Answer:
[tex]\huge\boxed{4^{-2}}[/tex]
Step-by-step explanation:
If we have the expression [tex]4^6 \cdot 4^{-8}[/tex], our goal is to simplify it.
Using exponent rules, we know that [tex]a^b \cdot a^c = a^{b+c}[/tex].
Therefore, we can add our exponents (since we have the same base, 4) to get our simplified expression.
[tex]6 + -8[/tex]
Adding a negative is the same as subtracting a positive.
[tex]6 - 8 = -2[/tex]
Now we raise 4 to that power.
[tex]4^{-2}[/tex]
Hope this helped!
How many times greater is the thickness of a dime than the thickness of a dollar bill? Round your answer to the nearest whole number.
Dime Thickness = 0.135 cm Dollar Thickness = 1.0992 x 10^-2 cm
Dime Thickness = 0.135 cm. Dollar Thickness = 1.0992 x 10^-2 cm. To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill:0.135 cm / 1.0992 x 10^-2 cm = 12.3 times.
Therefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill. Round off the answer to the nearest whole number is 12.
To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill. To do that, let's use the given values to find out the ratio of the thicknesses of a dime and a dollar bill.
Thickness of a dime = 0.135 cmThickness of a dollar bill = 1.0992 x 10^-2 cmLet us divide the thickness of a dime by the thickness of a dollar bill to find the ratio of thicknesses.0.135 cm / 1.0992 x 10^-2 cm= 12.3 timesTherefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill.
The answer should be rounded off to the nearest whole number, which is 12. So, it can be concluded that the thickness of a dime is 12 times greater than the thickness of a dollar bill.
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a) Work out (5 x 10^3)x(9 x 10^7)
Give your answer in standard form.
Answer:
45000000000
Step-by-step explanation:
when multiplying exponents, you multiply base numbers with no exponent (9 and five in this case) and numbers with exponents (10 in this case). 9 X 5 is 45 and 10 to the power of 7 times 10 to the power of 2 is 10 to the power of 9 or 1000000000. 45 X 1000000000 is 45000000000.
The standard form of (5 x 10³) x (9 x [tex]10^7[/tex]) is 450000000000.
The standard form of (7 x [tex]10^5[/tex]) ÷ (2 x 10²) is 3500.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(5 x 10³) x (9 x [tex]10^7[/tex])
= 5 x 9 x [tex]10^{3 + 7}[/tex]
= 45 x [tex]10^{10}[/tex]
= 450000000000
(7 x [tex]10^5[/tex]) ÷ (2 x 10²)
= (7 x [tex]10^5[/tex])/(2 x 10²)
= 7/2 x [tex]10^{5 -2}[/tex]
= 3.5 x 10³
= 35/10 x 1000
= 3500
Thus,
The standard values are 450000000000 and 3500.
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two opposite integer are 12 unit apart on a number line .what are the integers?
Answer:
6 and -6
Step-by-step explanation:
Since they're 12 units apart that means one of them is 6 and the fact they're opposites means the other is -12
write a system of constraints whose graph is a parallelogram
To create a system of constraints that defines a parallelogram, we need to establish conditions that satisfy the properties of a parallelogram: opposite sides are parallel and equal in length, and opposite angles are congruent.
Here's an example of a system of constraints that represents a parallelogram:
Let's consider a parallelogram with vertices (x, y):
1. Constraint 1: Opposite sides are parallel.
This can be represented by the equation: y = ax + b, where a is the slope and b is the y-intercept.
2. Constraint 2: Opposite sides are equal in length.
This can be represented by the equation: [tex](x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2[/tex] are the coordinates of two opposite vertices.
3. Constraint 3: Opposite angles are congruent.
This can be represented by the equation: [tex]m_1 = m_2[/tex], where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of two adjacent sides.
By combining these three constraints, we can define a system of equations that represents a parallelogram. The specific values of a, b, ([tex]x_1, y_1[/tex]), and ([tex]x_2, y_2[/tex]) will determine the properties and shape of the parallelogram.
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Answer whether the following statement is TRUE or FALSE. (a) [3 pts.] If the random variable X is constant, the expectation of X is always zero. (b) [3 pts.] If the random variable X is constant, the variance of X is always zero. (c) [3 pts.] If two random variables are independent, they always have zero covariance. (c) [3 pts.] If two random variables have zero covariance, they are always independent.
(a) False. If the random variable X is constant, the expectation of X will be equal to that constant value, not necessarily zero.
(b) True. If the random variable X is constant, it has no variation in its values, and hence its variance will be zero.
(c) True. If two random variables X and Y are independent, their covariance will always be zero.
(d) False. Although having zero covariance implies independence for some cases,
(a) False. If the random variable X is constant, the expectation of X will be equal to that constant value, not necessarily zero. The expectation represents the average value of a random variable, so if X is constant, its expectation will be equal to that constant.
(b) True. If the random variable X is constant, it has no variation in its values, and hence its variance will be zero. Variance measures the spread or dispersion of a random variable's values around its mean. Since X is constant, there is no spread, resulting in a variance of zero.
(c) True. If two random variables X and Y are independent, their covariance will always be zero. Covariance measures the linear relationship between two random variables. When variables are independent, there is no linear relationship between them, and thus their covariance is zero.
(d) False. Although having zero covariance implies independence for some cases, it does not hold universally. Zero covariance only guarantees independence if the variables are jointly normally distributed. There can be cases where variables have zero covariance but are still dependent. Independence requires more than just zero covariance; it implies that the variables are completely unrelated to each other.
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The football team gained 8 yards on the first play. Lost 6 uards on the next. Gained 3 yards in the third play and lost 12 yards on their final play. What was their final change in yardage after the four plays
4x + 4 = 2x + 36
HELP ASAP
Answer:
x= 16
i send you a picture how to do it
If f(x) = x/2 plus 8 what is f(x) when x = 10
[tex]f(x)=\frac{x}{2}+8[/tex]
Given y = f(x)
Substitute x = 10.
[tex]f(10)=\frac{10}{2} +8\\f(10)=5+8\\f(10)=13[/tex]
Therefore f(x) = 13 when x = 10
Toby and clara are telemarkers yesterday Clara reached 4 people in 10 phone calls,while Toby reached 3 people in 8 phone calls if they continue at those rates who will reach 40 phone calls.
Answer:
Clara
Step-by-step explanation:
Very very easy:
Amount Of people Clara reached: 4
4 multiplied by 10 is 40! ^^
Can you please help me! ( Thank you so much! ). :)
A factory has two bottle filling machines, which run at the same time. Machine B fills bottles at a rate of x, which is 1.5 times the rate of Machine A. The factory is considering buying a new machine that would replace the other two machines. It can fill at a rate of 3x.
If the factory buys the new machine to replace the other two, which of the following expressions show the increase in rate?
Answer:
[tex]\dfrac{4}{3}x[/tex]
Step-by-step explanation:
Given that:
Rate of bottle filling for Machine B = [tex]x[/tex]
Rate of filling of Machine B is 1.5 times the rate of Machine A.
Let the rate of bottle filling for Machine A = [tex]y[/tex]
As per question statement:
[tex]x=1.5y\\\Rightarrow y=\dfrac{2}{3}x[/tex]
Now, combined rate of both the machines, i.e. A and B = [tex]x+y[/tex]
[tex]\Rightarrow x+\dfrac{2}{3}x\\\Rightarrow \dfrac{5}{3}x[/tex]
Bottle filling Rate of new Machine = [tex]3x[/tex]
It is given that both the machines are replaced by the new machine.
Now, increase in the rate can be calculated by subtracting the combined rate of both the machines from the bottle filling rate of new machine.
i.e.
[tex]3x-\dfrac{5x}3\\\Rightarrow \dfrac{9x-5x}{3}\\\Rightarrow \bold{\dfrac{4x}{3}}[/tex]
So, the following expression shows the increase in rate:
[tex]\dfrac{4}{3}x[/tex]
I need help 2x + 1 when x = 2
Answer:
2(2) + 1 = 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
2*2=4+1=5
The acceleration, in feet per second per second, of an object is given by the acceleration function (t) = 2 sin t + 1. The initial velocity is v (0) = 0 and the initial position is $ (0) =3. Find the equation of velocity function. Find the position function and the average value of the position function from time t = 2 seconds to t = 5 seconds Show all your work For an indefinite integral, use the notation INT in place of the symbol. For example, f (x + 1) dx should be written as INT (€ + 1) dx. For a definite integral, use the notation INT (a,6). For example, f? (c + 1) dx should be written as INT (1,2) (€ + 1) dx. For a definite integral that has been integrated, use the notation EVAL (a,6) . For example, 2 + 2) should be written as +3 EVAL (1,2)
The average value of the position function from t = 2 seconds to t = 5 seconds is approximately: Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]
To find the equation of the velocity function, we need to find the antiderivative of the acceleration function. The antiderivative of 2 sin(t) is -2 cos(t), and the antiderivative of 1 is t.
So, the velocity function v(t) is given by integrating the acceleration function:
v(t) = INT(2 sin(t) + 1) dt
[tex]= -2 cos(t) + t + C[/tex]
Since the initial velocity is v(0) = 0, we can substitute this value into the equation to find the constant C:
[tex]0 = -2 cos(0) + 0 + C\\0 = -2(1) + C\\C = 2[/tex]
Therefore, the equation of the velocity function is:
[tex]v(t) = -2 cos(t) + t + 2[/tex]
To find the position function, we integrate the velocity function:
[tex]s(t) = INT(-2 cos(t) + t + 2) dt\\= -2 sin(t) + 0.5t^2 + 2t + D[/tex]
Since the initial position is s(0) = 3, we substitute this value into the equation to find the constant D:
[tex]3 = -2 sin(0) + 0 + 0 + D\\3 = 0 + 0 + D\\D = 3[/tex]
Therefore, the position function is:
[tex]s(t) = -2 sin(t) + 0.5t^2 + 2t + 3[/tex]
To find the average value of the position function from t = 2 seconds to t = 5 seconds, we use the formula for the average value of a function over an interval:
Average value =[tex](1 / (b - a)) * INT(a, b) f(t) dt[/tex]
In this case, the interval is from t = 2 seconds to t = 5 seconds, so we have:
Average value =[tex](1 / (5 - 2)) * INT(2, 5) (-2 sin(t) + 0.5t^2 + 2t + 3) dt[/tex]
Evaluating the definite integral:
Average value = [tex](1 / 3) * [(-2 cos(t) + (1/6)t^3 + t^2 + 3t) EVAL(2, 5)][/tex]
Average value =[tex](1 / 3) * [(-2 cos(5) + (1/6)(5^3) + 5^2 + 3(5)) - (-2 cos(2) + (1/6)(2^3) + 2^2 + 3(2))][/tex]
Calculating the values:
Average value ≈[tex](1 / 3) * [(-2 cos(5) + 125/6 + 25 + 15) - (-2 cos(2) + 8/6 + 4 + 6)][/tex]
Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]
Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is approximately:
Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]
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you borrowed $1,690 for 5 1/2 years at 5.7% compounded semianually. what total will you pay back?
Answer:
You will pay $2,302 back.
Step-by-step explanation:
Compound interest occurs when the interest is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
We are given the following conditions: Principal amount P=$1,690, duration=5 1/2 years, interest rate r=5.7% compounded semi-annually.
Note we don't actually have the value of n or t because they must be taken from the duration and the compounding period.
The interest compounds semi-annually i.e. twice a year. Thus, n=2.
The interest rate is converted to decimal r=0.057 and we apply the formula:
[tex]{\displaystyle A=1,690\left(1+{\frac {0.057}{2}}\right)^{2*5.5}}[/tex]
[tex]{\displaystyle A=1,690\left(1+0.0285\right)^{11}}[/tex]
A=$2,302
You will pay $2,302 back.
Chef Rita is cooking for a Sunday brunch. She knows that 222222 pancakes can feed 888 people. She is wondering how many people (p)(p)left parenthesis, p, right parenthesis she can feed with 555555 pancakes. She assumes each person eats the same quantity of pancakes.
How many people can Rita feed with 555555 pancakes?Explain how poor physical health may affect your social health.
Answer:
she can feed 2,220 people with 555555 pancakes.
Step-by-step explanation:
Answer:20 people
Step-by-step explanation:
we can solve the problem by setting a simple proportion.
We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:
Solving the proportion, we find
So, 55 pancakes can feed 20 people.
A group of students and their leader visited the zoo 1 adult 4 students in one van paid $12 for the tiger tour. In the second van 3 adult 3 students paid $18 for the same tour. Find the adult price and student price of the tour
Answer:
Adults cost $4, and Students $2.
Step-by-step explanation:
I have adults be x, and Students y, and convert the two groups to equations.
1x + 4y = 12, and 3x + 3y = 18. I divide the last equation by 3, to get x + y = 6.
Then I subtract y, to get x = 6 - y, then we use substitution.
6 - y + 4y = 12
6 +3y = 12, then subtract 6 from both sides, 3y = 6. divide by 3, and get y = 2. we can plug this into our x + y = 6, to get x + 2 = 6. i.e x = 4.
So Adults cost 4 dollars, and Students cost 2 dollars.
Just lots of simple math, take your time with these questions.
Find an equivalent ratio in simplest terms:
66 : 42
Submit Answer
Math
Answer:
11:7
Hope this helps
Karen drove 780 miles in 12 hours.
At the same rate, how many miles would she drive in 9 hours?
Answer:
585
Step-by-step explanation:
divide 780 by 12
780/12=65
The answer you get is her speed, so 65miles/hour
So if she did this for nine hours, multiply 65 by 9
65*9=585
7/9 - 1/5 =. put answer in simplest form
35-9/45 = 26/45
The answer is 26/45.
Answer:
26/45
Step-by-step explanation:
35/45-9/45=26/45
Please answer only if you know for sure :) Comes from pre-calc btw
Let d be the number of dollars you spent on gas and let g be the number of gallons you purchased. Which expression represents the price you paid per gallon?
Answer:
The expression represents the price you paid per gallon is:
Price paid per gallon = [tex]\frac{d}{g}[/tex]Step-by-step explanation:
To identify the expression is right, I'll show you with an example: suppose that you paid $56 buying 7 gallons of gas, now you can replace those values in the expression I gave you:
Price paid per gallon = [tex]\frac{d}{g}[/tex]Price paid per gallon = [tex]\frac{56}{7}[/tex]Price paid per gallon = 8And you can check this value by multiplying the price paid by the gallon and the number of gallons, which you obtain the number of dollars you spent:
Number of dollars (d) = 8 * $7 = $56What is the perimeter of the rectangle, if the formula for perimeter is Prectangle = 21 + 2w?
6 cm
Please help
Help Needed !! What Kind Of Angles Does This Triangle Have? Acute,Obtuse,Right,Equiangular
Explain Your Answer
Hillary paid $8 for 12 donuts. What is the approximate unit cost of each donut
Answer:
$0.67
Step-by-step explanation:
Divide 8(dollars) by 12 (donuts) and you get 0.66666666666666666666666666666667
But, round it and you get .67
Select the expression that is equivalent to the given expression:
Answer:
(113^6*37^3*54^12)
hope it helps you
3. Suppose a unit cube is dilated by some scale factor k a. Write an expression for the surface area of the dilated cube. b. Write an expression for the volume of the dilated cube. c. Compare and contrast the expression for surface area and the expression for volume.
a. The expression for the surface area of a dilated cube is 6k², where k is the scale factor.
b. The expression for the volume of a dilated cube is k³, where k is the scale factor.
c. The expressions for surface area and volume differ in terms of the power of the scale factor: surface area is proportional to k², while volume is proportional to k³.
a. When a unit cube is dilated by a scale factor k, all sides of the cube are multiplied by k. Since a cube has six faces, the surface area of the dilated cube can be calculated by multiplying the area of one face (which is k²) by 6. Therefore, the expression for the surface area of the dilated cube is 6k².
b. The volume of a cube is calculated by multiplying the length, width, and height of the cube. In this case, each side of the unit cube is scaled by a factor of k, so the expression for the volume of the dilated cube is k³.
c. Comparing the expressions for surface area and volume, we observe that the power of the scale factor differs. The surface area is proportional to k², indicating that the surface expands in two dimensions (length and width) when the scale factor increases. On the other hand, the volume is proportional to k³, demonstrating that the space inside the cube expands in three dimensions (length, width, and height) as the scale factor increases. This means that the volume of the dilated cube increases faster than its surface area as the scale factor grows, resulting in a greater change in volume compared to the change in surface area.
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An ant starts at the point (1, 0) on the unit circle and walks counterclockwise a distance of 2 units around the circle. Find the a and y coordinates (accurate to 2 decimal places) of the final location of the final location of the ant.
To find the final location of the ant after it has walked counterclockwise a distance of 2 units around the unit circle, we need to calculate the coordinates (x, y) of the point.
Since the ant starts at the point (1, 0) on the unit circle, we can think of this point as being at an angle of 0 degrees or 0 radians.
To find the coordinates after walking a distance of 2 units counterclockwise, we can calculate the new angle using the arc length formula:
s = rθ
where s is the arc length, r is the radius of the circle (which is 1 in this case), and θ is the angle in radians.
In this case, the arc length is 2 units and the radius is 1, so we have:
2 = 1θ
Solving for θ, we find:
θ = 2 radians
Now, we can use this angle to find the coordinates (x, y) of the final location on the unit circle:
x = cos(θ)
y = sin(θ)
Plugging in θ = 2, we get:
x = cos(2) ≈ -0.42
y = sin(2) ≈ 0.91
Therefore, the approximate coordinates of the final location of the ant are (-0.42, 0.91).
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What Kind Of Sides And Angles Does This Triangle Have?
Answer:
2 acute and 1 right angle (the right angle is a 90 degree angle)
Step-by-step explanation:
What is the ratio of 2,753 to 1,750 as a decimal? ( Rounded to two decimal places)
Answer:
-0.17
Step-by-step explanation:
When multiplying terms with the same sign, we will get a _______ product.
When multiplying terms with different signs, we will get a ________ product
Answer:
same,different
Step-by-step explanation:
Answer:
positive; negative
Step-by-step explanation:
If a student is multiplying two positive numbers, the answer will always be positive.
EX: 3 x 4 = 12
The same applies for two negatives. If two negatives are multiplied it will make a positive answer. This is where the phrase "two negatives make a positive" come from.
EX: -3 x -4 = 12
However, if one number is positive and one is negative, then the answer will always be negative.
EX 1: -3 x 4 = -12
EX 2: 3 x -4 = -12
