Step-by-step explanation:
(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷
(1 + i)² = 1 + 2i - 1 = 2i
((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =
= 128×-1×-1×-1×i = -128i
Clock a runs 1 minute fast per hour. Clock b runs 7 minutes slow per day. If the clocks show the same time at noon, how many minutes ahead of clock b will clock a be 48 hours later?.
The answer is, 720 minutes ahead of clock b will clock a be 48 hours later.
How to read time?
The three hands on the clock's face display the time in hours, minutes, and seconds. The hour hand, minute hand, and second hand all display the hours, minutes, and seconds respectively.
A clock has 12 large divisions that are marked. Each of the large divisions has five smaller divisions. For a minute, the little separation remains in place. Five minutes have elapsed once the minute hand transitions from one large division to the next.
we will get after 360 hrs, clocks A and B will both have the same time.
Clock A will show the correct time, whereas clock B will be running faster by 12 hrs and therefore show the same time. A clock that moves forward by 12 hours will appear to display the same time once more. 12hours*60minutes/hour= 720 minutes.
Hence the answer will be 720 minutes.
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16/31+13/31+27/31+24/31+24/31
Answer:Mixed Number Form:
3 11/31
Step-by-step explanation:
Combine the numerators over the common denominator.
16+13+27+24+24/31
Simplify by adding numbers.
Add 16 and 13.
29+27+24+24/31
Add 29 and 27.
56+24+24/31
Add 56 and 24.
80+24/31
Add 80 and 24.
104/31
The result can be shown in multiple forms.
Exact Form:
104/31
Decimal Form:
3.35483870...
Mixed Number Form:
3 11/31
Write the quadratic equation whose roots are, -4 and 6 and whose leading coefficient is 4
[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=6\implies &x-6=0 \end{cases}\qquad \implies (x+4)(x-6)=\stackrel{y}{0} \\\\\\ (x^2-2x-24)=\stackrel{y}{0}\implies 4(x^2-2x-24)=\stackrel{y}{0}\implies {\Large \begin{array}{llll} 4x^2-8x-96=y \end{array}}[/tex]
Check the picture below.
Find the take-home percent of gross pay: Gross pay: $627 Total Deductions: $185
Are the ratios 4:3 and 18:15 equivalent?
Answer: No
Step-by-step explanation: Ratios can be expressed as fractions. The ratio of 4:3 = 4/3, and 18:15 = 18/15. If you multiply the numerator and denominator by 5 (to get the same denominator as 18/15), you get 20/15.
20/15 doesn't equal 18/15.
What is the acceleration of the moon toward earth due to their mutual attraction the massive earth is 5. 98×10 to the 24th power kilograms the distance between them is 3. 8×10 to the eighth power meters and G equals 6. 673×10 to the -11th power newton meter squared per kilograms squared?
Answer:
2.76×10^-3 m/s²
Step-by-step explanation:
You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².
AccelerationThe acceleration of one body by another is ...
a = GM/r²
where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.
Applicationa = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg
a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²
Arrange these values in order of size, starting with the smallest:
36/100, 0.4, 0.32
Answer:
.32, 36/100, and 0.4
Step-by-step explanation:
An iPhone marked for $268 wa old for $334 due to it great
popularity to cutomer. By what percent did the price go up?
(Round to the nearet tenth)
In linear equation, 24.6 percent did the price go up .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Increased price= Selling Price - Original Price
Percent Increased = Increased price / Original Price × 100%
The increase of price: 334 – 268 = $66
The original price: $268
Thus, the Percent Increase: 66 ÷ 268 = 0.246 = 24.6
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what equals x 30x+1616=2561
Answer:
x=31.5
Step-by-step explanation:
30x+1616=2561
30x=2561-1616
30x=945
x=31.5
In his last game, the Ram's quarterback completed 10 out of 18 passes he threw. At this rate how many passes will he attempt if he completes 15 passes?
Answer:
23 is your answer for your question
omg this is the right one this is hard or i am dum
Answer: This is the numerator!
Step-by-step explanation:
The fraction line is well, the line.
The denominator is the number on the bottom.
And the numerator is the number on top!
This means that 3 is the numerator!
Answer: its the numerator because its on top
the expression quantity three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity
The expression is 11(t/40-2)
From the question, we have
3/4t-5+2/5t-(5/8t+17)
=2t/5+3t/4-5t/8-22
=2t/5+t/8-22
=11t/40-22
=11(t/40-2)
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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What is an equation of the line that passes through the points (6,−2) and (−4,−2)?
The equation of the line that passes through the points (6,−2) and (−4,−2) is y = -2
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Let's represent the equation of the line in slope intercept form as follows:
The equation of the line passes through the points (6,−2) and (−4,−2).
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = -2 + 2 / -4 - 6
m = 0 / - 10
m = 0
Therefore, let's find y-intercept using (6, -2).
-2 = 0(6) + b
b = -2
Therefore, the equation of the line is y = -2.
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Rewrite the following polynomial in standard form. x-9+x^2/2
Answer:
2x − 9
Step-by-step explanation:
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Maxwell is a plant manager at NV Electric Company. He has been employed there for 20
years and will be retiring at the end of this year. His pension is calculated on the average
of his last 4 years' salaries. In those years, he earned $85,000; $86,756; $88,888; and
$94,000. His employer will credit him 1.2% of that average for each year he worked.
Calculate Maxwell's pension, rounded to the nearest cent and use a $ in front of the
amount.
Maxwell's pension is $21,278.64.
Given:
Maxwell is a plant manager at NV Electric Company. He has been employed there for 20 years and will be retiring at the end of this year. His pension is calculated on the average of his last 4 years' salaries. In those years, he earned $85,000; $86,756; $88,888; and $94,000.
His employer will credit him 1.2% of that average for each year he worked.
Average = 85000+86756+88888+94000 / 4
= 3,54,644/4
= 88,661
1.2% of average = pension for each year
= 1.2*88661/100
= 106393.2/100
= $1063.932.
she worked for 20 years
20 years pension = 20*1063.932
= $21,278.64
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select all the expressions that are enwall to 89.75 */* 10
A.897.5 */* 100
B.8.975 */* 10^2
C.8.975 */* 10^0
D.8,975 */* 1,000
E.89,750 */* 10^3
help pls!
Answer: A.897.5 */* 100
Step-by-step explanation:
The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes. What does the slope mean for this situation?
Answer:
A
Step-by-step explanation:
So x is the number of minutes, this means that for each minute, 3.00$ is spent at the taxi therefore, the rate of change of the cost of the taxi ride is $3.00 per minute.
Can someone help me really quick
(Please Explain how you know this is correct.)
As per the given graph, the price per gallon at Miguel's Gasoline station is $4.4
Graph:
Graph means a pictorial representation or a diagram that represents data or values in an organized manner.
Given,
Question 6
Six customers are buying gasoline at Miguel's Gasoline Station. The number of gallons bought and the total cost of their purchases are plotted on the graph.
Here we need to find the price per gallon at Miguel's Gasoline Station.
In order to find the price, we have to take the points from the given graph.
Then we the points as, (4,10) and (9, 22)
By looking in the graph, the plotted points will form the straight line on the graph.
So, we have to use the formula for straight line to find the cost on one liter,
For, that we have to find the following,
m = (22 - 10) / (9 - 4)
m = 12/5
And the value of y intercept is,
10 = 12/5 (4) + c
50 = 48 + c
c = 2
The equation for the graph is y = 12/5x + 2
Therefore, the cost of 1 liter of the material is,
y = 12/5 (1) + 2
y = 12/5 + 2
y = 12+10/5
y = 22/5
Therefore, the cost is 4.4.
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you are testing a claim about a population proportion of 0.2. find the test statistic given the following sample results:successes: 89sample size:225
Using the test statistic formula, the test statistic is 7.3408.
In the given question,
We have to testing a claim about a population proportion of 0.2.
We have to find the test statistic given the following sample results:
Success (x) : 89
Sample Size (n) : 225
So estimation point,
p = x/n
p = 89/225
p = 0.396
We have to check the test hypothesis for:
H(0): P = 0.2
H(a): P > 0.2
Test Statistic Z = (p - P)/√P(1-p)/n)
Z = (0.396 - 0.2)/√(0.2(1-0.2)/225)
Z =0.196/√(0.2*0.8/225)
Z =0.196/√(0.16/225)
Z =0.196/√0.000711
Z =0.196/0.0267
Z = 7.3408
Hence, the test statistic is 7.3408.
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Find the area of the shaded area
The area of the shaded circular region is 197.82 unit².
What is the area of a circle?The space a circle takes up on a two-dimensional plane is known as the area of the circle. The region contained within the circle's circumference or perimeter is another way to define the circle's area. A = πr², where r is the circle's radius, is the formula for calculating a circle's surface area.
The radius of the inner circle = 9 units
So, the area of the inner circle is given by
a = πr²
= 3.14 × 9²
= 3.14 × 81
= 254.34 unit²
The radius of the outer circle = 12 units
So, the outer circle area is given by
A = πR²
= 3.14 × 12²
= 3.14 × 144
= 452.16 unit²
So, the area of the circular shaded region is given by
Area = area of the outer circle - an area of the inner circle
= 452.16 - 254.34
= 197.82 unit²
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62 60 ÷ 4 = x 4 = x 4 So 60 ÷ 4 =
The answer is 15.
From the question, we have
60 ÷ 4 = 15
The answer is 15.
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
Complete question:
Solve: 60 ÷ 4
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What's the answer to question 1
Answer:
x ≥ - 2
Step-by-step explanation:
4x ≥ - 8 ( divide both sides by 4 )
x ≥ - 2
Answer
x ≥ 2
----------------------------------------------------------------
4x ≥ 8
[tex]x \geq \frac{8}{4}[/tex]
x ≥ 2
(4)
6. Aim Julio is playing a game where he rolls a ball from one corner of the room to
the opposite corner, without touching the walls. In how many different directions
could Julio roll the ball to reach its target? How do you know?
There are many ways Julio can roll the ball to reach it target. We can evaluate this situation by using probability.
What is Probability ?Probability is the ratio of favorable outcomes to all other potential outcomes of an event.The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes.The following formula can be used to determine an event's probability.Positive Results/Total Results = x/n = Probability(Event)Let's look at a simple example to better understand probability.Imagine that we need to predict whether it will rain or not.The right response to this question is "Yes" or "No."Whether it rains or not is uncertain.Probability can be applied here.Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.Hence, we can evaluate the outcome by using probability.
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Kerry has an investment account which compounds interest annually at a rate of 4. 4%. After 3 years, she has $7080 in the account. How much money did she initially place in the account? round your answer to the nearest whole number. Do not include a $ in your answer.
She initially placed $6222 in the account.
With annual compound interest accruing at a rate of 4.4% after three years, she has now $7080 in the account.
From the question, we have
7080 = A * (1 + 4.4/100)^3
7080 = A * 1.1379
A = 7080/1.1379
= 6221.99 = $ 6222 (approx.)
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Jessica is 3 times older than Michael. The difference of their ages is 26 years. Find the ages of each.
Answer:
Micheal is 13
Jessica is 39
Step-by-step explanation:
3M=J
J-26=M
J=M+26
3M=M+26
2M=26
M=13
3(13)=J
39=J
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Graph each inequality.
27. y ≥x+7
28. y> 2|x+3| - 3
29. 4x-3y < 2
30. y≤ - 1/2|x+2|-3
The graph for each inequality is attached below.
We are given four inequalities. The first inequality is y ≥ x + 7. The second inequality is y > 2|x+3| - 3. The third inequality is 4x - 3y < 2. The fourth inequality is y ≤ (-1/2)|x + 2| - 3. In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. An inequality compares two values to determine if one is less than, larger than, or simply not equal to the other. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. A graph of every inequality is attached below.
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Ethan buys a video game on sale. If the video game usually costs $39. 99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
Answer:
$31.99
Step-by-step explanation:
20 : 100 = x : 39.99
x = 39.99 * 20 / 100
x = 39.99 * 0.2 = 7.998
final price
39.99 - 7.998 = $31.992
what hypothesis test should be used to test straight h subscript 1 italic colon italic space italic space sigma to the power of italic 2 subscript italic 1 over sigma to the power of italic 2 subscript italic 2 italic space italic space italic greater than italic space italic 1 one-sample test of means one-sample test of proportions one-sample test of variances two-sample test of means (independent samples) two-sample test of means (paired samples) two-sample test of proportions two-sample test of variances
An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
What is Hypothesis?In a scientific setting, a hypothesis (plural: hypotheses) is a tested claim regarding the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed. The hypothesis is a succinct statement of the researcher's expectation of the study's findings, which may or may not be confirmed by the results, in a scientific experiment or study. The scientific method's fundamental step is hypothesis testing.It is customary to refer to the researcher's prediction as the alternative hypothesis and any other result as the null hypothesis, or, more simply put, the opposite of what was anticipated. (However, the words are switched around if researchers are speculating that there won't be any difference or change, for instance, that the occurrence of one variable won't rise or fall in concert with thehence,sample test of means one-sample test of proportions one-sample test of variances two-sample test of means (independent samples) two-sample test of means (paired samples) two-sample test of proportions two-sample test of variances.
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Find the 70 term of the arithmetic sequence 18, 34, 50
The 70th term of the arithmetic sequence is 1,122
Given,
In the question:
The Arithmetic Sequence is given as:
18, 34, 50 ,...
To find the 70th term of the sequence.
Now, According to the question:
First term is = 18
Second term is = 34
Common difference(d) = second term - first term
d = 34 - 18
d = 16
Write the general term through the pattern ;
[tex]a_n[/tex] = 16n + 2
We have to find the 70th term
Put the value of n = 70 in above general term:
[tex]a_7_0[/tex] = 16 x 70 + 2
[tex]a_7_0[/tex] = 1,122
Hence, The 70th term of the arithmetic sequence is 1,122.
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A recipe uses 2 cups of sugar to make 32 brownies. how many X cups of sugar are needed for 72 brownies?
Answer:
4.5
Step-by-step explanation:
