Answer:
b. 7
d. 120°
f. 60°
Step-by-step explanation:
The properties of a parallelogram are:
Opposite sides are parallel and congruent.Opposite angles are equal.Adjacent angles are supplementary.The diagonals bisect each other.The sum of the interior angles is 360 degrees.For Question:
b.
AE=CE=7 since diagonals of parallelogram bisect each other
d.
m ∡ DCB= m ∡DAB=120° Opposite angle in a parallelogram is congruent or equal.
f.
m ∡ ADC=?
Here
m ∡ADC+ m ∡DAB=180° being co interior angle
m ∡ADC+120°=180°
m ∡ADC=180°-120°=60°
m ∡ADC=60°
Answer:
b) AE = 7
d) m∠DCB = 120°
f) m∠ADC = 60°
Step-by-step explanation:
Part bThe diagonals of a parallelogram always bisect each other.
Therefore, point E (the point of intersection of the two diagonals) is the midpoint of diagonal AC. So AE = EC.
As EC = 7, then AE = 7.
\(\hrulefill\)
Part dAs the measure of the opposite angles of a parallelogram are equal, then m∠DCB is equal to m∠DAB. From inspection of the given parallelogram, we can see that m∠DAB = 120°. Therefore:
m∠DCB = 120°
\(\hrulefill\)
Part fAdjacent angles of a parallelogram are supplementary (sum to 180°).
Angle DAB and angle ADC are adjacent angles, so their sum is 180°.
Therefore:
⇒ m∠ADC + m∠DAB = 180°
⇒ m∠ADC + 120° = 180°
⇒ m∠ADC + 120° - 120° = 180° - 120°
⇒ m∠ADC = 60°
Express 75 as a product of its prime factors write the prime factors in ascending order and give your answer in index form
Step-by-step explanation:
75 = 3 x 5 x 5 in prime factorization
Answer:
Step-by-step explanation:
3x5x5
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool from time to time. The graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours.
Which of the following statements best describes the amount of water in the pool ?
1) it is increasing during the time interval 4
2) it is increasing during the time interval 10
3) it is decreasing during the time interval 4
4) it is decreasing during the time interval 10
The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.
How to determine the the interval of the water in the pool?To determine the time interval of the water in the pool the following is carried out.
At 0 hour, the water is at the level of = 40 gallons
At 1 hour, the water decreased to = 25 gallons.
At 2 hours, the water decreased to = 10 gallons.
The water remained at a constant level till 4 hours.
Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.
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What is the constant of proportionality between y and x in the graph?
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
Suppose Deandre places $5000 in an account that pays 8% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
The amount in the account at the end of 1 year is $5400.
The amount in the account at the end of 2 year is $5832.
What do you mean by interest rate?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
According to data in the given question,
We have:
Deandre places $5000 in an account that pays 8% interest compounded each year.
And no withdrawals are made from the account.
Now, we need to determine the amount of 8% interest on the $5000,
\(=\frac{5000}{100}*8\\ =400\)
Then, the amount in the account at the end of 1 year =$5000+$400
=$5400.
Now, we need to determine the amount of 8% interest on the $5400,
\(=\frac{5400}{100}*8\\ =432\)
So, the amount in the account at the end of 2 year =$5400+$432
=$5832.
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Find the present value of an annuity which pays ` 200 at the end of each 3 months for 10 years assuming
money to be worth 5% converted quarterly?
(a) ` 3473.86
(b) ` 3108.60
(c) ` 6265.38
(d) None of thes
The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.
To find the present value of an annuity, we can use the formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.
Plugging in these values into the formula, we get:
PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05
Simplifying the equation, we find:
PV ≈ 200 * (1 - 0.12198) / 0.05
PV ≈ 200 * 0.87802 / 0.05
PV ≈ 35160.4 / 0.05
PV ≈ 7032.08
Therefore, the present value of the annuity is approximately `7032.08.
None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.
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Which of the following statements can be assumed from the diagram?
Answer:
the last answer choice is one of them for sure.
Step-by-step explanation:
Line A and F intersects line BC
What is 8.6 increased by 75%
Answer:
15.05
Step-by-step explanation:
8.6 is 100% of 8.6.
To increase it by 75%, you'll end up with 175% of 8.6
175% of 8.6 =
= 1.75 * 8.6
= 15.05
A die was rolled 36 times and 4 appeared 5 times. What is the probability of getting 4?2/364/365/366/36
We were told from the question that a die was rolled 36 times and 4 appeared 5 times. we are to find the probability of getting a 4.
The die was rolled 36 times.
The probability of getting a 4 is 5 because 4 appeared 5 times.
That is:
The experimental probability of getting a 4 is 5 out of 36 trials.
So, the probability of getting a 4 is:
= 5/36.
Therefore, the correct option is the third option which is 5/36
Marissa decides to save AND invest for retirement. She makes an initial deposit of $2000 in her savings account which earns 1.5% annually. Her contributions are $150 a month. Then, she makes an initial deposit of $1,000 in the US stock market through an index fund contributing $300 a month with a 6.8% return annually. What is the balance of Marissa’s retirement account after 30 years?
Using compound interest formula, her balance after retirement is $430797.77
What is Marissa's BalanceTo calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.
First, we'll calculate the balance of her savings account:
Initial deposit: $2000
Interest rate: 1.5%
Monthly contribution: $150
Number of months: 30 years * 12 months/year = 360 months
Using the compound interest formula, the balance of her savings account after 30 years will be:
2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))
A = $71280.33
Next, we'll calculate the balance of her index fund:
Initial deposit: $1000
Interest rate: 6.8%
Monthly contribution: $300
Number of months: 30 years * 12 months/year = 360 months
Using the compound interest formula, the balance of her index fund after 30 years will be:
A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))
A = $359517.44
Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.
Her balance = $71280.33 + $359517.44 = $430797.77
Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.
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3x+(8x-16) simplest form
Step-by-step explanation:
3x × 8x- 3x×16
24x -48x
-24x
A model scale is 1 cm = 8m.
If the actual object is 40 meters, the model is
____ cm long.
Answer:
5
Step-by-step explanation:
1 =8
'
8=40
=40/8
=5
how much money deposited now will provide payment of Rs. 15000 at the end of each half year for 10 years, if interest is 16% compounded six-monthly
The interest is 16% compounded semi-annually, is Rs. 121,179.10.
To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.
Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)
So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:
Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.
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not sure help please
Answer:
The area of a trapezoid is 1/2 (b₁ + b₂) * h where b₁ and b₂ are the bases and h is the height. The answer is 1/2 * (3 + 4) * 1 = 3.5.
8 over 12 divide 7 over 8
Answer: 19/25
Step-by-step explanation: 8/12 / 7/8 is (rounded) 0.76, and 0.76 as a fraction is 19/25.
Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression. Answer exactly. 4 sin 30 ∘ =
The expression is simplified to 2
How to determine the valueIt is important to note that the table of exact values for trigonometric identity differ with the particular identity in study.
From the table of exact values, we have that;
sin 15 = 0. 25
sin 30 = 0. 5000
sin 45 = 0. 7071
sin 60 = 0. 8600
sin 75 = 0. 9659
sin 90 = 1
To determine the value of the expression, we have to substitute the value of sin 30 as 0. 5000
4 sin 30°
⇒ 4 × 0. 5000
multiply through
⇒ 2
The value determined is 2
Thus, the expression is simplified to 2
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A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, V2V3 might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.
Required:
a List the sample points in this experiment of ordering paper on two successive days.
b Assume the vendors are selected at random each day and assign a probability to each sample point.
c Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P( A), P( B), P( A U B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
Find the given attachments
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).8,20,50,...Find the 10th term.
Cómo se hace y cómo es el proceso ayuda porfaaaaa
Answer:
30: 100
31: -13
32: -45
33: 14
34: -32
35: -22
36: 17
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated? 1 5 3 4 TY - y = 8 0-10 times the first equation and 3 times the second equation O 10 times the first equation and 3 times the second equation 0 -3 times the first equation and 5 times the second equation O 3 times the first equation and 5 times the second equation
Answer:
The correct answer is A.
Step-by-step explanation:
1/5*-10/1=-10/5= -2
2/3*3/1=6/3= 2
----------------------------
0.
Answer:
a –10 times the first equation and 3 times the second equation
Step-by-step explanation:
The ski lift at Thunder Mountain called Devils Canyon is quite dangerous. Usually 2% of the skiers whoattempt the run will injure themselves due to falls. What is the probability that no more than 5 of the next 100 skiers who attempt this run will injure themselves. Answer Choices. A. 0.1867. B. 0.7652. C. 0.8899. D. 0.9845
Given that, there is a 2% of probability that a skier that attempts to run will injure himself on a fall.
You have to calculate the probability that no more than 5 skiers hurt themselves due to a fall in the next 100 skiers that will attempt the run.
This scenario describes a binomial experiment, where:
- The number of trials is fixed: n=100
- The trials are independent of each other.
- The probability of success is constant throughout the experiment, p=0.02
You have to calculate the probability that 5 or fewer skiers get injured, you can express this probability as follows:
\(P(X\leq5)\)The possible outcomes that are included in this expression are X=5, X=4, X=3, X=2, X=1, and X=0.
So, the probability can be expressed as follows:
\(P(X\leq5)=P(X=5)+P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0)\)Using the formula of the binomial probability, you can determine each one of the probabilities listed above.
\(P(X=x)=\frac{n!}{(n-x)!x!}*p^x*q^{(n-x)}\)Where
p is the probability of success
q is the probability of failure
n is the sample size
x is the number of successes
For this exercise:
p=0.02
q=1-p=1-0.02=0.98
n=100
-Calculate the probability of x=5
\(\begin{gathered} P(X=5)=\frac{100!}{(100-5)!5!}*0.02^5*0.98^{(100-5)} \\ P(X=5)=\frac{100!}{95!*5!}*0.02^5*0.98^{95} \\ P(X=5)=0.0353 \end{gathered}\)-Calculate the probability of x=4
\(\begin{gathered} P(X=4)=\frac{100!}{(100-4)!4!}*0.02^4*0.98^{(100-4)} \\ P(X=4)=\frac{100!}{96!*4!}*0.02^4*0.98^{96} \\ P(X=4)=0.0902 \end{gathered}\)-Calculate the probability of x=3
\(\begin{gathered} P(X=3)=\frac{100!}{(100-3)!}*0.02^3*0.98^{(100-3)} \\ P(X=3)=\frac{100!}{97!*3!}*0.02^3*0.98^{97} \\ P(X=3)=0.1823 \end{gathered}\)-Calculate the probability of x=2
\(\begin{gathered} P(X=2)=\frac{100!}{(100-2)!2!}*0.02^2*0.98^{(100-2)} \\ P(X=2)=\frac{100!}{98!*2!}*0.02^2*0.98^{98} \\ P(X=2)=0.2734 \end{gathered}\)-Calculate the probability of x=1
\(\begin{gathered} P(X=1)=\frac{100!}{(100-1)!1!}*0.02^1*0.98^{(100-1)} \\ P(X=1)=\frac{100!}{99!*1!}*0.02^1*0.98^{99} \\ P(X=1)=0.2707 \end{gathered}\)-Calculate the probability of x=0
\(\begin{gathered} P(X=0)=\frac{100!}{(100-0)!*0!}*0.02^0*0.98^{(100-0)} \\ P(X=0)=\frac{100!}{100!*0!}*0.02^0*0.98^{100} \\ P(X=0)=0.1326 \end{gathered}\)Now you can determine the probability of 5 or fewer skiers getting injured in a fall:
\(\begin{gathered} P(X\leq5)=P(X=5)+P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0) \\ P(X\leq5)=0.0353+0.0902+0.1823+0.2734+0.2707+0.1326 \\ P(X\leq5)=0.9845 \end{gathered}\)The probability that no more than 5 skiers will suffer an injury is 0.9845.
Read this introduction to a magazine article. Headphones are everywhere! People are locked in their worlds of downloaded music, relying on their private music libraries for entertainment. In doing so, they are ignoring a diverse world of radio offerings that could enrich and entertain. Local radio stations provide music and news, while National Public Radio (NPR) broadcasts discourse and entertainment for all tastes. What will most likely be included in the magazine article that follows this introduction? examples of radio programs safety tips for headphones suggestions for music downloads historical radio broadcasts
The most likely be included in the magazine article that follows this introduction is A. examples of radio programs
What is a radio program?A radio program, radio programme, or radio show is a piece of content designed for radio broadcast. It could be a one-time production or part of a recurring series.
Headphones are ubiquitous! People are trapped in their downloaded music worlds, relying on their personal music libraries for entertainment. They are thus ignoring a diverse world of radio offerings that could enrich and entertain them. Local radio stations broadcast music and news, whereas National Public Radio (NPR) broadcasts debate and entertainment for people of all ages.
Based on the information given, it should be noted that after the introduction, the next thing is to simply give the examples of the radio shows. This is important in order to buttress the introduction.
In conclusion, based on the information, the correct option is A.
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Answer:
Step-by-step explanation:
a i was told by my teacher
Suppose the dimensions of a rectangle with a perimeter of 18 inches are quadrupled. Find the perimeter of the new rectangle in inches
The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.
What are the side lengths of the first triangle?The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:
5 inches + 5 inches + 4 inches + 4 inchesWhat are the side lengths of the new triangle?5 inches x 4 = 20 inches
4 iches x 4 = 16 inches
What is the new perimeter?20 + 20 + 16 +16= =72 inches
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find the exact value of x. 45 degree and 10 side
Answer:
The exact value of the other leg is 10.
Step-by-step explanation:
Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.
Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:
c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.
Substituting known values, we get:
(10√2)^2 = 10^2 + b^2
200 = 100 + b^2
b^2 = 100
b = 10
Therefore, the exact value of the other leg is 10.
HELP PLEASE NEED IT THANKS
Answer:
<
Step-by-step explanation:
1) Substitute 5 into the question
\(\frac{4(5)}{4}\)\(2(5)-3\)2) Work out the sides
\(\frac{4(5)}{4} =5\)\(2(5)-3=7\)3) Put it into an inequality
5 < 7
Hope this helps, have a great day!
Amy walks 2 miles 60° north of east from her house as represented in the vector diagram.
On a coordinate plane, a vector has angle 60 degrees and length 2 miles.
If Amy’s house is represented as the coordinate (0, 0), what is the component form of the vector representing Amy’s destination rounded to the nearest hundredth?
⟨0.50, 0.87⟩
⟨0.87, 0.50⟩
⟨1.00, 1.73⟩
⟨1.73, 1.00⟩
Answer:
C
Step-by-step explanation:
edge 2021
The required coordinates of Amy's position are (1.00, 1.73).
Amys walk 2 miles 60° northeast from her house. Vector coordinates to be determined.
Coordinate is defined as the abscissa and ordinate of the x-axis and y-axis respectively.
Amy walk 2 miles on 60° northeast, from origin.
x coordinate = 2cos60
= 2 * 1/2
= 1
y coordinate = 2sin60
= 2*√3/2
= 1.73
Thus, the required coordinates of Amy's position are (1.00, 1.73).
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Write an expression equal to "eight more than a number divided by five"
Answer:
eight more than a number divided by five
\(\frac{x+8}{5}\)
Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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dude what is this i dont understand
Answer:
g(1) = 1
Step-by-step explanation:
the absolute value function always gives a positive result, that is
| - a | = | a | = a
to evaluate g(1) substitute x = 1 into g(x)
g(1) = - 3| 1 - 2| + 4
= - 3| - 1| + 4
= - 3(1) + 4
= - 3 + 4
= 1
Apple pie is my favorite. I bake a
lot of it because I never got my
fair share as a kid. Last year i
got a little carried away and
had 7 pies left over. I cut the
pie into pieces to freeze and
save for later. Each piece was
of a whole pie. How many
pieces of pie did I freeze?
Answer:
58
Step-by-step explanation:
You would have to turn 7 1/4 into a whole fraction.
Do,
7 * 4 = 28
28 + 1 = 29
Your new fraction would be,
29/4
Now you have to make them equal denominators with 1/8.
Lets see,
Now multiply 4 * 2 is 8.
So multiply 29 times 2.
Which is 58.
Your new fraction is,
58/8
So therefore you would have 58 pieces.