The solution is, he is now 21 yrs old.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
William is 6 years older than Camila.
Nine years ago he was twice Camila’s age.
let, he is now = x yrs
Camila’s age = y yrs.
so, we get,
x-y = 6 .....(1)
and, x-9 = 2(y-9) ....(2)
solving we get,
x-9 = 2(x-6-9)
or, x = 21
Hence, The solution is, he is now 21 yrs old.
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The probability that it rain in any given day in September is 0.3. Stating any assumption made, calculate the probabilitythat in a given week in September it will rain on at most two days
The probability that in a given week in September, it will rain on at most two days is 0.12.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The probability that it rains on any given day in September = 0.3.
P ( rains ) = 0.3
And,
The probability that it will not rain on any given day in September.
P (no rain) = 1 - 0.3
P(no rain) = 0.7
Now,
The probability is that in a given week in September, it will rain on at most two days.
= P (x ≤ 2)
= P(no rain) + P(rain) + P(rain)
= 0.7 + 0.3 + 0.3
= 0.12
Thus,
The probability that in a given week in September, it will rain on at most two days is 0.12.
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. For the first 40 hours Kayla works per week, she gets paid $12/hr. For each hour over 40
worked, she gets paid $18/hr. Write a piecewise function to represent her total pay with
respect to the number of hours worked. How much will she make for working 50 hours?
Answer:
$660
Step-by-step explanation:
If she gets $12/ an hour and works for 40 hours, 12*40=480. For every hour over 40, she gets $18/an hour, so if she works for 50 hours, you do 18*10 since she only worked 10 hours over 40. 18*10=180. To get the total amount, you do 480+180, which is 660.
Hope this helps! Please give brainliest!
Answer:
Therefore, Kayla will make $660 for working 50 hours.
Step-by-step explanation:
Let H be the number of hours worked in a week. The total pay can be represented as a piecewise function as follows:
f(H) =
12 * min(H, 40) +
18 * max(0, H - 40) if H >= 0
So, for H = 50 hours worked, we have:
f(50) = 12 * min(50, 40) + 18 * max(0, 50 - 40)
= 12 * 40 + 18 * (50 - 40)
= 480 + 180
= $660
Therefore, Kayla will make $660 for working 50 hours.
Question 10 Part 1 of 3
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium
population continues to grow for a while, but then stops growing and begins to decline. The size of
the population at time t (hours) is b=8^6 +8^3t-8^2 t^2. Find the growth rates at t=0 hours,
t=4 hours, and t=8 hours.
The growth rate at t=0 hours is _____bacteria per hour
The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is 1,000,016.
How to calculate the number of bacteria over time?To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.
0 hours:
Population = 10^6 + (10^4)0 -(10^3)0^2
Population = 10^6 - 10^3
Population = 10^3 or 1,000
4 hours:
Population = 10^6 + (10^4)4 -(10^3)4^2
Population= 10^6 + 40,000 - 16,000
Population= 1,000,024
8 hours:
Population = 10^6 + (10^4)8 -(10^3)8^2
Population= 10^6 + 80,000 - 64,000
Population= 1,000,016
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el avión más grande el airbus a380 tiene una longitud de 239 ft 6 pulgadas una embarga dura de 261 ft y 10 pulgadas y una altura de 79 ft 1pulgada expresa estás dimensiones en metros
examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer
You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The lengths for this problem are given as follows:
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What is the equation of the line that passes through the point (6, -5) and has a slope of -1/3?
y=mx+b
m=slope
b= y-intercept
x=6
y=-5
-5= -1/3(6)+b
-5= 2+b
-2 -2
-7 = b
y= -1/3x-7
Answer:
y=-1/3x-3
Step-by-step explanation:
Solve the following quadratic- like equation y 1/2-4y 1/4+3=0
The value of the quadratic like equation is given as y = 1 and y = 81.
What is substitution method?The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be favoured over the cross-multiplication method and the elimination method for straightforward equations without a lot of complicated calculations.
The equation is:
[tex]y^{\frac{1}{2} } - 4y^{\frac{1}{4} } + 3 = 0[/tex]
Using the exponent property we can write the equation as follows:
[tex](y^{\frac{1}{2} })^{\frac{4}{4} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{\frac{4}{2} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{2} - 4y^{\frac{1}{4} } + 3 = 0[/tex]
Now suppose the value of [tex]y^{\frac{1}{4} } = x[/tex].
x² - 4x + 3 = 0
x² - 3x - x + 3 = 0
x(x - 3) -1 (x - 3) = 0
(x - 1)(x - 3) = 0
x = 1
x = 3
Now, back substituting the value of [tex]y^{\frac{1}{4} } = x[/tex].
[tex]y^{\frac{1}{4} } = 1\\\\y^{\frac{1}{4} } = 3\\[/tex]
Raise to four on both sides of the equation we have:
y = 1
y = (3)⁴
y = 81
Hence, the value of the quadratic like equation is given as y = 1 and y = 81.
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An angle measures 64.2° more than the measure of its complementary angle. What is the measure of each angle?
On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.
What are angles?An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.
An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.
x = first angle
Complementary angle is 14.2 degrees more than the cοmplementary angle.
First angle = x
Second angle = x + 14.2°
Complementary angle
x+x+14.2=90
2x+14.290
2x 90 14.2
2x = 75.8 x = 37.9
First angle is 37.9°.
Second angle will be:
x+14.2°
⇒37.9°+ 14.2°
⇒52.1°
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Given the following parallelogram, solve for x.
X =
(18x - 79) °
(7x + 9) °
how to solve this question
Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?
The numbers could be:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
Shawn rounded a number to the nearest tenth and got 6.5.
When he rounded it to the nearest whole number, he got 6.
Now,
The number = 6.45
Rounded to the nearest tenth = 6.5
Rounded to the nearest whole number = 6
The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
Thus,
The possible numbers are:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
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Correct the one error. Just ten more day's and I'll be in London!
Just ten more days and I'll be in London!
Answer:
Just ten more days and I'll be in London!
Can anyone explain this question about complex numbers ?
Answer:
Step-by-step explanation:
(a) Using de Moivre's Theorem, we have that:
z^n = cos(nθ) + i sin(nθ)
1/z^n = cos(-nθ) + i sin(-nθ)
So, we can find z^n + 1/z^n as:
z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)
And z^n - 1/z^n as:
z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)
(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):
2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0
Expanding the right hand side using the trigonometric identities, we get:
2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0
Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.
(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.
Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.
Write the phrase as an expression
the sum of 18 and 35:
6 times 50:
25 less than a number b:
a number x divided by 4:
the total of a number t and 11:
100 decreased by a number k:
Answer:
1. 18 + 35
2. 6 * 50
3. b - 25
4. x / 4
5. t + 11
6. 100 - k
Step-by-step explanation:
Question 2
Answer: y =
<
-
Find the equation of the line with Slope = passing through the point (-35,10). Write your answer
in the form y = mz+ b.
I+
Submit Question
>
5
7
Write your answers as integers or as reduced fractions in the form A/B.
Question Help: Video Message instructor
An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 10 = -5/7(x - (-35))
y - 10 = -5/7(x + 35)
y - 10 = -5x/7 - 25
y = -5x/7 - 15
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can you please write out how you got the below answer?
Answer:
degree 2 and 10
Step-by-step explanation:
the degree of a polynomial is the value of the largest exponent of the variable.
r(x) = 10x² + 4x - 7
has largest exponent 2
this is a polynomial of degree 2
the leading coefficient is the coefficient of 10x²
that is leading coefficient is 10
Determine whether the ordered pair is a solution to the system of equations or inequalities y<4x-1; y>x. Yes or no?
(1,3)
(0,0)
Answer:
Step-by-step explanation:
To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.
Here's the step-by-step process for each ordered pair:
(1,3):
Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.
Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.
Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.
(0,0):
Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.
Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.
Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.
1/4 (8x plus 2) = 20
Answer:
x = 9.75
Step-by-step explanation:
1 / 4 * ( 8x + 2) = 20
( 8x + 2) = 20 / (1/4)
8x + 2 = 20 * 4
8x + 2 = 80
8x = 78
x = 9.75
Answer:
x=39/4 (39 over 4 as a fraction)
Please helpppp
if y+3/y-3 = 6
What is the value of y?
f(x) =3(x-2) (x+4)
f(x) = (3x+12) (x-2)
f(x) =3(x+4) (x+2)
f(x) = 3 (x-4) (x+2)
Answer:
Answer is in the attached photo
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note to find the value of y, we will have to make y the subject.
A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score?
A. B in 3 three-credit classes
B. D in 1 three-credit class
C. in 1 four-credit class
D. C in 1 two-credit class
Weighed averages show that the student has a grade point average of 2.33.
How is the grade point determined?The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.
A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.
B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.
C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.
D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.
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Simplify 8⁶÷8 Please im have trouble
Answer: 8^5
Step-by-step explanation: 8^6 is 8*8*8*8*8*8, so when you divide by 8 it cancels one of the 8s. Therefore you are left with 8*8*8*8*8 or 8^5.
Please help me with this question please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.
In the given figure, there are two pairs of vertical angles~
That are :
[tex]\qquad \sf \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]
and
[tex]\qquad \sf \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]
Also, vertical opposite angles are equal in measure.
For a certain year, the combined revenue of Nintendo and Sony was $44 billion. If that year the revenue for Sony was $12 billion more than the revenue for Nintendo, how much was the revenue for Nintendo?
Answer:
Nintendo's revenue was $21 billion
Step-by-step explanation:
For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets.
{10, 15, 14, 20, 11}
...
Step-by-step explanation:
A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.
To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.
To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.
Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.
Plot 1 1/2 and 2 2/5
The numbers on a number line is
|-------|-------|-------|-------|
0 1 2 3 4
* *
1 1/2 2 2/5
How to represent the numbers on a number lineFrom the question, we have the following parameters that can be used in our computation:
Plot 1 1/2 and 2 2/5
To plot 1 1/2 and 2 2/5 on a number line, we can follow these steps:
Find a suitable scale for the number line. Let's use the interval of 1 between each tick mark.Plot the first number, 1 1/2. 1 1/2 is halfway between 1 and 2Plot the second number, 2 2/5. This is between 3 and 3Read more about number line at
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Tony saved enough money to afford a car. He needs to determine if he can afford the car insurance. Tony earns $160 per week. Tony's yearly pay is $8,320 and his monthly pay is $693.
Tony's monthly car insurance will be 1/30 of his rounded yearly pay. Can he afford it?
Explain why or why not.
Tony can afford the car insurance, and he has enough money($426.33) left over each month to cover other expenses.
What is car insurance?Automobile, truck, motorbike, and other types of road vehicles are covered by vehicle insurance. Its main purpose is to offer financial security against property loss or personal injury brought on by auto accidents, as well as against liability that can emerge from related events.
According to the information given,
Tony's yearly pay is $8,320
and his monthly pay is $693.
If we round his yearly pay to $8,000, his monthly car insurance will be 1/30 of that amount, or $266.67.
Since Tony's monthly pay is $693, and his monthly car insurance will cost $266.67, he can afford the insurance. He will have $426.33 remaining each month after paying for the insurance.
Therefore, Tony can afford the car insurance, and he has enough money left over each month to cover other expenses. However, this calculation assumes that Tony has no other major expenses or debts, and it is always a good idea to budget carefully and consider all potential costs before making a significant purchase.
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Evaluate the expression:(2-1/2 • 7 1/3)^6
Write the answer in the most simplified form. Use fractions instead of decimal numbers.
The simplified form of the expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex] is [tex]6\frac{1}{8}[/tex].
What is the simplified form of the expression?Given the expression in the question:
[tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex]
To simplify the given expression [tex]( 2^{-\frac{1}{2}} * 7^{\frac{1}{3} )^6[/tex], first, rewrite the expression using the negative exponent rule:
[tex]( \frac{1}{2^{\frac{1}{2} }} * 7^{\frac{1}{3} )^6[/tex]
Next, combine the fractions:
[tex]( \frac{7^{\frac{1}{3} }}{2^{\frac{1}{2} }} )^6[/tex]
Simplify the numnerator:
[tex]\frac{49}{(2^{\frac{1}{2} })^6}[/tex]
Simplify the denpminator:
[tex]\frac{49}{8}\\ \\6\frac{1}{8}[/tex]
Therefore, the simplified form is [tex]6\frac{1}{8}[/tex]
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A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of
100
100100 teachers from a statewide database containing every teacher, and they find
55
5555 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample
z
zz interval for a proportion.
Which conditions for constructing this confidence interval did their sample meet?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
The data is a random sample from the population of interest.
(Choice B)
B
n
p
^
≥
10
n
p
^
≥10n, p, with, hat, on top, is greater than or equal to, 10 and
n
(
1
−
p
^
)
≥
10
n(1−
p
^
)≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10
(Choice C)
C
Individual observations can be considered independent.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
What do you mean by SRS (Simple Random Sample)?Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.
To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.
A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.
B) np^≥10n p^ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.
C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.
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[tex] {x}^{\frac{2}{3} }{ } = 64 [/tex]
Solve the following equation
The value of x in the given equation using laws of exponents is; x = 512
How to use Laws of Exponents?The different laws of exponents include;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
We have the equation as;
x^(2/3) = 64
We can write 64 as (∛512)²
This can be further expressed as;
512^(2/3)
Thus, we have;
x^(2/3) = 512^(2/3)
Thus, by identity rule;
x = 512
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What is the average rate of change? Problem in the picture
The average rate of change of the function f(x) over the interval (-1, 2) is; 3.
What is the difference quotient of the function over the given interval?As evident in the task content; the given function is as represented by the graph of f(x).
Hence, the average rate of change of the function over the given interval; (-1, 2) is;
= ( f (2) - f (-1) ) / (2 - (-1))
where; f (2) = 5 and f (-1) = -4.
Therefore, the average rate of change is;
= (5 - (-4)) / (2 - (-1))
= 9 / 3.
= 3.
Ultimately, the difference quotient of f (x) over the given interval is; 3.
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