The product of (x y^2 z)^3 and (-9x^2 y z)^2 is found by applying the exponent to each variable inside the parentheses and then multiplying the results together, using exponent rules to simplify. The final simplified expression is 81x^7 y^8 z^5.
Explanation:To find the product of the expressions (x y^2 z)^3 and (-9x^2 y z)^2, we use the properties of exponents. First, we apply the power to each factor inside the parentheses, which means raising each base to the power outside, and then we multiply the corresponding exponents when the same base is found in both terms.
For the first expression (x y^2 z)^3, we get x^3 y^6 z^3, and for the second expression (-9x^2 y z)^2, we have 81x^4 y^2 z^2 after squaring -9 to get 81 and applying the exponent 2 to each variable.
Next, we multiply these results together: x^3 y^6 z^3 × 81x^4 y^2 z^2 = 81x^{3+4} y^{6+2} z^{3+2}, which simplifies to 81x^7 y^8 z^5. The rule of exponent addition when multiplying like bases, x^p x^q = x^{(p+q)}, is applied here to combine the variables with the same base. Our final simplified product is 81x^7 y^8 z^5.
The final answer is [tex]81 x^7 y^8 z^5.[/tex]
To find the product of the expression [tex](x y^2 z)^3 * (-9x^2 y z)^2[/tex], we can follow these steps:
1. Expand the first expression: [tex](x y^2 z)^3 = x^3 (y^2)^3 z^3 = x^3 y^6 z^3.\\[/tex]
2. Expand the second expression: [tex](-9x^2 y z)^2 = (-9)^2 (x^2)^2 y^2 z^2 = 81 x^4 y^2 z^2.[/tex]
3. Multiply the expanded expressions: [tex](x^3 y^6 z^3) * (81 x^4 y^2 z^2) = 81 x^3 x^4 y^6 y^2 z^3 z^2 = 81 x^7 y^8 z^5.[/tex]
Therefore, the final answer is [tex]81 x^7 y^8 z^5[/tex].
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). find the probability that for one such phone number, the last four digits include at least one 0.
Answer:.344 if you have to round to the third decimal
Step-by-step explanation:
!!!!!!!I NEED HELP WITH THESE PROBLEMS. THANK YOU!!!!!
1. Mike's salary is $6,500 per month. He saves 1/5 of his monthly salary and spends the rest.
How much money does Mike save every month?
$ ?
How much money does Mike spend every month?
$ ?
2. Fill in the missing values that makes the equation true.
−2/5×30= ?/2 x -4 = ?
3. Alex takes 1 hour and 30 minutes to get to the office.
How many hours does Alex spend getting to the office over 4 days?
? hours
4.Fill in the missing values that make the equation true.
−4/7×49= ?/6 x -14 = ?
5. Drag the equivalent expressions into the appropriate columns.
5(1/5+3c) 1/4(1/2 - 4c)
(5+15c), (1+15c), (1/8 - c), (1/8 - 4/4c), (-1/8 + -c), (5/5 + 15c)
6. Drag the equivalent expressions into the appropriate columns.
a(b + c) -x(m - n)
(ab - ac), (ab + ac), -(xm - xn), (-xm + -xn)
7. Part 1
18 × ? = 1
Part 2
Select all the statements that explain why the missing value you chose for Part A makes the equation true.
Answer Choices
A. The product of a rational number and its multiplicative inverse is always 1.
B. The sum of a rational number and its additive inverse is always 0.
C. The product of two positive rational numbers is always positive.
D. The product of any two rational numbers is always 1.
E. It is the multiplicative inverse of the multiplier.
F. It is the additive inverse of the multiplier.
8. This is an equation.
(-7)(-17)=1
Select all of the statements that explain why this equation is true.
Answer Choices
A. The fraction -17 is the multiplicative inverse of -71 .
B. The fraction -17 is the additive inverse of -71 .
C. The product of any two rational numbers is always 1.
D. The product of two negative rational numbers is always positive.
E. The product of a rational number and its multiplicative inverse is always 1.
F. The sum of a rational number and its additive inverse is always zero.
URGENT! PLEASE ANSWER!
Layla is using the model to solve a division problem. Which question would the model be most helpful in solving?
How many 1/6s are in 4?
How many 1/6s are in 2/3?
How many 2/3s are in 4?
How many 2/3s are in 1/6?
Answer:
the answer is B
Step-by-step explanation:
The model would be most helpful in solving the problem 'How many 1/6s are in 2/3?'. This is found by dividing 2/3 by 1/6 through fractional division, giving a result of 4.
Explanation:The model would be most helpful in solving the question 'How many 1/6s are in 2/3?'. Let me explain why:
To solve this, you simply need to divide 2/3 by 1/6. When we say 'how many 1/6s are in 2/3', it means how many times can 1/6 fit into 2/3. Division is the process of finding out how many times one number (the divisor) is contained within another (the dividend).
So we divide 2/3 by 1/6. But rather than directly divide, in fractional division we multiply the first fraction by the reciprocal of the second. The reciprocal of 1/6 is 6/1.
So, 2/3 * 6/1 = 4.
That means, there are 4 1/6s in 2/3.
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Which expression below best shows how to estimate an answer for 5 3/4 divided by -3 3/8
6 divided by (-3)
6 divided by (-4)
5 divided by (-3)
5 divided by (-4)
Please answer ASAP!!
The best estimate for the division of 5 3/4 by -3 3/8 is 6 divided by -3 because rounding each number to the nearest whole provides the most accurate estimation.
To estimate an answer for 5 3/4 divided by -3 3/8, we should round each number to the nearest whole number. The number 5 3/4 rounds up to 6 because the fractional part (3/4) is more than half. The number -3 3/8 rounds to -3 because the fractional part (3/8) is less than half. Therefore, the closest estimation of the original division problem using whole numbers is 6 divided by (-3).
Janet took out a loan of $50,000 from Bank of America at 8% on March 19, 2015, which is due on July 8, 2015. Using exact interest, the amount of Janet's interest cost is:
The amount of Janet's interest cost from a loan of $50,000 at an interest rate of 8% from March 19 to July 8, 2015 is $1,160. The calculation is done using the simple interest formula, with time approximated as 0.29 years.
Explanation:The problem asking for the simple interest incurred on a loan taken by Janet can be solved using the formula of simple interest, which is I=PRT in financial mathematics. I is interest, P is the principal amount (initial loan), R is the interest rate, and T is the time.
P (Principal) = $50,000R (Rate of Interest) = 8% per annumT (Time) = Time interval from March 19 to July 8 that turns out to be approximately 3.5 months or about 0.29 years.Substituting these values into the formula, we get:
I = 50000 * 0.08 * 0.29
Calculating this out will give you the total interest, $1160.
So, the amount of Janet's interest cost is $1,160.
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Which expression is equivalent?
11 − 9(−2x − 3)
A) 18x + 38
B) −4x + 6
C) 18x − 38
D) −4x − 6
The expression equivalent to 11 - 9(-2x - 3) is 18x + 38 after applying the distributive property and rules for multiplying numbers with different signs. This corresponds to option A.
Explanation:To find which expression is equivalent to 11 − 9(−2x − 3), we need to apply the distributive property and the rules for multiplying numbers with different signs. The distributive property tells us to multiply the number outside the parentheses by each term inside the parentheses. So, let’s apply this to the expression:
First, distribute the -9 to both -2x and -3: -9(−2x) + -9(−3).According to the multiplication rules for signs, multiplying two negative numbers results in a positive number. So, -9(−2x) becomes +18x, and -9(−3) becomes +27.Now the expression looks like this: 11 + 18x + 27.Add the constant terms 11 and 27 to get 38. The expression is now 18x + 38.Therefore, the expression equivalent to 11 − 9(−2x − 3) is 18x + 38, which corresponds to option A.
16,4,1,1/4,... Which exponential function describes the given sequence?
Answer: Is D.
Step-by-step explanation:
19,050,000 in scientific notation
can you please help me?
Larry's bank charges a variable finance rate of 1.5 percent on purchases up to $100, and one percent for purchases over $100. If his unpaid balance is $246.07 this month, what is his finance charge?
A. $1.46
B. $2.46
C. $3.69
D. $2.96
Final answer:
To find the finance charge for an unpaid balance of $246.07, apply 1.5% on the first $100 and 1% on the remainder. The total charge is $2.9607, which rounds to $2.96, matching answer D.
Explanation:
To calculate Larry's finance charge for the unpaid balance of $246.07, we'll first divide the balance into the portions that are charged at different rates as per the bank's policy. So, the first $100 is charged at a higher rate of 1.5%, and the remaining balance ($146.07) is charged at a lower rate of 1%.
Calculate 1.5% on the first $100: $100 × 0.015 = $1.50
Calculate 1% on the remaining $146.07: $146.07 × 0.01 = $1.4607
Sum both charges to find the total finance charge: $1.50 + $1.4607 = $2.9607
After rounding to the nearest cent, Larry's total finance charge is $2.96, which corresponds to answer choice D.
evaluate the expression p(11,7)
The expression p(11,7) is evaluated by calculating the permutation of 11 items taken 7 at a time, resulting in a value of 55440.
The expression p(11,7) is a notation used in mathematics to represent a permutation.
To evaluate the permutation p(n, k), where n is the total number of items and k is the number of items to be arranged, we use the formula n! / (n-k)!.
Let's calculate the permutation for p(11, 7):
First, we find the factorial of 11, which is 11!, or 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
Then, we find the factorial of (11-7), which is 4!, or 4 x 3 x 2 x 1.
The permutation is calculated as follows:
p(11, 7) = 11! / 4!
After cancelling out the common terms in the numerator and the denominator, we have:
p(11, 7) = 11 x 10 x 9 x 8 x 7, which is equal to 55440.
Therefore, the value of the expression p(11,7) is 55440.
Solve. 25 -4x = 15 - 3x + 10 - x
The sum of 3 numbers is -4. The second number decreased by the third is equal to the first. The sum of the first and second numbers is -5. Write the system of equations and find the numbers.
To assess the precision of a laboratory scale, we measure a block known to have a mass of 1 gram. we measure the block n times and record the mean x¯ of the measurements. suppose the scale readings are normally distributed with unknown mean µ and standard deviation σ= 0.001 g. how large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001
For a 95% confidence interval with ±0.0001 margin of error, sample size[tex]\( n \approx 385 \)[/tex] measurements are needed.
To determine the sample size [tex]\( n \)[/tex] needed to achieve a margin of error of [tex]\( \pm 0.0001 \)[/tex] for a 95% confidence interval for the mean [tex]\( \mu \)[/tex], we can use the formula for the margin of error of a confidence interval:
[tex]\[\text{Margin of Error} = Z \times \frac{\sigma}{\sqrt{n}}\][/tex]
Where:
[tex]- \( Z \) is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to \( Z = 1.96 \)).\\- \( \sigma \) is the standard deviation of the measurements (given as \( 0.001 \) g).\\- \( n \) is the sample size.[/tex]
Given that the margin of error [tex](\( \text{MOE} \)) is \( 0.0001 \)[/tex], we can rearrange the formula to solve for \( n \):
[tex]\[n = \left(\frac{Z \times \sigma}{\text{MOE}}\right)^2\][/tex]
Substituting the given values:
[tex]\[n = \left(\frac{1.96 \times 0.001}{0.0001}\right)^2\]\[n = \left(\frac{0.00196}{0.0001}\right)^2\]\[n = \left(19.6\right)^2\]\[n = 384.16\][/tex]
Since [tex]\( n \)[/tex] must be a whole number (you can't have a fraction of a measurement), we round up to the nearest whole number. So, [tex]\( n = 385 \).[/tex]
Therefore, you would need to take at least 385 measurements to ensure that the margin of error for the 95% confidence interval of the mean [tex]\( \mu \) is \( \pm 0.0001 \) g.[/tex]
Wilbur's widgets, a widget company, produces 100 widgets. its average fixed cost is $5 and its total variable cost is $300. what is the total cost of producing 100 widgets?
a. $300
b. $305
c. $500
d. $800
The total cost of producing 100 widgets will be $800. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Wilbur's widgets, a widget company, produce 100 widgets. its average fixed cost is $5 and its total variable cost is $300.
Then the equation is given as,
y = 5x + 300
Where 'x' is the number of widgets and 'y' is the total cost.
Then the total cost of producing 100 widgets will be given as,
y = 5 × 100 + 300
y = 500 + 300
y = $800
The total cost of producing 100 widgets will be $800. Then the correct option is D.
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there is less gravity on the planet trang than on earth. In fact, you could jump about 2 and 2/3 times as high on trang than on earth.if u can jump 4 and 1/4 feet on earth,how high could you jump on trang?
please help
A carpet layer is given a roll of carpet which has already been cut for a 12-ft wall. The wall measures 1.5 cm on a drawing. The length of the room is 6 iron the drawing. How far,in feet, will he cut the length of the carpet?
Answer: 48
Step-by-step explanation:
Do 12 divided by 1.5 = 8
8 * 6 = 48
so 48 is your answer
:3
Which of the binomials below is a factor of this trinomial? x^2+14x-24
Answer:
[tex](x-12)[/tex] is a factor
Step-by-step explanation:
[tex]x^2-14x+24[/tex]
The product is 24 and sum is [tex]-14[/tex]
To factor it we need to find out two factors whose product is 24 and sum is [tex]-14[/tex]
[tex]-12 \cdot -2= 24[/tex]
[tex]-12 +(-2)= -14[/tex]
Two factors are [tex]-12 , -2[/tex]
[tex]x^2-14x+24[/tex]
[tex](x-12)(x-2)[/tex]
[tex](x-12)[/tex] is a factor
Every 3 days Marco fills up his car with gas. Every 8 days he washed his car. On what day will Marco fill his car with gas and wash it
Shane is trying to find the 5th term of a sequence where f(1)=4 and f(n)=2*f(n-1)+1 for each whole number greater than one. He reasons that he can find the 5th term by calculating (4*2*2*2*2)+1. Explain Shane's error
Note I am doing this for Shane not me
The Mistake made by Shane is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(1)=4 and f(n)=2f(n-1)+1
f(2)= 2f(1)+1
f(2) = 9
and, f(3)= 2f(2) + 1
f(3) = 19
and, f(4)= 2f(3)+1
f(4) = 37
so, for finding the 5th term of the function
f(5) = 2 f(4) + 1
So, we need f(4) and then value of f(4) is multiplied by 2.
As, f(5) = 2(37)+1 = 75
and, according to Shane f(5)= (4*2*2*2*2)+1 = 65
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PLEASE HELP NEED TO PASS MY CLASS
i have 3 1/8 pounds of macaroni and want to make 10 equal serving of macaroni salad. how many pounds of macaroni do i have for each serving
of the 40 students who auditioned for the school play, 3/4 of them were called back for a second audition. How many students were called back for another audition.
Ethel Meyer sells wheelchairs. SHE EARNS AN 11 PERCENT COMMISSION ON THEE FIRST $5,000 AN 14 PERCENT ON ALL SALES OVER $5000.HOW MUCH COMMISSION WILL SHE EARN ON $14,000 IN SALES?
Alex is constructing a square in which two of its vertices are points X and Y. He has already used his straightedge and compass to construct the lines and arcs shown.
What should Alex do for his next step?
A. Use a straightedge to draw a horizontal line that contains point Z.
B. Place the point of the compass on point X and draw any arc above it.
C. Use a straightedge to draw XZ¯¯¯¯¯ .
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Answer:
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Step-by-step explanation:
All sides of a square has to be equal.
Here it is given that X an Y are 2 of the vertices of the square. We can say that XY is the length of one side of the square.
So e should make sure that a length of the square on the YZ line is same as the XY line.
So,
Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Answer:
D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.
Step-by-step explanation:
Verified by test results
Hope this helps:)
What is the unit rate of y=0.75x
What is the probability of randomly drawing an odd number between 24 and 33?
Final answer:
The probability of drawing an odd number between 24 and 33 is 50%, as there are 5 odd numbers (25, 27, 29, 31, 33) within the 10 numbers in this range.
Explanation:
The probability of randomly drawing an odd number between 24 and 33 is calculated by identifying all the odd numbers in that range and dividing by the total number of possibilities.
The odd numbers between 24 and 33 are 25, 27, 29, 31, and 33. Since there are 10 total numbers (24 through 33), and 5 of these are odd, the probability is 5 out of 10, which simplifies to ½ or 50%.
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile
Using the Pythagorean theorem: After applying the theorem, the hypotenuse, which represents the distance between the two points, is approximately 6.1 miles when rounded to the nearest tenth of a mile.
Explanation:To solve the problem of determining the distance from Frostburg Mall to Sojourner Truth Park, we can employ the Pythagorean theorem, which is used to find the length of the hypotenuse of a right-angled triangle.
Given that the mall is located 3 miles west and 4 miles south of the City Center, while the park is 3 miles east and 5 miles north, we can calculate the total east-west distance and the total north-south distance.
First, we add the east-west distances: 3 miles west of City Center to Mall plus 3 miles east from City Center to Park, which equals 6 miles in total.
Next, we calculate the north-south distance: 5 miles north from City Center to Park minus 4 miles south from City Center to Mall, resulting in 1 mile to the north.
We now have a right triangle where one leg is 6 miles and the other leg is 1 mile. Applying the Pythagorean theorem (a² + b² = c²), where 'a' and 'b' are the legs and 'c' is the hypotenuse:
c² = 6² + 1²
c² = 36 + 1
c² = 37
Finding the square root of 37, c ≈ 6.08 miles.
Therefore, the distance from the Frostburg Mall to the Sojourner Truth Park is approximately 6.1 miles to the nearest tenth.
Suppose that a least squares regression line equation is ˆy = 1.65 − 2.20x and the actual y value corresponding to x = 10 is −19, what is the residual value corresponding to y = −19?
a. 1.35
b. −1.35
c. 2.10
d. −2.10
The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.
Choose the correct function to represent the transformation
Function transformation involves changing the form of a function
The function that represents the transformation is: g(x) = 1/2(5^(x -3))
The parent function is given as:
f(x) = 5^x
When the function is vertically compressed by a factor of one-half, the function becomes
f'(x) = 1/2(5^x)
When the function is shifted 3 units right, it becomes
f"(x) = 1/2(5^(x -3))
Rewrite the function as:
g(x) = 1/2(5^(x -3))
Hence, the function that represents the transformation is: g(x) = 1/2(5^(x -3))
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The correct function representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]
Step 11. **Vertical Compression by a Factor of One-Half:**
To vertically compress the function by a factor of one-half, we multiply the function by [tex]\( \frac{1}{2} \)[/tex]. This affects the [tex]\( y \)[/tex]-coordinates of all points on the graph. So, the function becomes: [tex]\( \frac{1}{2} \cdot 5^x = \left(\frac{1}{2}\right)5^x \).[/tex]
2. **Shifted to the Left Three Units:**
To shift the function to the left three units, we add 3 to the [tex]\( x \)[/tex] -coordinate. This affects the input values. So, the function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} \).[/tex]
3. **Shifted Down Two Units:**
To shift the function down two units, we subtract 2 from the [tex]\( y \)-[/tex]coordinate. This affects the output values. So, the final transformed function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} - 2 \).[/tex]
Step 2 :Now, let's compare this transformation with the provided options:
A) [tex]\( g(x) = 5^{\left(\frac{n}{2}\right)+3} - 2 \)[/tex]
This option doesn't match the transformation. It introduces a variable [tex]\( n \)[/tex] and doesn't involve the original function [tex]\( 5^x \)[/tex].
B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \)[/tex]
This option matches the transformation. It has the vertical compression by [tex]\( \frac{1}{2} \)[/tex], shifting to the left by three units, and shifting down by two units.
C) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x+5} - 2 \)[/tex]
This option doesn't match the transformation. It shifts the function to the right by five units instead of to the left.
D) [tex]\( g(x) = 5^{\left(\frac{1}{2}\right)^{x-3}} - 2 \)[/tex]
This option introduces a fractional exponent, which doesn't correspond to the given transformations. It also has an incorrect shift to the right by three units.
Therefore, the correct option representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]
Complete Question :
The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.
Choose the correct function to represent the transformation
A) g(X)=5^(((n)/(2))+3)-2
B) g(x)=((1)/(2))5^(x-2)-2
C) g(x)=((1)/(2))5^(x+5)-2
D) g(x)=5^(((1)/(2))^(x-3))-2