Answer:
x = 1/8Step-by-step explanation:
Given the expression 0.25÷3=x÷1 1/2, we are to look for the value of x from the given equation. Rewriting the equation we will have;
[tex]\dfrac{0.25}{3} = \dfrac{x}{1\frac{1}{2} }[/tex]
On simplification;
[tex]0.25 * \frac{1}{3} = x * \frac{2}{3} \\ \\ \frac{25}{100}*\frac{1}{3} =\frac{2x}{3}\\\\ \frac{1}{4} * \frac{1}{3} = \frac{2x}{3}\\\\ \frac{1}{12} = \frac{2x}{3}\\\\cross \ multiply\\\\2x * 12 = 3\\\\24x = 3\\\\Divide \ both \ sides \ by \ 24\\\\24x/24 = 3/24\\\\x = 1/8[/tex]
Hence the value of x in the expression is 1/8
Lauren has 108 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 9 kids on her block. Write an equation to show how many pieces of candy each kid will receive. 9 + x = 108 x = 108 − 9 x = one hundred eight divided by nine x = nine divided by one hundred eight
Answer:
9 x =108
Step-by-step explanation:
Let the number of candies be x.
According to the question,
x=108/9
We can also write it as,
9 x=108
By the way ,each child will get 12 candies.
Thank you!
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.
2(cos20∘+isin20∘))3=__________
Answer:
After solving the power:
[tex]\bold{2(cos60^\circ+isin60^\circ)}[/tex]
Rectangular form:
[tex]\bold{1+i\sqrt3}[/tex]
Step-by-step explanation:
Given the complex number:
[tex]2(cos20^\circ+isin20^\circ)^3[/tex]
To find:
The indicated power by using De Moivre's theorem.
The complex number in rectangular form.
Rectangular form of a complex number is given as [tex]a+ib[/tex] where a and b are real numbers.
Solution:
First of all, let us have a look at the De Moivre's theorem:
[tex](cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )[/tex]
First of all, let us solve:
[tex](cos20^\circ+isin20^\circ)^3[/tex]
Let us apply the De Moivre's Theorem:
Here, n = 3
[tex](cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ[/tex]
Now, the given complex number becomes:
[tex]2(cos60^\circ+isin60^\circ)[/tex]
Let us put the values of [tex]cos60^\circ = \frac{1}{2}[/tex] and [tex]sin60^\circ = \frac{\sqrt3}{2}[/tex]
[tex]2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }[/tex]
So, the rectangular form of the given complex number is:
[tex]\bold{1+i\sqrt3}[/tex]
George's height is 1.75 meters and Martha's height is 160 centimeters. How much taller is George than Martha in millimeters?
George should be 150 mm taller than Martha.
Calculation of the height in millimeters:
Since George's height is 1.75 meters and Martha's height is 160 centimeters.
So here we convert the meters to mm
So,
[tex]= 1.75\times 100\\\[/tex]
= 1750 mm
Now 160 cm to mm
So,
[tex]= 160\times 10[/tex]
= 1,600 mm
So, the difference should be
= 1,750 - 1,600
= 150 mm
Therefore, George should be 150 mm taller than Martha.
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If 4 pounds of cherries cost $10, what is the unit price
Answer:
2.5$ per pound
Step-by-step explanation:
The cost of 4 pounds of cherries cost 10$
So to khow the price of 1 pound we must divide 10 by 4.
● 10/4 = 2.5
So 1 pound costs 2.5$
Find the missing probability. P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=? A. 7/8 B. 1/4 C. 117/400 D. 19/40
Answer:
B
Step-by-step explanation:
P(AUB)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4
The value of P(B) is 1/4.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = p/q
Given data as :
P(A) = 7/20,
P(A∪B) = 191/400,
P(A∩B) = 49/400 ,
P(AUB) = P(A) + P(B) - P(A∩B)
Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,
191/400 = 7/20 + P(B) - 49/400
Rearrange the terms in the equation,
P(B) = 191/400 + 49/400 - 7/20
P(B) = 240/400 - 7/20
P(B) = 12/20 - 7/20
P(B) = 5/20
P(B) = 1/4
Hence, the value of P(B) is 1/4.
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BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...
Answer:
-21
Step-by-step explanation:
1-2+4-8+16-32
=-21
Answer:
The sum of the first 6 terms of the infinite series will be - 21.
Step-by-step explanation:
In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,
[tex]\sum _{{k=0}}^{{n}}(-2)^{k}[/tex]
Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,
1 - 2 + 4 - 8 + 16 - 32
= - 1 + 4 - 8 + 16 - 32
= 3 - 8 + 16 - 32 = - 5 + 16 - 32
= 11 - 32 = Solution : - 21
Find the missing side or angle.
Round to the nearest tenth.
Answer:
[tex] b = 2.7 [/tex]
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]
Plug in the values into the formula
[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]
Cross multiply
[tex] 2*sin(80) = b*sin(47) [/tex]
Divide both sides by sin(47) to make b the subject of formula
[tex] \frac{2*sin(80)}{sin(47} = b [/tex]
[tex] 2.69 = b [/tex]
[tex] b = 2.7 [/tex] (nearest tenth)
Maya is interning at a law firm over the summer and is paid b the hour. If her hourly wage is $52 which represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answer: [tex]w= 52 h[/tex] .
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid per hour.
Total wages = (Hourly wage) x (Number of hours worked)
If her hourly wage is $52, then the total wages(w) = 52 x (Number of hours(h))
i.e. w= 52 h
Hence, the proportional relationship between the wages she earns (w) and the number of hours (h) described by [tex]w= 52 h[/tex] .
line m in the xy-plane above is to be reflected through the x-axis. if the slope of line m is 2/3,whats is the slope of the image of line m under the reflection.
Answer: The new slope is -(2/3)
Step-by-step explanation:
Ok, we know that our line can be written as:
y = (2/3)*x + b
where b is the y-intercept, and here does not really matter.
Ok, remember that if we have a point (x, y) and we reflect it over the x-axis, the new point will be (x, -y).
For our linear equation, the point (x, y) can be written as:
(x, y = (2/3)*x + b) = (x, (2/3)*x + b)
Now, after the reflection, our point is:
(x, - ( (2/3)*x + b)) = (x, -(2/3)*x - b)
Then our new line is y = -(2/3)*x - b
The new slope is -(2/3)
Which given answer is correct and how do you solve for it?
Answer:
b
Step-by-step explanation:
Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)
Answer:
Please refer to the attached graph.
Slope = -3.125
Step-by-step explanation:
Given
Time is placed on x axis.
Initially, height of rock climber is 25 feet above sea level.
[tex]t_1 =0\ sec[/tex]
[tex]h_1[/tex] = 25 feet
After 8 seconds, he is at sea level.
[tex]t_2 =8\ sec[/tex]
[tex]h_2[/tex] = 0 feet
To find:
Graph of the given points and Slope of the line depicted.
Solution:
Kindly refer to the attached graph.
Here, we have been given two points to be plotted on the xy coordinate plane.
1st point is (0, 25): Time is 0 and height above sea level is 25 ft
2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)
First of all, mark these points and join them with a straight line.
Please refer to attached graph.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]
Using the formula:
[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]
The miss Petra psychic hotline charges 5$ For the first minute and 2$ for each additional minute. Give an equation the describes the situation
Answer:
y=2(x-1)+5
Step-by-step explanation:
We know that it is 5 dollars for the first minute so we know the equation will start off with +5.
Than for the rest of the minutes, we have to make sure to subtract one from them, because the first number is worth 3 dollars more. Which is why it is x-1.
Then we multiply the new value times 2, because each additional minute is 2 dollars more.
Polar coordinates: which is not the same?
Answer:
The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.
Step-by-step explanation:
Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.
Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.
Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)
We know that :
7.518 - 1.236 = 6.282 = ( About ) 2π
5.047 + 1.236 = 6.283 = ( About ) 2π
1.236 + 1.906 = 3.142 = ( About ) 2π
Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).
A baseball player has a batting average of 0.26. What is the probability that he has exactly 6 hits in his next 7 at bats
Answer:
0.0016
Step-by-step explanation:
Batting average, p = 0.26
n = 7
x = 6
With p = 0.26 as success rate
1-p is equal to failure rate which is = 0.74
We have to solve this by using the binomial distribution formula.
P(X= x)
= nCx * p^x * (1-p)^(n-x)
P(X = 6)
=7C6 × 0.26^6 ×(1-0.26)^(7-6)
= 7 × 0.0003089 × 0..74¹
= 0.0016
So probability that he has exactly 6 hits in his next 7 bats is equal to 0.0016.
Laura is bowling 5 games. Her first 4 scores were 135, 144, 116, and 132.
To end up with an average score of at least 136.8, what is the lowest score Laura will need in the fifth game?
Answer:
it doesnt add up. the question doesnt make sense.
Step-by-step explanation:
Answer:
157
Step-by-step explanation:
To find the average score, add all individual scores and divide the sum by the number of individual scores.
She has 5 individual scores. Let's say her scores are A, B, C, D, and E.
average score = (A + B + C + D + E)/5
Now we plug in the average and the 4 known scores for A through D, and we solve for E.
average score = (A + B + C + D + E)/5
136.8 = (135 + 144 + 116 + 132 + E)/5
E = 157
Answer: 157
1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand.
How many animals were going to the river?
Answer:
91 animals
Step-by-step explanation:
Because every elephant saw 3 monkeys, there were 9 * 3 = 27 monkeys and because every monkey had 1 tortoise in each hand and we know that monkeys have 2 hands, there were 27 * 2 = 54 tortoises. To find the total number of animals that were going to the river, we can calculate 1 + 9 + 27 + 54 = 91 animals.
Answer:
10
Step-by-step explanation:
Only the rabbit and the 3 monkeys are described as going to the river. The tortoises seem to be going to the river by virtue of being taken there by the monkeys. Those on the path to the river were ...
1 rabbit
3 monkeys
6 tortoises
A total of 10 animals.
The average salary of all assembly-line employees at a certain car manufacturer is $42,000 is it a sample or population
Answer:
Population parameters
Step-by-step explanation:
Population parameters usually find from the average values, in a simple way we can say that finding the average value comes in the Population Parameters.
In the given question, car manufacturing companies provide sample of average.
So, given scenario is a type of "Population parameters".
What is the probability that a student who has no chores has a curfew ?
Answer:
15/22
Step-by-step explanation:
Of the 66 students who have no chores, 45 have a curfew. So the probability is 45/66 = 15/22.
State whether each ratio forms a proportion.
1) 6:3, 18:9 2) 3:4, 30:40 3) 14/18,28/36 4) 2/5,5/2
Answer: Please Give Me Brainliest, Thank You!
#1, #2, #3 do, but #4 doesn't
Step-by-step explanation:
#1
18/9=2
6/3=2
#2
30/3=10
40/4=10
#3
28/14=2
36/18=2
x/5=-2 . And how did you get it?
[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]
Answer:
[tex]\huge \boxed{{x=-10}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{5} =-2[/tex]
We need the x variable to be isolated on one side of the equation, so we can find the value of x.
Multiply both sides of the equation by 5.
[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]
Simplify the equation.
[tex]x=-10[/tex]
The value of x that makes the equation true is -10.
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 2nd longest side on quadrilateral EFGH?
Answer:
24
Step-by-step explanation:
For ABCD the three longest are:
60,40,30
60 to 40 is 20
40 to 30 is 10
so each time it's decreasing by 1/2
For EFGH the two shortest are:
6 and 12
12 to 6 is 1/2
Assuming there is a pattern
it logically would be 24
as 12(2)=24
what is 90.125 written in expanded from?
Answer:
The answer is 90+0+0.1+0.02+0.005.
Step-by-step explanation:
The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.
The Rogers family drove 220 miles in 5.5 hours. How many miles would they drive at this same rate in 4 hours? A. 88 mi B. 147 mi C. 160 mi D. 179 mi Please show ALL work! <3
Answer:
160 miles
Step-by-step explanation:
We can use a ratio to solve
220 miles x miles
--------------- = ----------------------
5.5 hours 4 hours
Using cross products
220 *4 = 5.5x
880 = 5.5x
Divide each side by 5.5
880/5.5 = x
160 miles
Answer:
[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]
Step-by-step explanation:
We can solve this problem by ratios.
Let x be the missing value.
[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]
Cross multiply.
[tex]5.5 \times x = 220 \times 4[/tex]
[tex]5.5x=880[/tex]
Divide both sides by 5.5.
[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]
[tex]x=160[/tex]
Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.
Answer: Jake is 9 and his dad is 33.
Step-by-step explanation: 9x3=27+6=33 9+33=42
Answer:
Jake is 9 and Jake's dad is 33
Step-by-step explanation:
To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake
J+D=42
3J+6=D
Solve by substitution
How many multiples of 4, that are smaller than 1,000, do not contain any of the digits 6, 7, 8, 9 or 0? I really need a answer.
Answer:
Step-by-step explanation:
We could start by listing multiples of 4 and looking for patterns. Do
you know what a multiple of a number is? It's that number multiplied
by another number. So the first multiple of 4 is 4x1, the second
multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc.
Let's make a table of multiples of 4 from 1 to 100, with columns A-E
across the top and rows 1-5 down the left-hand side:
A B C D E
1 4 8 12 16 20
2 24 28 32 36 40
3 44 48 52 56 60
4 64 68 72 76 80
5 84 88 92 96 100
Now let's look at these multiples, remembering that there will be nine
more tables like this one from 101-1000.
Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase
all of columns B, D, and E because there's a 6 or an 8 or a 0 in each
number in those columns. Now we're left with just:
A C
1 4 12
2 24 32
3 44 52
4 64 72
5 84 92
Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because
they have 6, 7, 8, or 9, leaving:
A C
1 4 12
2 24 32
3 44 52
Just 6 numbers left!
So if from 1-100 there are 6 multiples of four that do not contain any
of the digits 6, 7, 8, 9, or 0, how many multiples of four like this
are there from 1-1000?
Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply rule : [tex]a^1 =a[/tex]
[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]
[tex]\displaystyle \frac{1}{g^{-1}}[/tex]
Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]
Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]
Answer:
[tex]\frac{1}{g^1}[/tex]
= [tex]\frac{1}{g}[/tex]
[tex]\frac{1}{g - 1}[/tex]
= [tex]\frac{g^1}{1}[/tex]
= [tex]\frac{g}{1}[/tex]
= g
Hope this helps!
When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
Answer:
Because it increases the risk of Type 1 error
Step-by-step explanation:
ANOVA is the analysis of the variance .
When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .
For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.
This has two disadvantages .
First the procedure is too lengthy and tediuos.
Second the overall level of significance greatly increases as the number of t- tests increases.
The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.
a ball is thrown upward with an initial height of 3 feet with an initial upward velocity 37 ft/s the balls heigh in feet after t second is given by h=3=+37t-16t^2
Answer:
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Step-by-step explanation:
Given
[tex]h=3+37t-16t^2[/tex]
Required
Find all values of t when height is 23 feet
To solve this, we simply substitute 23 for h
[tex]23=3+37t-16t^2[/tex]
Collect like terms
[tex]16t^2 - 37t - 3 + 23=0[/tex]
[tex]16t^2 - 37t +20=0[/tex]
Solve t using quadratic formula;
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where a = 16, b =-37 and c = 20
[tex]t = \frac{-(-37)\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]
[tex]t = \frac{37\±\sqrt{1369 - 1280}}{32}[/tex]
[tex]t = \frac{37\±\sqrt{89}}{32}[/tex]
[tex]t = \frac{37\±9.43}{32}[/tex]
[tex]t = \frac{37+9.43}{32}[/tex] or [tex]t = \frac{37-9.43}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]
[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]
Which table has a constant of proportionality between 7 and x of 1/4? Choices are in the image
Answer:
A. has a constant proportion of 1/4.
3 1/2 ft into inches
Answer:
42 inches
Step-by-step explanation:
1 ft = 12 inch
Answer:
42 inches.
Step-by-step explanation:
Unit of measurement:
1 foot = 12 inches.
3 ft x 12 inches = 36 inches.
1/2 foot x 12 inches = 12/2 = 6 inches.
36 inches + 6 inches = 42 inches
42 inches is your answer.
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