This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.
If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula[tex]R125/(2^t)[/tex] = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula [tex]R125/(2^t)[/tex] for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.
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Any two angles are _____ if the sum of their measures is 90° or ____ if the sum of their measures is 180°
1)
adjacent angles
vertical angles
complementary
supplementary
right angles
in a circular group O is the centre ,AB the diameter,C and D are any two points on the circumference so that C is the mid - point of arc BD prove that triangle AOC and triangle COA are equal in area
Step-by-step explanation:
1st method:-
Using congurency:-
In ∆AOC AND ∆COD
1) CO= CO {common side}
2) <OAC = <ODC { inscribed angel on same base CO}
3)OD = OC {radius}
4)∆AOC ≅ ∆COD {SAS fact}
5)∆AOC = ∆ COD {area of congurent traingle is equal}
2nd method:-
Using property of traingles:-
Construction:- Join DA and CB
<ACB = 90° { angle substended by diameter}
CO⊥AB
Now we know that,
Area of traingle = 1/2 B*H
CO is height { of both traingle's}
AO is base {of both traingle's}
Now, ∆AOC= 1/2*CO*AO--1
and, ∆ COD = 1/2 *CO*AO--2
∆AOC= ∆COD {from above 1 and 2}
consider a deck of 52 cards. one deals 4 cards in a row with no replacement. what is the probability that the first three cards are 3 aces and the last one is a king ?
The probability of the first three cards being 3 aces and the last one being a king is 1/66,300.
The probability of drawing an ace from a deck of 52 cards is 4/52 (since there are 4 aces in the deck), and the probability of drawing a king is 4/52 as well.
Since the cards are dealt with no replacement, the probability of drawing three aces in a row is
(4/52) × (3/51) × (2/50) = 1/5525
This is because after each card is drawn, there is one less ace in the deck, and one less card overall.
Now, we need to multiply this probability by the probability of drawing a king as the fourth card. Since there are only 48 cards left in the deck at this point (since three cards have already been drawn), the probability of drawing a king is
4/48 = 1/12
Therefore, the probability of drawing 3 aces and 1 king in a row is
(1/5525) × (1/12) = 1/66300
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What is the cost of 4 kilograms if the unit rate is $3.25kg?
The cost of 4 kilograms is $13 if the unit rate is $3.25kg.
What is the unit rat?
The unit rate is a rate in which the second term in the ratio is 1. For example, if you have a rate of 60 miles per hour, the unit rate would be 60 miles per 1 hour, or simply 60 miles per hour. Another example is if you have a unit price of $2.50 per pound of apples, the unit rate would be $2.50 per 1 pound, or simply $2.50 per pound.
If the unit rate is $3.25/kg, then the cost of 1 kg is $3.25. To find the cost of 4 kg, we can multiply the cost of 1 kg by 4:
4 kg x $3.25/kg = $13
Therefore, the cost of 4 kilograms is $13 if the unit rate is $3.25kg.
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In the first week of July, a record 1,060 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week,130 more people went to the pool than in the second week. In the fourth week, 232 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the local swimming pool over four weeks, starting with a record high of 1,060 people in the first week, was 20%.
To find the percent decrease in the number of people who went to the pool over the four weeks, we need to first find the total number of people who went to the pool over the four weeks and then calculate the percentage decrease from the first week to the fourth week.
Number of people in the first week = 1,060
Number of people in the second week = 1,060 - 110 = 950
Number of people in the third week = 950 + 130 = 1,080
Number of people in the fourth week = 1,080 - 232 = 848
Total number of people over the four weeks = 1,060 + 950 + 1,080 + 848 = 3,938
Percentage decrease in the number of people who went to the pool over the four weeks = ((1,060 - 848)/1,060) * 100% = 20%
Therefore, the percent decrease in the number of people who went to the pool over the four weeks is 20%.
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A shirt is discounted at 65% off. The original price is $85.
What is the sales price?
O $24.50
O $42.50
O $29.75
O $32.75
It's 29.75
I divided 85 with 100, which gave me 0.85. Then i calculated the new price(35% of the original one) and i multiplied them.
Hope this helps.
ACT is normally distributed with µ = 21.0 and σ = 5.5. What proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28)?
The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is 0.607.
How to determine the proportionThe proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is given by the formula:
P(18 < X < 28) = P(Z < (28 - 21)/5.5) - P(Z < (18 - 21)/5.5)
We can then calculate the z-scores for the lower and upper bounds of the range as follows:
Z1 = (28 - 21)/5.5 = 1.27Z2 = (18 - 21)/5.5 = -0.55
Using a z-table or calculator, we can find the probabilities associated with these z-scores:
P(Z < 1.27) = 0.898P(Z < -0.55) = 0.291
Therefore,P(18 < X < 28) = P(Z < 1.27) - P(Z < -0.55) = 0.898 - 0.291 = 0.607
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If c = 47. 74 ft and a = 28. 82 ft, find B
The value of B using Sine law is approximately 41.7 degrees.
To use the sine law to find angle B, we need to have either the length of side b or the sine of angle B. However, we can use the sine law to set up an equation involving sine B and then solve for it.
the sine law states:
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.
In this case, we are given a = 28.82 ft, c = 47.74 ft, and we want to find B. We can set up the following equation using the sine law:
a/sin A = c/sin C
Substituting the given values:
28.82/sin A = 47.74/sin C
Now, we need to find sin A and sin C. Since the angles in a triangle add up to 180 degrees, we have:
A + B + C = 180
We know that A and C are the angles opposite to sides a and c, respectively, so we can use the sine ratio to express them in terms of a and c:
sin A = a/cos B
sin C = c/cos B
Substituting these expressions into the equation above, we get:
28.82/(a/cos B) = 47.74/(c/cos B)
Simplifying and solving for cos B, we get:
cos B = (28.82 * c) / (a * 47.74)
Now that we know cos B, we can use the identity sin^2 B + cos^2 B = 1 to find sin B:
sin B = sqrt(1 - cos^2 B)
Substituting the given values, we get:
sin B = sqrt(1 - ((28.82 * 47.74) / (a * c))^2)
Calculating this expression gives:
sin B = 0.667
Therefore, angle B is:
B = sin^-1(0.667) = 41.7 degrees (rounded to one decimal place)
So, angle B is approximately 41.7 degrees.
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_____The given question is incomplete, the complete question is given below:
If c = 47. 74 ft and a = 28. 82 ft, find B using sine law.
Can someone help me with this I’ll give you brainlest
Answer:
g(4)=-2 and g(-4)=1
Step-by-step explanation:
Find the surface area of the triangular prism shown below. units^2 2 5, 5, 7, 4, 6
Therefore, the surface area of the given triangular prism is approximately 126.56 square units.
What is surface area?Surface area is a measure of the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces or surfaces of an object. Surface area is usually expressed in square units, such as square inches, square centimeters, or square meters, depending on the unit system being used.
For example, if you have a cube with side length "s", its surface area can be calculated by finding the area of each face and adding them together. Since a cube has six square faces of equal size, the formula for its surface area would be:
Surface Area of Cube = 6s²
by the question.
To find the surface area of a triangular prism, we need to calculate the area of all its faces and then add them together.
First, let's find the area of the two triangular bases. Each base is a right triangle with base 5, height 4, and hypotenuse 7. We can use the Pythagorean theorem to calculate the height of the triangle:
[tex]4^2 + (5/2)^2 = h^2[/tex]
[tex]16 + 6.25 = h^2[/tex]
[tex]22.25 = h^2[/tex]
[tex]h = \sqrt(22.25)[/tex]= 4.71
So, the area of each base is:
[tex]A = 1/2 * base * height = 1/2 * 5 * 4.71 = 11.78[/tex]
Next, we need to find the area of the three rectangular faces. The two congruent rectangular faces have dimensions of 5 by 6, and the remaining rectangular face has dimensions of 7 by 6. The area of each rectangular face is simply the product of its dimensions:
[tex]A1 = 5 * 6 = 30[/tex]
[tex]A2 = 5 * 6 = 30[/tex]
[tex]A3 = 7 * 6 = 42[/tex]
Finally, we can calculate the total surface area of the prism by adding up the areas of all five faces:
[tex]Total surface area = 2A(base) + A1 + A2 + A3[/tex]
[tex]Total surface area = 2(11.78) + 30 + 30 + 42[/tex]
[tex]Total surface area =126.56[/tex]
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99 cookies were diveded into three piles in the ratios of 1:1/2:1/3. how many cookies were in the middle pile
To the total of 99 cookies, there are 27 cookies in middle pile.
Let's call the number of cookies in the first pile "x". Then, the number of cookies in the second pile is 1/2 of x, or (1/2)x, and the number of cookies in the third pile is 1/3 of x, or (1/3)x.
We know that the total number of cookies is 99, so we can write an equation:
x + (1/2)x + (1/3)x = 99
To solve for x, we can first find a common denominator:
(6/6)x + (3/6)x + (2/6)x = 99
(11/6)x = 99
x = (6/11) * 99
x = 54
So, there are 54 cookies in the first pile, (1/2)x = (1/2)*54 = 27 cookies in the second pile, and (1/3)x = (1/3)*54 = 18 cookies in the third pile. In the middle pile there are 27 cookies.
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Please view the image to understand the problem.
The table of values is completed below and the function of the sequence is T(n) = n(n + 2)
Completing the table of valuesFrom the question, we have the following parameters that can be used in our computation:
Pattern Counters
1 3
2 8
3 15
4 24
When the pattern is 5, we have
Counters(5) = 5 * (6 + 1)
So, we have
Counters = 35
So, the table is
Pattern number 1 2 3 4 5
Number of counters 3 8 15 24 35
The expression for the n-th termIn (a), we have
Counters(5) = 5 * (6 + 1)
Express 6 as 5 + 1
So, we have
Counters(5) = 5 * (5 + 1 + 1)
So, we have
Counters(n) = n * (n + 1 + 1)
As an n-th term, we have
T(n) = n(n + 2)
Hence, the function is T(n) = n(n + 2)
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You have $
48
to order pizza for you and your friends. Slices of pizza are $
3.20
each. The inequality representing this scenario is 3.20
n
≤
48
, with n
representing the number of pizza slices you can order.
Select all the numbers that represent the amount of pizza slices you can order for you and your friends.
It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.
To determine how many pizza slices you can order with $48, we divide the total amount of money by the cost of each slice of pizza, which is $3.20. This gives us:
48 ÷ 3.20 = 15
So you can order up to 15 slices of pizza with $48. However, since you cannot order a fraction of a slice, the actual number of slices must be a whole number. Therefore, the possible numbers of pizza slices you can order are:
0 slices
1 slice
2 slices
3 slices
4 slices
5 slices
6 slices
7 slices
8 slices
9 slices
10 slices
11 slices
12 slices
13 slices
14 slices
15 slices
So, any of the above numbers represents the amount of pizza slices you can order for you and your friends. It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.
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2. Mrs. Garcia had two thirds of a pumpkin pie left. Her sons ate of three eighths
what was left. What fraction of the whole pie did her
sons eat?
Answer: 1 1/24
Step-by-step explanation:
2/3 - 3/8 = 25/24. Reduce it and you get 1 1/24
ratio of triangle 9:8:7, permimeter is 144 , find the measure of each side of the triangle
Step-by-step explanation:
There are (9+8+7) = 24 parts that add up to 144
each part is then 144/24 = 6
then each side is 9 parts = 9*6 = 54
8 parts = 8 * 6 = 48
7 parts 7 * 6 = 42
What fraction of a semicircle is an angle that measures 29pi/18 radians? Express your answer as a fraction in simplest terms.
Answer:
A semicircle has an angle measure of pi radians. Therefore, the fraction of a semicircle that an angle of 29pi/18 radians represents is:
(29pi/18) / pi = 29/18
So the fraction of a semicircle that an angle of 29pi/18 radians represents is 29/18.
Step-by-step explanation:
La suma de las edades de Andrés, Carlos y Rodolfo es de 90 años. La edad de Andrés excede en 4 años a la edad de Carlos y en 11 a la de Rodolfo. Determina las edades de los tres
Andrés is 35 years old, Carlos is 31 years old, and Rodolfo is 24 years old based on the sum is given.
Let's assume the age of Andrés is x years.
According to the problem, Carlos' age is (x - 4) years and Rodolfo's age is (x - 11) years.
Now, we know that the sum of their ages is 90, so we write an equation:
x + (x - 4) + (x - 11) = 90
Simplify following equation:
3x - 15 = 90
Adding 15 to both sides, we get:
3x = 105
Dividing by 3, we get:
x = 35
So Andrés' age is 35 years.
Carlos' age is (x - 4) = 31 years.
Rodolfo's age is (x - 11) = 24 years.
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Translation: The sum of the ages of Andrés, Carlos and Rodolfo is 90 years. Andrew's age exceeds Carlos' age by 4 years and Rodolfo's by 11. Determine the ages of all three
Subtract the sum of three hundredths and 256 tenths from 41435 hundredths
The resultant substraction value of the sum of three hundredths and 256 tenths from 41435 hundredths is equals to the 388.72.
Subtraction is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation representing the removal of an object from a collection. This is indicated by the symbol '-'. For example, there are 5 − 2 books meaning 5 books with 2 taken away, resulting in a total of 3 books. We have sum of three hundredths and 256 tenths. First, 3 hundredths means 3 out of 100, which can be denoted as = 3/100 = 0.03. Similarly, 256 tenth means 256/10 = 25.6. So, the sum of three hundredths and 256 tenths = 25.60 + 0.03 = 25.63 and 41435 hundredths = 414.35. Now, substract 25.63 from 414.35
= 414.35 - 25.63
= 388.72
Hence, required value is 15.805.
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i really need help with this question, ill give brainliest
Answer:
25.455844, soo around 25
Step-by-step explanation:
compute{i-j j-k k-i]
Answer:
Step-by-step explanation:
(i-j)×(j-k)×(k-i)
{(i×j)-(i×k)-(j×j)+(j×k)}×(k-i)
(k+j-i)×(k-i)
( j+i+k-j)
(i+k)
Find the Length of the mi dsegment of the trapezoid. A. 42
b. 12. 5
c. 38. 5
d. 51. 5
The length of the midsegment of the trapezoid is 38.5. The midsegment is the line segment that connects the midpoints of the two parallel sides of the trapezoid. It divides the trapezoid into two congruent triangles.
To find the length of the midsegment of the trapezoid, we need to first find the midpoint of the two parallel sides of the trapezoid. To do so, we need to use the midpoint formula, which is (x1 + x2) ÷ 2, (y1 + y2) ÷ 2, where (x1, y1) and (x2, y2) are the coordinates of the two points.
For example, if the coordinates of the two points are (1,2) and (5,7), then the midpoint of the two points will be (1+5) ÷ 2, (2+7) ÷ 2 = (6, 4.5).
Once we have the coordinates of the two midpoints, we can use the distance formula to find the length of the midsegment. The distance formula is √((x2-x1)² + (y2-y1)²).
So if the coordinates of the two midpoints are (3,6) and (9,2), then the length of the midsegment will be √((9-3)² +(2-6)²) = √(36+16) = √52 = 38.5.
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HELP DUE IN 2 HOURS 4.7y^2+5.3+4y-3.3-2y+y^2
Answer:
5.7y^2 +2y +2
Step-by-step explanation:
You want to simplify the expression 4.7y^2+5.3+4y-3.3-2y+y^2.
SimplifyIdentify like terms and combine their coefficients:
4.7y^2+5.3+4y-3.3-2y+y^2
= (4.7 +1)y^2 +(4 -2)y +(5.3 -3.3)
= 5.7y^2 +2y +2
Choose the ordered pair that is a solution to the equation represented by the graph.
A. (0,-3)
B. (2,0)
C. (2,2)
D. (-3,0)
so (0,-3) and (2,0) is a solution. (2,2) and (-3,0) is not a solution. as the equation of the line passing through the points (0,-3) and (2,0) is y = (3/2)x - 3 we need to substitute points to check valid or not
what is equation ?
An equation is a mathematical statement that asserts that two expressions are equal. In other words, an equation says that one expression on the left side of the equals sign is the same as the expression on the right side of the equals sign. An equation typically includes variables
In the given question,
To determine the equation of the line passing through the points (0,-3) and (2,0), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (0,-3) and (x₂, y₂) = (2,0)
m = (0 - (-3)) / (2 - 0) = 3/2
So the equation of the line is:
y = (3/2)x - 3
Now we can check which ordered pair is a solution to this equation by plugging in the x and y values into the equation and seeing if it holds true.
A. (0,-3)
y = (3/2)x - 3
-3 = (3/2)(0) - 3
-3 = -3
This is true, so (0,-3) is a solution.
B. (2,0)
y = (3/2)x - 3
0 = (3/2)(2) - 3
0 = 0
This is true, so (2,0) is a solution.
C. (2,2)
y = (3/2)x - 3
2 = (3/2)(2) - 3
2 = 0
This is false, so (2,2) is not a solution.
D. (-3,0)
y = (3/2)x - 3
0 = (3/2)(-3) - 3
0 = -9/2
This is false, so (-3,0) is not a solution.
Therefore, the solutions to the equation represented by the graph are A. (0,-3) and B. (2,0).
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80 in. = ___ft and _____ in. PLEASE HELPPP
Answer:
6 and 2/3 feet
Step-by-step explanation:
1 feet=12 inches
x feet=80 inches
80/12=6 and 2/3 feet
I need help please……….
Answer the answer is a
Luisa comprará 6 camisas por $124.50. Si cada camisa tiene el mismo precio, ¿cuánto
cuesta cada una?
9
C. $27.05
D. $27.50
B. $20.75
A. $20.07
If each shirt is the same price, the cost of each one include the following: B. $20.75.
How to determine the unit price?In Mathematics, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the unit price for the shirt, we would divide the cost of shirts by the number of shirts based on the following mathematical equation (formula);
Unit price = Cost of shirts/Number of shirts
By substituting the given parameters into the unit price formula, we have the following;
Unit price = $124.50/6
Unit price = $20.75.
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Complete Question:
Luisa will buy 6 shirts for $124.50. If each shirt is the same price, how much does each one cost?
A. $20.07
B. $20.75
C. $27.05
D. $27.50
Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the
two data sets to have a positive, a negative, or no correlation?
amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas
Based on my knowledge, I would expect a negative correlation between the amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas.
As the car travels, the amount of gas in the tank decreases. Thus, if the car has traveled a long distance since being filled up, it is likely that there is less gas in the tank. Therefore, there should be a negative correlation between the amount of gas in the tank and the distance traveled, meaning that as the distance traveled increases, the amount of gas in the tank decreases.
A scatter plot of these two variables should show a downward-sloping trend, indicating the negative correlation.
Therefore the correct answer is negative correlation.
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4.) A man deporerted GHZ 14100.00 at 3% per
amum compound interest If at the end of 4 years
he transfers the total amount to another bank offering 12% per annum
a. How much interest did he get at the end of 7 years
b. Calculate the total amount he received at the end of 7 years
At the end of 7 years:
a. The man received approximately GHZ 6425.13 as interest.
b. The total amount received by the man is approximately GHZ 22,294.80.
The interest for the first 4 years at 3% compound interest:
Principal amount (P) = GHZ 14,100.00
Rate of interest (R) = 3% = 0.03
Time period (T) = 4 years
The formula for compound interest:
[tex]A = P (1 + R)^T[/tex]
A = 14,100 x (1 + 0.03)⁴
A = 14,100 x (1.03)⁴
A ≈ GHZ 15,869.67
Interest for the first 4 years = A - P
Interest = 15,869.67 - 14,100
Interest ≈ GHZ 1769.67
The total amount at the end of 7 years at 12% per annum:
(P) = GHZ 15,924.57
(R) = 12% = 0.12
(T) = 3 years (remaining 7 years - initial 4 years)
A = 15,869.67(1 + 0.12)³
A = 15,869.67(1.12)³
A ≈ GHZ 22,294.80
a. Interest for the remaining 3 years = A - P
Interest = 22,294.80 - 15,924.57
Interest ≈ GHZ 6425.13
b. Total amount received at the end of 7 years = Principal amount + Interest for 4 years + Interest for 3 years
Total amount = 14,100 + 1769.67 + 6425.13
Total amount ≈ GHZ 22,294.80
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Explain how to determine whether two ratios are equivalent
Answer:
Ratios are fractions, right? Set the two fractions equal to each other and then cross-multiply them. If each side of the equation is equal, then the ratios are equal; if not, then the ratios are not equivalent.
Ex. 1
Comparing ratios 4:2 and 2:1
[tex]\frac{4}{2} = \frac{2}{1}[/tex]
Cross-multiplying, we get 4 = 4, but we can also simplify each side of the equation to get 2 = 2.
Ex. 2
Comparing ratios 3:5 and 6:7
[tex]\frac{3}{5} =? \frac{6}{7}[/tex]
Cross-multiply, we get 21 = 30, so the ratios are not equal. This is an example of a case where you can't simplify the ratios.
Ex. 3
Comparing rations 5:12 and 10:24
[tex]\frac{5}{12} = \frac{10}{24}[/tex]
Cross-multiply, 120 = 120 so the ratios are equal.
Hope this helps!
What is the complement of Q in P?
The complement of set Q {-4, -3, -2} if the universal set is P {-5, -4, -3, -2, -1} is defined by:
¬Q = {-5, -1}
What is the complement of Q in P?If we have a set A defined in an universal set U, we define the complement of A as all the elements of U that are not elements of A.
In this case we have the sets:
P = {-5, -4, -3, -2, -1}
Q = {-4, -3, -2}
Here we want to find the complement of Q in P, so P is the universal set for this problem.
The elements of P that are not elements of Q are:
{-5, -1}
So that is the complement that we are looking for.
Learn more about complements of sets at:
https://brainly.com/question/24341632
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