selling price should be
Answer:
$594.50
Step-by-step explanation:
1. Divide markup into decimal form
45/100 = .45
2. multiply by cost of Refrigerator
.45 x 410 = $184.50
3. Add markup cost to original Refrigerator cost.
184.50 + 410 = $594.50
Which of the following terms, when added to the given polynomial, will change the end behavior?
y = –2x7 + 5x6 – 24
a)–x8
b)–3x5
c)5x7
d)1,000
e)–300
Answer:
1.A
2.C
Step-by-step explanation:
The end behaviour of the polynomial function y = -2x⁷ + 56x⁶ - 24 will change for a) - x⁸ and c) 5x⁷.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Given, a polynomial function y = -2x⁷ + 56x⁶ - 24.
So, the given polynomial function has a degree of 7 and its end behavior will be changed by adding or subtracting terms that are of degree 7 and higher.
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The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is........
You toss a coin a randomly selecte a number from 0 to 9. What is the probability of getting tails and selecting a 9?
A.0.05
B.0.95
C.0.25
D.0
the area of a square is 225 square inches. find the length of a side of the square.
What is the average rate of change of f(x), represented by the graph, over the interval [0,2]?
A: 2
B: 1
C: 0.5
D: -0.5
The school cafeteria is baking cookies for lunch. each student gets 3 cookies with their lunch. if there are 231 children buying lunch, how many cookies do they have to make?
Four students are playing the same video game. Their scores for the first three level are added together to see if the student has enough points to move on to round 2
This question is a high school-level mathematics problem involving statistics and data interpretation related to video game scores and soccer game performance.
Explanation:The question involves analyzing and interpreting different sets of data related to video game scores, hours played, and goals scored in soccer games. This requires an understanding of statistics and mathematical data interpretation techniques. Problems similar to these are often encountered in high school mathematics classes, especially those focusing on statistics and probability.
For example, when dealing with video game scores, a student may need to sumup numbers, compare totals, or calculate averages. In the case of the hours of video games played, one may need to aggregate data and analyze distributions. With soccer goals per game, the student might have to compute means and assess performance across different groups. Furthermore, the mention of a 'communist model' of grading ties into mathematical concepts of averaging and distribution of data.
These types of problems help students appreciate the practical applications of mathematics in understanding and interpreting real-world scenarios such as video game scoring systems and sports team performance analysis.
distributive property of the product of 127 and 32
Suzanne bought 50 apples at the apple orchard she bought four times as many red apples has green apples how many more red apples and green apples that Suzanne buy
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3427 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 65.75 feet per second and Plane B is gaining altitude at 35.5 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude.
Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. are the given families of curves orthogonal trajectories of each other? that is, is every curve in one family orthogonal to every curve in the other family? x2 + y2 = ax x2 + y2 = by
Yes, the given curves are orthogonal. A further explanation is below.
Given equation is:
[tex]x^2+y^2=ax[/tex]By differentiating both sides, we get
→ [tex]2x+2yy'=a[/tex]
→ [tex]y'=\frac{a-2x}{2y} = m_1[/tex]
again,
[tex]x^2+y^2=by[/tex]By differentiating both sides, we get
→ [tex]2x+2yy' =by'[/tex]
→ [tex]y' = \frac{-2x}{2y-b}[/tex]
For both curves are orthogonal, we get
→ [tex]m_1 \ m_2 = -1[/tex]
By substituting the values, we get
→ [tex]\frac{(a-2x)}{2y} \ \frac{(-2x)}{2y-b} = -1[/tex]
→ [tex]-2ax +4x^2=-4y^2+2yb[/tex]
→ [tex]4(x^2+y^2)=2ax+2yb[/tex]
Since,
[tex]ax=x^2+y^2[/tex][tex]by=x^2+y^2[/tex]then,
→ [tex]4(x^2+y^2) =2(x^2+y^2)+2(x^2+y^2)[/tex]
→ [tex]4x^2+4y^2=4x^2+4y^2[/tex] (true)
Thus the above response is appropriate.
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What is the image of E for a dilation with center (0, 0) and a scale factor of 6?
(30, 6)
(-30, 6)
(30, -1)
(-30, 1)
Answer:
-30, 6
Step-by-step explanation:
6x-5= =30
1x6=6
a patient is to take 4 1/4 tablespoons of medicine per day in 5 equally divided doses. how much medicine is to be taken in each dose?
Follow below steps:
A patient is to take 4 1/4 tablespoons of medicine per day in 5 equally divided doses. How much medicine is to be taken in each dose?
Convert 4 1/4 tablespoons to a proper fraction, which is 17/4 tablespoons.
Divide 17/4 by 5 to find out how much medicine is to be taken in each dose. This equals 17/4 ÷ 5 = 17/4 × 1/5 = 17/20 tablespoons.
Value of the expression
Josh rented a truck for one day. There was a base fee of$14.99,and there was an additional charge of81cent for each mile driven. Josh had to pay$117.05 when he returned the truck. For how many miles did he drive the truck
52 companies; 25% increase
Gwen has a £5 note and a £2 coin
A liter of cola costs £1.25
Gwen buys as many liter bottles as she can
How much money will she have left over
She will have £0.75 left over after the purchases.
First, we calculate the total amount of money Gwen has:
£5 (note) + £2 (coin) = £7
Next, we determine how many liter bottles of cola Gwen can buy:
Each bottle costs £1.25
Number of bottles she can buy = £7 ÷ £1.25
= 5 bottles
Now, we compute the total cost of 5 bottles:
5 bottles × £1.25/bottle
= £6.25
Finally, we find out how much money Gwen will have left over:
Total money - Total cost = £7 - £6.25
= £0.75
Gwen will have £0.75 left over after buying as many liter bottles of cola as she can.
Complete the square
Melanie connected a brown garden hose, a green garden hose, and a black garden hose to make one long hose. The brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. What is the farthest distance the one long hose can reach?
Answer:
35.65 feet.
Step-by-step explanation:
We have been given that the brown hose is 10.75 feet long, the green hose is 16.4 feet long, and the black hose is 8.5 feet long. We are asked to find the distance that one long hose can reach.
The length of one long hose will be equal to sum of distances of each hose.
[tex]\text{The length of one long hose}=10.75\text{ ft}+16.4\text{ ft}+8.5\text{ ft}[/tex]
[tex]\text{The length of one long hose}=35.65\text{ ft}[/tex]
Therefore, the one long hose can reach 35.65 feet.
The student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?
The probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).
Given:
Probability of selecting a female student (success), ( p = 0.60 )
Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )
Sample size, ( n = 8 )
We need to calculate the probability of selecting at least 7 female students from the sample.
Calculate the probability of selecting exactly 7 female students:
[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]
[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]
[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]
[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]
[tex]\[ = 0.1119744 \][/tex]
Calculate the probability of selecting exactly 8 female students:
[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]
[tex]\[ = (0.60)^8 \][/tex]
[tex]\[ = 0.60^8 \][/tex]
[tex]\[ = 0.16777216 \][/tex]
Add the probabilities from Step 1 and Step 2 to get the final probability:
[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]
[tex]\[ = 0.1119744 + 0.16777216 \][/tex]
[tex]\[ = 0.27974656 \][/tex]
So, the probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
The circumference of circle p is 800 mm, the circumference of circle q is 200 cm, and the circumference of circle r is 4 m. What is the sum of the distance around each circle
Let us use the following conversions:
1 cm = 10 mm
1 meter = 100 cm = 1000 mm
Given:
p = 800 mm
q = 200 cm = 2000 mm
r= 4 m = 4000
X = sum of the distance around each circle
X = p+q+r
X = 800+2000+4000
X = 6800 mm or 680 cm or 6.80 m
Find the measure of angle y. Round your answer to the nearest hundreth.
if R and S are two points in a plane, the perpendicular bisector of line RS is the set of all points equidistant from R and S. True or false?
Answer: True
Step-by-step explanation: