We have 8^(-4) over 8^(-10). The bases are both 8, so we subtract the exponents (numerator minus denominator).
[tex]\frac{8^{-4}}{8^{-10}} = 8^{-4-(-10)} = 8^{-4+10} = 8^{6}[/tex]
The final answer is choice C) 8^6
how do you decide whick of two numbers is greater when both numbers are positive,both numbers ate negative, and one number is positive and one number is negative
Final answer:
To compare two numbers, understand that positive numbers are greater than negative ones, among positives or negatives, larger numerical values determine greatness, and among two negatives, those closer to zero are greater.
Explanation:
Comparing two numbers to decide which is greater involves understanding their signs and values. Here's how you can determine this:
If both numbers are positive, the one with the higher numerical value is greater. For example, between 3 and 5, 5 is greater because 3 < 5.If both numbers are negative, the one with the lower absolute value is greater because it is closer to zero. For example, between -4 and -2, -2 is greater because -4 < -2.If one number is positive and the other is negative, the positive number is always greater than the negative one. This is because positive numbers are always to the right of negative numbers on the number line, indicating they are greater.Remember, the key to comparing numbers is understanding the role of positive and negative signs and the numerical value of the numbers.
Find the volume of the figure on the left
the volume is 408
l times w times h
(CO 4) Forty-nine percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).
Forty-nine percent of US teens have heard of a fax machine, then the probability that the teen has heard of a tax machine is p=0.49 and the probability that the tenn hasn't heard of a tax machine is q=1-p=1-0.49=0.51.
Use binomial distribution.
The probability that among 12 randomly selected teens exactly 6 have heard of a fax machine is
[tex]Pr(X=6)=C_{12}^6p^6q^{12-6}=\dfrac{12!}{6!(12-6)!}(0.49)^6(0.51)^6=\\\\\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{6!\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}(0.49\cdot 0.51)^6=924\cdot (0.2499)^6\approx 0.22505.[/tex]
The probability that among 12 randomly selected teens more than 8 have heard of a fax machine is
[tex]Pr(X>8)=C_{12}^9p^9q^{12-9}+C_{12}^{10}p^{10}q^{12-10}+C_{12}^{11}p^{11}q^{12-11}+C_{12}^{12}p^{12}q^{12-12}=\\\\\dfrac{12!}{9!(12-9)!}(0.49)^9(0.51)^3+\dfrac{12!}{10!(12-10)!}(0.49)^{10}(0.51)^2+\dfrac{12!}{11!(12-11)!}(0.49)^{11}(0.51)^1+\dfrac{12!}{12!(12-12)!}(0.49)^{12}(0.51)^0=220\cdot (0.49)^9(0.51)^3+66\cdot (0.49)^{10}(0.51)^2+12(0.49)^{11}(0.51)^1+(0.49)^{12}\approx 0.0638.[/tex]
In the past two weeks, Sue earned $513 at her part-time job. She worked a total of 54 hours. About how much did Sue earn per hour?
I think the answer you're looking for is $9.50.
513 / 54 = 9.5
Sue made $9.50 an hour.
Why does dividing by 10 shift each digit one place to the right?
Answer:
Step-by-step explanation:
As we move up the list -- as we push the digits one place right -- the number has been divided by 10 because each place to the right is worth 10 times less. ... As we move down the list -- as we push the digits to the left through the decimal point -- each number has been multiplied by 10
Dividing by 10 shifts each digit one place to the right due to our base-ten counting system. Each time we divide by 10, the number is broken into 10 equal parts, thereby moving its digits one place to the right. The same principle applies when dealing with larger powers of 10 and is often employed in scientific notation.
Explanation:The reason why dividing by 10 shifts each digit one place to the right relates directly to the base-ten number system we use, which relies on powers of ten. Whenever we divide by 10, we are asking how many times the number can be broken into 10 equal parts, thus moving its digits one place to the right.
For instance, if we take the number 250 and divide it by 10, the result is 25. We've essentially shifted the digits one place right. Similar to this when we are dealing with decimal numbers, the shift occurs with the decimal point. If we had 25.0 and divided by 10, the result would be 2.5
The same principle applies to larger powers of 10. If you divide by 100 (which is 10^2), you shift each digit two places to the right, and so on.
Another way to consider it is using scientific notation, which often uses powers of 10 to simplify large or small numbers. A number like 1,230,000,000 is written as 1.23 × 10⁹ in scientific notation. When we divide this number by 10, the exponent decreases by 1 to become 1.23 × 10⁸, effectively shifting each digit one place to the right.
Learn more about Dividing by 10 here:https://brainly.com/question/30586279
#SPJ3
an art teacher has one and a half pounds of red clay and 3/4 pounds of the yellow clay the teacher mixes the red play and yellow clay together each student in the class needs one eight pounds of the clay mixture to finish the assigned art project for the class how many students can get enough clay to finish the project
the teacher has 2 1/4 pounds of clay so none of the students have enough
What is the equivalent fraction for 40/100
The equivalent fraction for 40/100 is 2/5.
Explanation:To find the equivalent fraction for 40/100, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20. When we divide 40 by 20, we get 2, and when we divide 100 by 20, we get 5. So, the equivalent fraction for 40/100 is 2/5.
The equivalent fraction for 40/100 is 2/5, which is obtained by dividing both the numerator and the denominator by their greatest common divisor, 20. In decimal form, 40/100 is 0.40, and as a percentage, it is 40%.
Explanation:To find the equivalent fraction for 40/100, we look for a common factor that both the numerator (40) and the denominator (100) share. In this case, the number 20 is a common factor of both. Dividing the numerator and the denominator by 20, we reduce 40/100 to its simplest form:
40 ÷ 20 = 2
100 ÷ 20 = 5
Therefore, the equivalent fraction for 40/100 is 2/5.
Additionally, converting a fraction to a decimal involves dividing the numerator by the denominator, so 40/100 converted to a decimal is 0.40.
To convert this decimal to a percentage, we multiply by 100, yielding 40%.
eight is greater than or equal to the sum of a number and 3
an $1000 investment is made in a trust fund that pays 12% compounded monthly. how long will it take the investment to double?
What is the value of k?
Answer:
k=2
Step-by-step explanation:
We have got a right triangle LNO with sides = m,4 and 8
By Pythagorean theorem
m^2=4^2 +8^2
Or m^2 = 80 ... i
IN triangle NOM, 4^2 +k^2 = l^2
i.e. 16+k^2 = l^2... i
In triangle LNM, m^2+l^2 = (8+k)^2
Substitute for m^2 as 80,
i.e. 80+l^2 = 64+k^2 +16k ... iii
From i, l^2 = 16+k^2
Substitute in iii
80+16+k^2 = 64+k^2 +16k
16k = 32 or k =2
Ten times a number decreased by seven equals 101 plus that number. Find the number
Final answer:
A student's math problem involving an algebraic equation to find a number has been solved by isolating and solving variables, resulting in the number 12.
Explanation:
To solve the equation where ten times a number decreased by seven equals 101 plus that same number, we would set up the following equation:
10x - 7 = 101 + x
Now, we solve for x:
First, subtract x from both sides of the equation to get all the x terms on one side:
9x - 7 = 101
Next, add 7 to both sides of the equation to isolate the term with x:
9x = 108
Finally, divide both sides by 9 to solve for x:
x = 12
Hence, the number we are looking for is 12.
The equation x^2-9=0 has how many real solutions
So remember that the degree of the polynomial will indicate how many solutions there are, real or complex. Since the degree of the polynomial is 2, this means that there is a maximum of 2 real solutions in this equation.
Next, we are going to apply the difference of squares rule to this polynomial, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:
[tex]x^2-9=(x+3)(x-3)\\(x+3)(x-3)=0[/tex]
Now, we are going to apply the Zero Product Property, which states that if a × b = 0, this means that either a or b = 0 or a and b = 0. In this case, a = x + 3 and b = x - 3. Solve each as such:
[tex]x+3=0\\x=-3\\\\x-3=0\\x=3[/tex]
In short, there are 2 real solutions: x = 3 and x = -3.
The equation [tex]x^2-9=0[/tex] has two real solutions which are x=3 and x=-3. The solutions are obtained by applying the quadratic formula, which indicates that every equation containing an unknown squared will have two solutions.
Explanation:The equation[tex]x^2-9=0[/tex] is a quadratic equation. For any quadratic equation in the form ax²+bx+c = 0, the solutions or roots can be calculated using the quadratic formula: -b ± √(b² - 4ac) / 2a.
In this specific equation, [tex]x^2-9=0[/tex]can be rewritten as x²-9+9 = 9, which simplifies to x² = 9. The solutions can then be obtained using the principal square root or the negative square root, resulting in x = ± √9. Therefore, the two real solutions are x = 3 and x = -3.
It's important to note that every equation containing an unknown squared will have two solutions, which can be both meaningful or only one of them can be reasonable depending on the context of the problem.
Learn more about Quadratic Equations here:https://brainly.com/question/34196754
#SPJ11
Dario bakes a lasagna containing 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese. Dario cuts the lasagna into several equal slices, each containing exactly 1/4 pound of cheeses (of all types totalled). How many slices are there?
Dario could make 9 slices of lasagna with the provided amount of cheese, as each slice contains 1/4 pound of cheese and he has a total of roughly 2.33 pounds of cheese.
Explanation:To answer this question, we first need to calculate the total weight of the cheese used in the lasagna. This consists of 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese. To total these up, we convert them into fractions with a common denominator. Doing this, we find that, in total, 28/12 or approximately 2.33 pounds of cheese are used. As each slice of lasagna contains 1/4 pound of cheese, we can determine the total number of slices by dividing the total weight of the cheese by the weight of the cheese in each slice. This gives us: 2.33 ÷ 0.25 = 9.32. As we can't have a fractional number of slices, we round down to get 9 slices, which would be the amount of lasagna slices Dario could make with the provided amount of cheese.
Learn more about Fraction Division here:https://brainly.com/question/17205173
#SPJ3
-1(2x +3) -2(2x-1) simplified
- 6x - 1
distribute parenthesis and collect like terms
- 2x - 3 - 4x + 2
= (- 2x - 4x) + (-3 + 2) = - 6x - 1
For the past three months Grace used her cell phone for 42 minutes,62 minutes and 57 minutes. How many minutes would she have to use her cell phone this month for the average usage over the four months to be 55 minutes
This is A Math Problem
Answer:
The amount of minutes Grace has to use her cell phone this month is 59 minutes
Step-by-step explanation:
Let
x -----> amount of minutes Grace has to use her cell phone this month
we know that
The average usage during the four months is equal to the sum of the minutes used in the four months divided by four (the number of months)
so
[tex]55=\frac{42+62+57+x}{4}[/tex]
Solve for x
Multiply by 4 both sides to remove the fraction
[tex]55(4)=(42+62+57+x)[/tex]
[tex]220=(161+x)[/tex]
[tex]x=220-161[/tex]
[tex]x=59\ min[/tex]
therefore
The amount of minutes Grace has to use her cell phone this month is 59 minutes
what is 0.79 as a percent
it is 79% hoped i helped
Please anyone help fast
For 20 points
Simplify: 9(3 + 4)
simplify 9[3+4}
using bodmass
=9{7}
63
Windless Surfing Company’s marketing manager observes that if the price of designer windsocks is $40, then on average 70 windsocks are sold per month. Experience has shown that if the price is raised from $40, then for every $1 increase in price, two fewer windsocks are sold each month.
Answer:
The answer is x ≤ 50.
Step-by-step explanation:
As, A -70 = -2 (P -40)
A = -2P + 80 + 70
A = -2P + 150
Y = -2x + 150.
When y = 0,
Putting in the values
-2x = -150
x = 75.
-2x + 150 ≥ 50
-2x ≥ -100
x ≤ 50.
Michael has $550 in his savings account he took out $30.75 every month for one year what is the net change in Michael's account balance following these withdrawals
First You do 30.75 x 12 This is because he said every month for a year and a year has 12 months The answer to 30.75 x 12 is 369 Now all you have to do is 550 - 369 = 181.
Hope this helps :D
What is the prime factorization of 40? 2x3(4th power). 2(2nd power)x10. 2(third power)x5. 3(third power)x5.
40|2
20|2
10|2
5|5
1
[tex]40=2^3\cdot5[/tex]
Determine the domain of the function h(x)=9x/x(x^2-49)
Final answer:
The domain of the function h(x)=9x/x(x²-49) is all real numbers except for x = 0, x = -7, and x = 7, where the function is undefined due to division by zero. There are no additional nondifferentiable points within the domain, as the nondifferentiable points coincide with the excluded values.
Explanation:
To determine the domain of the function h(x)=9x/x(x^2-49), we need to identify all values of x for which the function is defined. Since this is a rational function, the function will be undefined where the denominator is zero. Thus, we set up the equation x(x² - 49) = 0 and solve for x.
First, factor the quadratic expression: x(x + 7)(x - 7) = 0. The solutions of this equation are x = 0, x = -7, and x = 7, which are the points where the function will be undefined.
Therefore, the domain of the function h(x) is all real numbers x except for x = 0, x = -7, and x = 7. These are the excluded values from the domain because they make the denominator equal to zero, which would result in division by zero.
Nondifferentiable Points
Aside from the excluded values, there may also be nondifferentiable points within the domain where the derivative does not exist or is not continuous. However, since all nondifferentiable points in this case coincide with the excluded values (the points where the denominator is zero), there will be no additional nondifferentiable points within the domain of the function.
The function p is defined as p(x)=x2+4x-12
Part A
Write an expression that defines p(x-6)+5
Part B
Describe the transformations that map the graph of p(x) to p(x-6)+5. Justify your answer algebraically or by using key features of the graph.
Given the function [tex]p(x)=x^2+4x-12.[/tex]
Part A.
To write the expression that defines [tex]p(x-6)+5,[/tex] you have to substitute x-6 instead of x into the function expression and then add 5 to the function:
[tex]p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.[/tex]
Part B.
1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).
2 transformation is translation 5 units up (+5 determines this transformation).
plz help. 99 pts
Graph f(x)=−34x−4 . Use the line tool and select two points to graph the line.
Answer:
In the picture
Step-by-step explanation:
A jet ski rental company charges a $100 rental fee, plus $20 per hour. Write and dole an equation to determine how many hours you can rent the jet ski for it if you have a budget of $175.
Solve the word problem
3 hours because if u have 175 dollers and u spend 100 so now u have 75. 75 -20 is 55. then 55 - 20 is 35. then 35 - 20 is 15 so then you have 15 dollers to spare. so 3
You can represent this problem as a linear equation 100 + 20x = 175. Solving for x gives you 3.75, hence with $175, you can rent the jet ski for 3.75 hours.
Explanation:To solve this problem, you need to set up a linear equation. Let's represent the number of hours of the jet ski rental as x. The jet ski rental company charges a $100 rental fee plus $20 per hour, so we can write this as a equation: 100 + 20x = 175.
Next, we need to solve for x. First, subtract 100 from each side of the equation, you obtain 20x = 75. Then, divide each side by 20 to solve for x. You'll find that x = 3.75. Therefore, with $175, you can rent the jet ski for 3.75 hours.
Learn more about Linear Equation here:https://brainly.com/question/32634451
#SPJ3
When a figure is translated, its orientation (blank) and the measures of its angles (blank).
Answer:
Its orientation may change and the measures of its angles stay the same.
Step-by-step explanation:
Answer:
When a figure is translated its orientation may change and the measures of its angles keeps the same measure.
Step-by-step explanation:
Whenever we translate a figure, we move a figure into some orientation given by this same vector. But the angles will remain the same since there is no distortion.
Just as the picture below
four times the sum of some number plus 1 is equal 12 times the difference of the number and 3. Find the number
4(x + 1) = 12(3 - x)
Distributive property on both sides.
4x + 4 = 36 - 12x
Add 12x to both sides.
16x + 4 = 36
Subtract both sides by 4.
16x = 32
Divide both sides by 16.
x = 2
Wich term best describes a figure formed by three segments connecting three noncollinear points ?
A triangle is the answer.
Answer:
ok the answer is
Step-by-step explanation:
69 gooba, go watch it NOW
Solve for t.
−5t≥70
Help Please
A. is this answer to this question.
The value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here the given inequality is :
−5t ≥ 70
Now, to solve for t we divide both side by -5 :
−5t/-5 ≥ 70/-5
t ≤ -14
It should be noted that negative -5 reverse the inequality sign.
Therefore, the value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
check and know more about inequality here :
https://brainly.com/question/21209456
#SPJ5
What is (-6,1) when it is reflected over y=x
ANSWER
The image point is [tex](1,-6)[/tex].
EXPLANATION
For a reflection in then line [tex]y=x[/tex], we simply swap the x and y coordinates.
Thus, in general the mapping for the reflection in the line [tex]y=x[/tex], is
[tex]P(x,y)\rightarrow P'(y,x)[/tex].
Hence,
[tex]P(-6,1)\rightarrow P'(1,-6)[/tex].
See graph.
The reflection of the point (-6,1) over the line y=x results in the point (1,-6).
Explanation:In the context of coordinate geometry, reflection over a line, specifically y=x, requires that we swap the x and y coordinates of a given point. So, when we have the point (-6,1), it is reflected to become (1,-6) over the line y=x. Hence, "this operation fundamentally changes the position of the point".
Learn more about Reflection over a line here:https://brainly.com/question/18376051
#SPJ3
Simplify. 3/5+(-1/4)÷7/10
Enter your answer, in simplest form, in the boxes.
Please help, look down below at the attachment cuz Im not sure I set the problem up right!
Answer:
1/10
Step-by-step explanation:
There are three simple fractions in this problem: 3/5, -1/4 and 7/10. Rules of order require that the division (-1/4) divided by 7/10 be carried out first; the correct product is -10/28, or -5/14. Then we have 3/5 + (-5/14).
Here the LCD is 70. Then 3/5 + (-5/14) becomes 42/70 - 35/70, which simplifies to 1/10.
Answer:
1/10
Step-by-step explanation: