Answer:
The sum of the first 6 terms of the series is 504.
Step-by-step explanation:
Given that,
Common ratio in a geometric series is, r = 0.5
First term of the series, a = 256
We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:
[tex]a,ar^1,ar^2,ar^3......[/tex]
The sum of n terms of a GP is given by :
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Here, n = 6
[tex]S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504[/tex]
So, the sum of the first 6 terms of the series is 504.
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 2.5 x + 3 intersect the circle with radius 4 and center (0, 3)?
Answer:
The point at which the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) is x = 1.49
Step-by-step explanation:
Here we have the equation of a circle = (x - h)² + (y-k)² = r²
Where (h, k) is the coordinate of the center
Therefore, we have
(x - 0)² + (y - 3)² = 4²
Which gives x² + (y - 3)² = 16
Since the line y = 2.5·x + 3 we have
x² + ( (2.5·x + 3 ) - 3)² = 16
x² + (2.5·x)² = 16
x² + 6.25·x² = 16
7.25·x² = 16
x² = 16/7.25 = 2.21
x = 1.49
That is the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) at x = 1.49.
The point of intersection in the first quadrant of the given line y = 2.5x + 3 and the given circle x² + (y - 3)² = 16, can be found by substituting the equation of the line into the equation of the circle and then solving for x and y.
Explanation:The subject of this question is the intersection of a line and a circle in the first quadrant of a coordinate plane. The circle is defined by the equation (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with center at the origin (0, 3) and radius 4, the equation is x² + (y - 3)² = 16.
The line is defined by the equation y = 2.5x + 3. To find the intersection point, we substitute this equation into the equation of the circle, resulting in x² + (2.5x)² - 6x + 9 = 16. Solving this quadratic equation gives the x-coordinates of the intersection points. Since we are only interested in the first quadrant, we pick the positive root. Substituting this value of x into y = 2.5x +3 gives the corresponding y-coordinate, defining the point of intersection in the first quadrant.
Learn more about Intersection of line and circle here:https://brainly.com/question/34183150
#SPJ
1) Determine which events are mutually exclusive and which are not, when a single card is drawn from a deck. a. Getting a 7 and getting a jack b. Getting a club and getting a king c. Getting a face card and getting an ace d. Getting a face card and getting a spade
Answer:
The events a) and c) are mutually exclusive.
Step-by-step explanation:
a) This is mutually exclusive, each card has a unique value between 2 and 10, or it is a jack, queen, king, or an Ace. A single card cant have two different values at the same time.
b) This is not mutually exclusive, since you can get a king of clubs. Each card can have any combination of one suit and one value.
c) A face card is either a Jack, a Queen or a King, it is not an Ace. For the same argument of a), a card cant have two different values, therefore this event is mutually exclusive.
d) This is not mutually exclusive, since a card can have any suit independently of the value it has (same argument than b), therefore, a card can be a face card and a spade at the exact time.
Therefore, events a and c are mutually exclusive.
a) Getting a 7 and getting a jack: Mutually exclusive events
b) Getting a club and getting a king: Not mutually exclusive events
c) Getting a face card and getting an ace: Mutually exclusive events
d) Getting a face card and getting a spade: Not mutually exclusive events
A standard deck of cards has 52 cards having 13 ranks each of 4 suites. The 13 ranks are
[tex]\text{Ranks}=\{Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King\}[/tex]
and the suites are
[tex]Suites=\{Clubs,Diamonds,Hearts,Spades\}[/tex]
a) Getting a 7 and getting a jack:
Since a 7 and a Jack are different rank elements, you either pick a 7 of a suite, or a Jack of a suite, but never both. So, the events are mutually exclusive.
b) Getting a club and getting a king:
Since a Club is a suite and a King is a Rank, the sample space will have a King of Clubs card. So, the events are not mutually exclusive.
c) Getting a face card and getting an ace:
A face card is a card with a face on it. Faces are Ranks, but an Ace is also a Rank. The sample space contains cards with only one Rank per card. So, the events are mutually exclusive.
d) Getting a face card and getting a spade:
Faces are Ranks, and a Spade is a suite. The sample space will contain face cards for the Spade suite of cards. So, the events are not mutually exclusive.
Learn more about probability here: https://brainly.com/question/15944614
The selling price of a chair is N14 000. The trader gives a 25% discount for cash. What is the cash price?
Answer:N10500
Step-by-step explanation:
10%of 14000=1400
20%=1400x2=2800
5%=1400 divided by 2=700
25%=2800+700=3500
14000-3500=10500
hope this helps
There were 30 voters. Exactly 10% of voters chose which candidate?
Candidate A-12
Candidate B-3
Candidate C-6
Candidate D-9
Answer:
CANDIDATE B
Step-by-step explanation:
What is the value of s?
Answer:
The answer to your question is 33°
Step-by-step explanation:
Data
∠1 = 39°
∠2 = 108°
∠3 = ?
Process
To solve this problem, remember that the sum of the internal angles in a triangle equals 180°.
Then,
∠1 + ∠2 + ∠3 = 180°
-Substitution
39° + 108° + ∠3 = 180°
-Solve for ∠3
∠3 = 180 - 39 - 108
-Simplification
∠3 = 180° - 147°
-Result
∠3 = 33°Which statement illustrates the distributive property?
3(4+5)= 3(4)+5
3(4+5)= 3(4)+3(5)
3[(4)+(5)] = 3(4)+3(5)
3[(4)(5)] = [3(4) ][ 3(5)]
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
A box contains four equal sized cards labeled 1, 3,5, and 7. Tim will select one card from the bow. What is the probability that Tim will select a card labeled 4?
Answer: The probability is zero.
Step-by-step explanation:
The labels on the 4 cards are 1, 3, 5 and 7. Because the cards are equal, the probability of dragging at random each one of them is equal to 1/4 = 0.25.
Now, the probability that Tim selects a card labeled with a 4 is equal to the number of cards labeled with a 4, divided the total number of cards.
We do not have cards labeled with a 4, so the probability is:
p = 0/4 = 0
because we do not have any card labeled with a 4, the probability of selecting one at random is equal to zero.
Final Answer:
The probability is zero.
Explanation:
The labels on the 4 cards are 1, 3, 5 and 7. Because the cards are equal, the probability of dragging at random each one of them is equal to 1/4 = 0.25.
Now, the probability that Tim selects a card labeled with a 4 is equal to the number of cards labeled with a 4, divided the total number of cards.
We do not have cards labeled with a 4, so the probability is:
p = 0/4 = 0
because we do not have any card labeled with a 4, the probability of selecting one at random is equal to zero.
Using 3.14 as an approximation for pi, find the diameter, circumference, and area of the circle with a radius of 5 cm. Do NOT include units in your answer. Part A Diameter Part B Centimeter Part C Area
The diameter of this circle is 10, the circumference is 31.4 and the area is 58.5.
Because the diameter of a circle is twice its radius, we have:
d = 2*r
d = 2*5 = 10
The following formula calculates the circumference of a circle:
2*pi*r = circumference
2*3.14*5 circumference
10 times 3.14 equals 31.4
The following formula calculates the area of a circle:
area = pi*r²
area = 3.14*(5)²
area = 3.14*25
area = 78.5
This circle has a diameter of 10, a circumference of 31.4, and an area of 58.5.
Complete question:
Find the diameter, circumference, and area of the circle with a radius of 5 cm.
The North Colony Trail at Royal Gorge, Colorado, is 18 miles long. Stacey has hiked four miles to a resting spot. She hikes the rest of the trail at two miles per hour. How far from the beginning of the trail is stacy six hours after leaving the resting spot?
Answer:
Stacey is 16 miles far from the beginning of the trail.
Step-by-step explanation:
Given:
Stacey's total hike journey to NCT, Colorado = 18 miles
Distance covered by her to, a resting spot = 4 miles
We have to find:
How far from the beginning of the trail is Stacey [tex]6[/tex] hours after leaving the resting spot.
According to the question.
Distance remaining = [tex](18-4) = 14[/tex] miles
Time taken = [tex]6[/tex] hours Speed maintained = [tex]2[/tex] mph
After leaving the resting spot she has covered a distance :
⇒ [tex]Distance = speed\times time[/tex]
⇒ [tex]Distance = 2\times 6[/tex]
⇒ [tex]Distance = 12[/tex] miles.
In [tex]6[/tex] hours she has covered [tex]12[/tex] miles and also she has covered [tex]4[/tex] miles before stopping here.
From the beginning she has covered :
⇒ [tex]Total\ distance =(4+12)[/tex]
⇒ [tex]Total\ distance = 16[/tex] miles.
Stacey is 16 miles far from the beginning of the trail.
A decision model that presumes an environment where problems are clearly defined, all possible action alternatives are known, and the consequences of the alternatives are clear is known as a ________ decision model.
a. behavioral.
b. classical.
c. optimizing.
d. satisficing.
Answer:
B. Classical
Step-by-step explanation:
By definition, classic decision model is where the problems are clearly defined, all possible actions and alternatives are known, and the consequences of the alternatives are clear.
The number of bacteria grown in a lab can be modeled by p(t)=300(2)^4t ,where t is the number of hours. Which expression is equivalent to ?
1) 300 (8)^t
2) 300 (16)^t
3) 300^t (4)^t
4) 300^2t (2)^2t
Answer:
2. 300(16)∧t
Step-by-step explanation:
p(t) = 300(2)∧4t
where b is the number of hours
2∧4t =2∧4(t) 2 x2 x2 x2 = 16∧t
p(t) = 300(2)∧4t = 300(16)∧t
Need help
Please tell me
One hundred students are enrolled in State University's course on introductory physics for math and science majors. In the group, 60 students are math majors and 40 are science majors. Sarah is in the class. She got all As in her high school science courses, and she would like to be a chemist someday. She lives on campus. Her boyfriend is also in the class. There is a _________________ chance that Sarah is a science major.
Answer:
40%
Step-by-step explanation:
Total Number of Students in Introductory Physics Course =100
Number of Math Majors = 60
Number of Science Majors = 40
Relevant Facts
Sarah got all As in her high school science coursesShe would like to be a chemist someday which is Science RelatedTherefore, there is a 40 out of 100 chance that Sarah is a science major.
Expressed in percentage, there is a 40% chance that Sarah is a science major.
There is a 40% chance that Sarah is a science major.
To determine the probability that Sarah is a science major, we use the information given about the composition of the student group. There are 100 students in total, 60 of whom are math majors, and 40 are science majors.
To find the probability that Sarah is a science major, we simply take the number of science majors and divide it by the total number of students. Therefore, the probability (P) is calculated as:
P(Sarah is a science major) = Number of Science Majors / Total Number of Students = 40/100 = 0.40 or 40%.So, there is a 40% chance that Sarah is a science major.
What is the value of d
Answer:71.5
Step-by-step explanation:
2d+37+1+38=2d+76=180
180-76=2d+143
143divided by 2 =71.5
Answer:
d = 57 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees, so:
2d + 1 + 38 + 27 = 180
2d = 180 - (1 + 38 + 27)
2d = 180 - 66 = 114
d = 114/2
d = 57 degrees.
Jake, Elijah, and Zaire had 65 Pokemon cards. Jake had two more cards than Elijah, and Elijah had three more cards than Zaire. How many cards did Jake have?
Answer: Jake has 24 cards
Step-by-step explanation:
Let x represent the number of Pokemon cards that Elijah has.
Jake had two more cards than Elijah. It means that the number of cards that Jake has is x + 2
Elijah had three more cards than Zaire. It means that the number of cards that Zaire has is x - 3
Jake, Elijah, and Zaire had 65 Pokemon cards. It means that
x + x + 2 + x - 3 = 65
3x - 1 = 65
3x = 65 + 1 = 66
x = 66/3 = 22
The number of cards that Jake has is
x + 2 = 22 + 2 = 24
Answer:
24
Step-by-step explanation:
Given:
Total number of cards, T = 65
Let's take number of Elijah's cards as E
Jake's cards = J
Zaires's cards= Z
So we have,
J+E+Z = 65
We are told Jake had 2 more than Elijah=
J= E+2
Elijah had 3 more than Zaire. number of Zaire's card will be=
Z= E-3
We now have:
E+2+E-3+E = 65
3E = 65+1
3E = 66
E = 66/3
E=22
Number of Elijah's card is 22
We are told Jake had 2 more cards than Elijah. Therefore number of Jake's cards will be=
E + 2
= 22 + 2 = 24
Number of Jake's cards = 24
Every 8 days the cafeteria sells pizza and every 10 days they sell banana pudding. Today they had both, how many days till they sell both again?
Answer:
40 days
Step-by-step explanation:
The next that the two lineup is forty days.
8,16,24,32,40
10,20,30,40
40 is when they meet up
help find perimeter and area
Answer: perimeter = 96mm, Area = 564mm².
Step-by-step explanation:
From the diagram, it is a trapezium, it has a rectangle joined together by a right angled triangle. Now to find the perimeter, we add all the dimensions together. To get the other side of the rectangle, which is also the perpendicular height of the figure, we take the Pythagoras. Let the perpendicular height = x
Therefore,
25² = ײ + 7²
625 = x² + 49
x² = 625 - 49
x² = 576
x. = √576
= 24.
Now the perimeter
= 20 + 25 + 7 + 20 + 24
= 96mm.
Area of the figure will be
= 1/2( a + b )h
Where a = 20, b = 20 + 7 = 27 and h = 24, now substitute for the values
( 20 + 27) x 24
---------------------
2
= 47 x 24/2
= 47 x 12
= 564mm²
U
Proving the Parallelogram Diagonal Theorem
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
Statements
✓ 1. ABCD is a parallelogram
Reasons
1. given
Correctl Assemble the next
statement.
) Intro
From the given parameters with reasons and statements, we have proven that AE = CE and BE = DE from; Properties of Parallelogram and ASA Congruence Postulate.
How to do a two - column proof?Statement 1; ABCD is a parallelogram
Reasons 1; given
Statement 2; ∠ABE and ∠CDE are alternate Interior angles
Reason 2; Definition of Alternate Interior angles
Statement 3; ∠BAE and ∠DCE are alternate Interior angles
Reason 3; Definition of Alternate Interior angles
Statement 4; AB = CD
Reason 4; Parallelogram side theorem
We want to prove that AE = CE and BE = DE
From properties of parallelogram, we can say that ∠CBD = ∠ABD and also ∠BCA = ∠DAC
Thus, it means that; ΔBEC ≅ ΔAED
Thus, from ASA Congruency postulate, we can say that;
AE ≅ CE and BE ≅ ED
Read more about two column proof at; https://brainly.com/question/1788884
Jeff owns a coffee shop near a commercial zone. He used to pay $10 per hour to his employees. During the last year he opened three coffee shops in that same area. He could afford to do so because of the low wages. However, Jeff is now paying $15 per hour to his employees. Answer the following questions based on the supply and demand schedule of labor.
Who creates the demand for coffee shops? Who creates the demand for coffee shop employees?
Answer:
The consumers in that commercial area create the demand for coffee shops. However, Jeff is the consumer for coffee shop employees.
Step-by-step explanation:
The consumers in that commercial area create the demand for coffee shops.
Jeff creates the demand for coffee shop employees.
What is demand?Demand is an economic term that refers to the number of products or services that consumers wish to purchase at any given price level. The mere desire of a consumer for a product is not demand. Demand includes the purchasing power of the consumer to acquire a given product at a given period.
What is supply?Supply is the number of goods an individual or business provides to the market which refers to the amount they produce at a specific point in time. For example, if Apple manufactures 100 iPhones, then this is the supply that is brought to the market.
Learn more about demand here https://brainly.com/question/1245771
#SPJ2
I need help asap :):):)
Answer: m + 4
Step-by-step explanation:
Expressions don't have equal signs and the values are separated by a symbol/s.
Answer:
m+4
An expression is the problem.
Ex: 2+3=5 2+3 Would be the expression here
Find the greatest common factor of 44 and 16.
Answer:
4
Step-by-step explanation:
If you prime factorization both
for 16 you get 2^4= 2^2*2^2
for 44 you get 2^2*11
they both have 2^2 so 4
Look at the attached picture⤴
Hope it will help u...
What is the probability that you turn to page 45?
Type your answer in the format:
3/4
with no spaces.
Answer:
1/60
Step-by-step explanation:
Solve the equation
45÷x=3/4
Brainliest would be appreciated
Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 during an afternoon it's population density is about 15 acre find the number of people in the park that afternoon one square mile is equal to 640 acres
Answer:
12,000 people were present
Step-by-step explanation:
In this question, we are asked to calculate the number of people in a park on an afternoon given the measurements of the park and its population density.
Firstly, we calculate the area of the park.
Mathematically the area is the product of the length and width = 0.5 * 2.5 = 1.25 square miles
Let’s convert this to acres. From the question, we know that one square mile is 640 acres, this mean that 1.25 square mile would be 1.25 * 640 = 800 acres
Now let’s consider the population density of 15 people per acre, the number of people present is thus 800 * 15 = 12,000 people
Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of ±2 percent with 90 percent confidence. What is the necessary sample size?
Answer:
Hence, the minimum required sample size (n) should be = 1692
Step-by-step explanation:
Solution:-
- The estimation error, E = 2%
- The confidence level, CI = 90 %
- Since the proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy are unknown we will assume the corresponding proportion to be p = 0.58
- The required sample size is a function of confidence value and error of estimation (E):
[tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]
Where,
- The critical value of the confidence level = 90% would be:
significance level ( α ) = 1 - CI = 1 - 0.90 = 0.1
Z-critical = Z_α/2 = Z_0.05 = 1.645
- The required sample size (n) can be calculated:
[tex]n = 0.5*( 1 - 0.5 ) * (\frac{1.645}{0.02})^2\\\\n = 1691.265[/tex]
- Hence, the minimum required sample size (n) should be = 1692
A jar contains 3 marbles marked with the numbers 1 through 3. You pick a marble at random. What is the probability of not picking the marble marked with the number 2? Enter your answer as a simplified fraction. The probability of not picking the marble marked with the number 2 is
Answer:
2/3
Step-by-step explanation:
PLZ PLZ❓❓❓HELP
Rosa bought 20 boxes of chocolate and 12 bugs of candy if a big of candy cast $0.43and a box of chocolate casts twice as much as a bug of candy how much did she spend on the bug of chocolate and candy all together.
Answer:
22.36
Step-by-step explanation:
20*.86=17.2
12 *.43= 5.16
Final answer:
To find the total amount Rosa spent on the chocolate and candy, multiply the cost of a box of chocolate by 20 and the cost of a bag of candy by 12. Then, add the two amounts together.
Explanation:
To find the total amount Rosa spent on the chocolate and candy, we need to calculate the cost of each item and then add them together.
Given that a bag of candy costs $0.43 and a box of chocolate costs twice as much as a bag of candy, we can calculate:
The cost of a box of chocolate = $0.43 x 2 = $0.86
Rosa bought 20 boxes of chocolate, so the total cost of the boxes of chocolate = 20 x $0.86 = $17.20
Rosa also bought 12 bags of candy, so the total cost of the bags of candy = 12 x $0.43 = $5.16
Finally, to find the total amount Rosa spent, we add the cost of the boxes of chocolate and the bags of candy together:
Total spent on chocolate and candy = $17.20 + $5.16 = $22.36
If a pyramid has a scale factor of five applied to it what is the volume scale factor
Answer:
125
Step-by-step explanation:
The volume scale factor is the cube of the scale factor of linear dimensions:
5³ = 125
The volume scale factor is 125.
Bed & Bath, a retailing company, has two departments—Hardware and Linens. The company's most recent monthly contribution format income statement follows: Department Total Hardware Linens Sales $ 4,190,000 $ 3,110,000 $ 1,080,000 Variable expenses 1,264,000 858,000 406,000 Contribution margin 2,926,000 2,252,000 674,000 Fixed expenses 2,290,000 1,480,000 810,000 Net operating income (loss) $ 636,000 $ 772,000 $ (136,000 ) A study indicates that $373,000 of the fixed expenses being charged to Linens are sunk costs or allocated costs that will continue even if the Linens Department is dropped. In addition, the elimination of the Linens Department will result in a 15% decrease in the sales of the Hardware Department.
Answer:
By eliminating Linens department net operating income fell by $574,800.00
Step-by-step explanation:
The question requires that the monthly contribution income statement be prepared when the Linens is closed or eliminated,incorporating the unavoidable fixed costs of $373,000 as well as the fall in sales of Hardware by 15%.
Monthly Contribution Income Statement:
Sales($3,110,000)*(1-15%) $2,643,500.00
Variable expenses($858,000)*(1-15%) ($729,300.00)
Contribution margin $1,914,200.00
Fixed expenses($1,480,000+$373,000) ($1,853,000.00)
Net operating income $61,200.00
Reduction in net operating=$636,000-$61,200.00=$574,800
Alternatively:
Lost contribution from closing Linens department $674,000.00
Lost contribution from Hardware(15%*$2,252,000) $ 337,800.00
Total lost contribution $1,011,800.00
Less avoidable fixed costs($810,000-$373,000) ($437,000.00)
Reduction in profits company-wide $574,800.00
The sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
Sunk Costs and Allocated Costs:
- $373,000 of the fixed expenses allocated to the Linens Department are sunk costs or allocated costs. These costs will continue even if the Linens Department is dropped. They should not be considered in the decision-making process as they will not change with the elimination of the department.
2. Impact on Hardware Department:
- Dropping the Linens Department will result in a 15% decrease in the sales of the Hardware Department. This means that the sales of the Hardware Department will decrease by $1,110,000 (15% of $3,110,000, Linens sales). This decrease in sales will impact the contribution margin of the Hardware Department.
3. Contribution Margin Calculation:
- The contribution margin of the Hardware Department before dropping Linens is $2,252,000. With a 15% decrease in sales, the new contribution margin for the Hardware Department is $1,142,000.
4. Net Operating Income:
- The net operating income of the Hardware Department after dropping the Linens Department is calculated by subtracting the fixed expenses of the Hardware Department and the revised contribution margin from the total sales.
5. Overall Impact:
- Dropping the Linens Department will result in a positive impact on the overall net operating income of Bed & Bath. The increased net operating income from the Hardware Department ($772,000) will offset the loss from dropping the Linens Department ($136,000).
Considering the sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
A supermarket gives a 10% discount on the marked prices of all items during the sale. Find the following marked prices:
1)the amount of discount given and
2)the sale prices: a)$45 b)$110
Answer:
For a $45 purchase the discount would be $-4.5
the sales price $40.5
For a $110 purchase the discount is $-11
The sales price $99
Step-by-step explanation:
To find the discount on an item first multiply the original cost of the item by the percentage discounted. in this case,
$45 × 0.10 = $4.5
$110 × 0.10 =$11
$4.5 and $11 are respective discount amounts
now simply subtract the amount of the discount from the original price
$110 - $11 = $99
$45 - $4.5 = $40.5
These are your final sale prices after discount.
3+3
(This is just to get you points or complete challenges)
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation: