Answer:
Step-by-step explanation:
hello :
let: A = 3√16+√-9
16=4² and -9 = 9i² =(3i)² .... ( i² = -1)
√16 =√4² = 4 and √-9 = √9i²= √(3i)² ± 3i
A= 12 ± 3i
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
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
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
Aidan works a different number of hours each week, depending on whether he is needed or not. For the last nine weeks, he has worked the following number of hours.
1, 3, 1, 1, 4, 5, 8, 6, 5
Which measure of central tendency would be the most effective for Aidan to use if he wants to demonstrate to his supervisor that he hasn't worked very many hours recently?
Answers
mean
median
mode
Answer:
Mean (Average) 3.7777777777778
Median 4
Range 7
Mode 1, appeared 3 times
Geometric Mean 2.8976123026694
Largest 8
Smallest 1
Sum 34
Count 9
Step-by-step explanation:
Im bored so i gave you everything
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.
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...
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
Find the angle between u = (8,-2) and v = (19,3). Round to the nearest tenth of a degree.
A. 32.5
B. 6.3
C. 42.5
D. 16.3
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
A scatterplot is produced to compare the size of a school building to the number of students at that school who play an instrument. There are 12 data points, each representing a different school. The points are widely dispersed on the scatterplot without a pattern of grouping. Which statement could be true?
Answer:
As the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.
Step-by-step explanation:
Answer:
a is the answer
Step-by-step explanation:
Which pair show equivalent expressions
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.
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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.
HELP I NEED HELP ASAP!!
WHAT IS THE VOLUME OF THE CUBE SHOWN?
I WILL GIVE LOTS OF POINT TO THE ONE WHO GIVES THE CORRECT ANSWER!!
Answer:
8/125 ft
Step-by-step explanation:2/5 x 2/5 x 2/5 = 8/125
Answer:
The answer to your question is Volume of a cube = 8/125 ft³
Step-by-step explanation:
Data
length of a side = 2/5 ft
Formula
Volume of a cube = side x side x side
Substitution
Volume of a cube = 2/5 x 2/5 x 2/5
-Just multiply the numerator and multiply the denominators
-Simplification
The Volume of a cube = 8/125 ft³
A section of a rectangular floor is covered with square floor tiles as shown below
Answer:
[tex]\frac{20}{9}[/tex] square feet
Step-by-step explanation:
We are given that
Side of square tile=[tex]\frac{1}{3} foot[/tex]
Total number of tiles used in rectangular floor=20
Area of square=[tex](Side)^2[/tex]
Area of square tile=[tex](\frac{1}{3})^2=\frac{1}{9}[/tex]square feet
Area of rectangular floor covered by square tiles =Area of 20 square tiles
Area of rectangular floor covered by square tiles=[tex]20\times \frac{1}{9}[/tex] square feet
Area of rectangular floor covered by square tiles=[tex]\frac{20}{9}[/tex] square feet
Hence, the area of rectangular floor covered by square tiles=[tex]\frac{20}{9}[/tex] square feet
Pablo buys a 4 pack of towels for $19.60 .
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Answer:
$4.90 per towel
Step-by-step explanation
If each towel costs and equal amount, you divide the full amount of the pack, $19.60, by the number of towels, which is 4, which gives you $4.90 as the answer.
Find the quotient
4 / 9/10
Answer:
4 × 10/9 = 40/9 is the solution
-8(5b + 2) -7(b - 5)
Answer:
-47b + 19
Step-by-step explanation:
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:
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.
Recall that h, the phase shift, is any value of x that occurs at the beginning of a cycle.
The green point begins the –cosine cycle. What value of x corresponds to this point?
Answer:
h=0.748
Step-by-step explanation:
The value of x that corresponds to this point on the phase shift is 0.748.
What is phase shift?The phase shift simply means when the graph of the sine and cosine function is shifted from their usual position.
The phase shift, is any value of x that occurs at the beginning of a cycle. In this case, value of x that corresponds to this point on the phase shift is 0.748.
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Which equation represents a proportional relationship?
A. y=-2x
B. -2x+3y=12
C. y=1/2x+3
D. -1x+2y=6
Which equation represents a proportional relationship?
C. y=1/2x+3
A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters per second. At a certain instant, the car is 24 meters from the intersection. What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
Answer:
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
Step-by-step explanation:
Given that,
A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.
From Pythagorean Theorem,
(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+
Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.
∴y²= x²+10²
[tex]\Rightarrow y=\sqrt{x^2+100}[/tex]
Differentiating with respect to t
[tex]\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}[/tex]
[tex]\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}[/tex]
Since the car driving towards the intersection at 13 m/s.
so,[tex]\frac{dx}{dt}=-13[/tex]
[tex]\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)[/tex]
Now
[tex]\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)[/tex]
[tex]=\frac{24\times (-13)}{\sqrt{676}}[/tex]
[tex]=\frac{24\times (-13)}{26}[/tex]
= -12 m/s
Negative sign denotes the distance between the car and the person decrease.
Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.
The rate of change of the distance between the car and the person is [tex]\(-\frac{65}{12}\)[/tex] meters per second, indicating decreasing distance.
To find the rate of change of the distance between the car and the person at the given instant, we can use the concept of related rates. We'll use the Pythagorean theorem to relate the distances involved.
Step 1:
Establish variables.
Let (x) represent the distance the car has traveled north from the intersection, and let (y) represent the distance between the car and the person.
Step 2:
Formulate the equation using the Pythagorean theorem.
[tex]\[x^2 + y^2 = 24^2\][/tex]
Step 3:
Differentiate both sides of the equation with respect to time.
[tex]\[2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\][/tex]
Step 4:
Plug in the given values and solve for [tex]\(\frac{dy}{dt}\)[/tex].
Given that the car is traveling north, [tex]\(\frac{dx}{dt} = 13\)[/tex]m/s.
When the car is 10 meters east, [tex]\(x = 10\).[/tex]
At that instant, when the car is 24 meters from the intersection, [tex]\(y = 24\).[/tex]
[tex]\[2(10)(13) + 2(24)\frac{dy}{dt} = 0\]\[260 + 48\frac{dy}{dt} = 0\]\[\frac{dy}{dt} = -\frac{260}{48} = -\frac{65}{12}\][/tex]
The rate of change of the distance between the car and the person at that instant is [tex]\(\boxed{-\frac{65}{12}}\)[/tex] meters per second. The negative sign indicates that the distance is decreasing.
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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.
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.
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Trace needs a new carpet for her house the living are is an open floor plan of a dining room 6 feet c 4 feet sitting area 10 feet x 15 feet and a breakfasg nook 5 feet x 5 feet how many square feet of carpet does she need
Answer:
199 square feet
Step-by-step explanation:
Given:
Trace needs a new carpet for her house.
Dimension of dining room = 6 feet by 4 feet.
Dimension of sitting area = 10 feet by 15 feet.
Dimension of breakfast nook = 5 feet by 5 feet.
Question asked:
How many square feet of carpet does she need ?
Solution:
First of all we will calculate the area of each part of the house and then add up.
[tex]Area \ of \ dining\ room=length\times width[/tex]
[tex]=6\times4\\ \\ =24\ square\ feet[/tex]
[tex]Area \ of \ sitting\ part=length\times width[/tex]
[tex]=15\times10\\ \\ =150\ square\ feet[/tex]
[tex]Area \ of \ breakfast\ nook=(side)^{2}[/tex]
[tex]=5^{2} =25\ square\ feet[/tex]
Total carpet needed will be needed = For dining + For sitting area + For breakfast nook
= 24 + 150 + 25
= 199 square feet
Therefore, she needs 199 square feet of a new carpet for her house.
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.
Can you please help me with this ima give you brainlylist
Answer: 16 pints
Step-by-step explanation:
There are 8 pints in a gallon so 8*2=
16 pints
Answer:
16 pints.
Step-by-step explanation:
Hello there!
There are 8 pints in a US gallon, so:
8x2=16 pints