Answer:
64-5 divided by 64-3 is 59 divided by 61. 59
8 squared is equal to 64. -----
61
Step-by-step explanation:
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{8^{-5}}{8^{-3}}\implies \cfrac{1}{8^{-3}\cdot 8^5}\implies \cfrac{1}{8^{-3+5}}\implies \cfrac{1}{8^2}\implies \cfrac{1}{64}[/tex]
7) Katie is baking muffins for a picnic. She can bake 24 muffins in 45 minutes. At this rate, how
many muffins can she bake in 90 minutes and how do you know?
Answer:
Katie can bake 48 muffins in 90 minutes.
Step-by-step explanation:
So, as you can see, it says she can bake 24 muffins in 45 mins. Some you make that a fraction:
24/45. The question asks how many muffins she can bake in 90 mins. So, next to the first fraction (proportion) write x/90.
Why x? Because you don't know how many muffins she made, so you'll use that to replace the number for now. X is the numerator because on the last proportion, you put the number of minutes as the denominator. X= how many muffins Katie baked.
So, you cross multiply. Multiply one numerator by the others denominator. Like this: 24×90 and 45×X. Write the answers under the denominator (Ex: 24 X
45 90
-----------
45x = 2160
Now, separate the variable (x) and the constant (45). To do something you must divide. Divide it by 45 to get x. Then, place your equal sign on the right side of that. Now, whatever you do to one side of the equal sign you must do to the other. So, divide 2160 by 45. If done coorectly, you should've gotten 48. X=48 muffins. Therefore, Katie baked 48 muffins.
Sorry about the length! I kinda got carried away lol
Also, for the explanation for how you know, my work above should explain that.
Well, I hope I was helpful!
There are exclusions that make the expression
x^3 - 1 / x^3 + x^2 + x undefined.
True
False
Answer:
True.Step-by-step explanation:
The given expression is
[tex]\frac{x^{3}-1}{x^{3}+x^{2}+x}[/tex]
This expression is rational, which means the denominator must be different to zero, otherwise, the function will be undefined. So, let's find if there are values that make the denominator zero.
[tex]\frac{x^{3}-1}{x^{3}+x^{2}+x}=\frac{x^{3}-1}{x(x^{2}+x+1)}[/tex]
So, if we evaluate the expression with [tex]x=0[/tex], we would have
[tex]\frac{x^{3}-1}{x(x^{2}+x+1)}=\frac{0^{3}-1}{0(0^{2}+0+1)}=\frac{-1}{0}[/tex]
As you can observe, there must be one exclusion, because it makes the expression undefined.
Therefore, the answer is true.
Polly buys 14 cupcakes for a party. The bakery puts them into boxes that hold 4 cupcakes each.
a. How many boxes will be needed for Polly to bring all the cupcakes to the party? Explain how you know.
b. If the bakery completely fills as many boxes as possible, what fraction of the last box is empty? How many more cupcakes are needed to fill this box?
Answer:
Part a) The number of boxes needed will be 4
part b) The fraction of the box that is empty is [tex]\frac{1}{2}[/tex]
Part c) Are needed 2 cupcakes to fill the last box
Step-by-step explanation:
Part a) How many boxes will be needed for Polly to bring all the cupcakes to the party?
To find out the number of boxes needed, divide the total number of cupcakes by 4 (maximum number of cupcakes that fit in each box).
so
[tex]\frac{14}{4}=3.5\ box[/tex]
Round up
The number of boxes needed will be 4
Part b) If the bakery completely fills as many boxes as possible, what fraction of the last box is empty?
we know that
The maximum number of cupcakes per box is 4
The first three boxes have 4 cupcakes
The last box has
[tex]14-3(4)=2\ cupcakes[/tex]
The fraction of the box that is empty is equal to the number of cupcakes missing to fill the box divided by the cupcake capacity of the box
[tex]\frac{2}{4}=\frac{1}{2}[/tex]
Part c) How many more cupcakes are needed to fill this box
Subtract the number of cupcakes in the box from the cupcake capacity of the box
The last box has 2 cupcakes
The cupcake capacity of the box is 4
so
[tex]4-2=2\ cupcakes[/tex]
therefore
Are needed 2 cupcakes to fill the last box
You and your family are planning the vacation of a lifetime around the world that would cost 25,000.You borrowed this amount from your bank with an annal interest rate of 10.5%.You decide to pay it back in 5 years.What is the interest that will accrue on this loan
Answer:
238.095238 is correct
Answer:$13,125
Step-by-step explanation:
-3^2 - 1^2 -(-2)^3+(-1)^2-(-1-5)^3
Answer: 215
Step-by-step explanation:
1.) Lawrence spent $1.89
on a bottle of paint and
Assessment
$0.45'on a brush.
Practice
A. What was the total amount he spent?
Answer:
the total amount spent was$2.34 cents
Answer:
He spent $ 2.34 in all.
Step-by-step explanation:
Given,
The amount spent on the bottle of paint = $ 1.89,
While, the amount spent on the brush = $ 0.45,
Hence, the total amount spent = amount spent on paint + amount spent on brush
[tex]= 1.89 + 0.45[/tex]
[tex]= \$ 2.34[/tex]
i.e. Lawrence spent total $ 2.34 in both.
|x−5|=2x |x−5|=2x .
Answer:
x=-5,x=5/3 Brainliest please? Thank you! <3
Step-by-step explanation:
x-5=2x ~ x-5=-2x
-5=x ~ x=5/3
Mark packed 1 inch cubes into a box with a volume of 120 cubic inches how many layers of 1 inch cubes did mark pack
Answer:
The number of layers of 1-inch cubes that Mark packed is determined by assuming that the larger box is also a cube.
120 = e³
The value of e from the equation is approximately 5. Thus, there are approximately 5 layers of 1-inch cubes.
Read more on Brainly.com - https://brainly.com/question/3427563#readmoreStep-by-step explanation:
Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?
To achieve an overall interest of 10.6% on her $3,000 investment, Hattie should put $900 into an account with a 12% interest rate and $2,100 into an account with a 10% interest rate.
Explanation:Let's denote the amount of money Hattie puts in the 12% interest account as x, and the amount she puts in the 10% interest account as 3000 - x. Her aim is that the total interest she earns from both accounts is 10.6% of her total investment ($3,000).
So, 0.12x (interest from the first account) + 0.10(3000-x) (interest from the second account) should equal 0.106*3000 (her total desired income).
By solving this equation we can determine the amount of money Hattie should place in each account:
0.12x + 0.10*3000 - 0.10x = 3180.02x = 318 - 3000.02x = 18x = 900So, Hattie should put $900 in the 12% account and the rest, which is $2,100, in the 10% account to get her goal of 10.6% total interest.
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To solve this problem, set up a system of equations using the amount of money Hattie puts into each account and the total interest earned. Solve the system to find the values of x and y.
Explanation:To solve this problem, we can set up a system of equations. Let's call the amount of money Hattie puts into the account that earns 12% per year x, and the amount of money she puts into the account that earns 10% per year y. We know that x + y = $3,000 (since she has $3,000 to invest). We also know that the total interest earned is equal to 10.6% of $3,000, which is 0.106 * $3,000 = $318.
The interest earned from the account that earns 12% per year is 0.12x, and the interest earned from the account that earns 10% per year is 0.1y. We can set up another equation based on this: 0.12x + 0.1y = $318.
Now we have a system of equations: x + y = $3,000 and 0.12x + 0.1y = $318. We can solve this system using substitution or elimination to find the values of x and y.
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5. If v=u+at, find:
a) u when a=2,t=3 and v= 10
b) t when a=4, u=5 and v=29
Answer:
Step-by-step explanation:
(a) Answer below
[tex]v = u + at[/tex]
[tex](10) = u + (2)(3)[/tex]
[tex]10 = u + 6[/tex]
[tex]u = 4[/tex]
(b) Answer below
[tex]v = u + at[/tex]
[tex](29) = (5) + (4)t[/tex]
[tex]29 = 5 + 4t[/tex]
[tex]24 = 4t[/tex]
[tex]t = 6[/tex]
[tex]\text{Hello there!}\\\\\text{Plug in and solve:}\\\\1. \\\\10=u+2(3)\\\\10=u+6\\\\\boxed{4=u}\\\\2.\\\\29=5+4(t)\\\\24=4(t)\\\\\text{Divide by 4}\\\\\boxed{6=t}[/tex]
5. Consider the following two sets of incomes. Each income is in thousands of dollars
per year.
Group 1: 32, 36, 38, 39, 42, 43, 44, 47, 49, 50
Group 2:32, 36, 38, 39, 42, 43, 44, 47, 49, 150
a. Find the average or mean salary for each group.
b. How does an extreme value affect the mean?
c. Do you think the mean of the second group is a good indication of the typical
salary in that group? Explain.
a:
Mean is found by adding all the numbers in a data set, then dividing by the amount of numbers added.
Group 1 Mean: 42
Group 2 Mean: 52
b:
The only extreme value in these data sets is 150. An extreme value makes a mean that makes no sense. It distorts it.
c:
No. Group 2 is not a good indication of the typical salary in the group. It has a value that is a lot higher than all the other salaries in the group.
the mass of a textbook is approximately 0.00165 metric ton . how is this number written in scientific notation
Answer:
1.65 X 10^-3 (i don't know if your teacher wants you to also add the unit at the end, but if your teacher does, then just add metric ton at the end. :-) )
Step-by-step explanation:
We want to bring the decimal point to the right of the first number, so you move the decimal point 3 times to the right, which would give you 1.65 metric ton.
So you should know that moving a decimal point to the right would make the power negative, and moving the decimal point to the left would make the power positive.
In this situation, the power would be negative, and a negative three, because you moved the decimal point 3 times to the right.
Hope this helped :-) <3
To dilate a pre-image about a point by a scale factor of 1/3, which of the following is a good step?
A) Make sure all the angles are 1/3 the size of the pre-image with the point of dilation in the center.
B)Pick a vertex, go the the dilation point and then go 1/3 of the distance on the same line to plot the image vertex.
C)Pick an angle and make sure the image vertex is 1/3 as wide.
D)Pick a side of the pre-image and cut it by 1/3, then do the same for all sides
Answer:
Step-by-step explanation:
D), and A
Answer:
Option A) Make sure all the angles are 1/3 the size of the pre-image with the point of dilation in the center.
Step-by-step explanation:
In order to dilate an image, it is necessary that the angles are all of the equal size and magnitude. This makes the dilation of the pre-image easier
A rectangle has a length of 30 cm and
height of 53 mm. What is the perimeter
of this rectangle in centimeters?
Final answer:
The perimeter of the rectangle is calculated using the formula P = 2l + 2w, converting the height from millimeters to centimeters and then applying the values to get a perimeter of 70.6 cm.
Explanation:
To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. In this case, the rectangle's length is given as 30 cm, but the height (which can be considered as the width in the context of the perimeter) is given in millimeters. First, we need to convert the height to centimeters by dividing the number of millimeters by 10, because there are 10 millimeters in a centimeter. So, 53 mm is equivalent to 5.3 cm. Now, we apply the formula to find the perimeter:
P = 2 × 30 cm + 2 × 5.3 cm = 60 cm + 10.6 cm = 70.6 cm.
Therefore, the perimeter of the rectangle is 70.6 cm.
There are 7 red, 8 green, and 6 blue marbles
in bag. Kate is going to select one marble at
random. What is the probability that she will
select a green or blue marble?
Answer:
14/21
Step-by-step explanation:
Total marbles = 7+8+6 = 21
7 Red
8 Green
6 Blue
Probability of choosing Red = 7/21
Probability of choosing Green = 8/21
Probability of choosing Blue = 6/21
Probability of choosing Green or Blue = 8/21 + 6/21 = 14/21
What is credit score meaning
Answer:
A credit score is a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual. A credit score is primarily based on a credit report, information typically sourced from credit bureaus.
Answer:
a number assigned to a person that indicates to lenders their capacity to repay a loan.
Step-by-step explanation:
Solve the equation for x in terms of c.
Answer:
x, 2/3(cx+1/2)- 1/4= 5/2 : x= 29/8c; c \neq 0
Step-by-step explanation:
D. The value of x in terms of c is [tex]x=\frac{29}{8c}[/tex]
What is the value of x ?
The given equation is [tex]\frac{2}{3}(cx+ \frac{1}{2})-\frac{1}{4}=\frac{5}{2}[/tex]
Solving we get,
First we have to add 1/4 in both sides,
[tex]\frac{2}{3}(cx+ \frac{1}{2})-\frac{1}{4}+\frac{1}{4}=\frac{5}{2}+\frac{1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{5}{2}+\frac{1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{10+1}{4}[/tex]
⇒ [tex]\frac{2}{3}(cx+ \frac{1}{2})=\frac{11}{4}[/tex]
⇒ [tex](cx+ \frac{1}{2})=\frac{11}{4}*\frac{3}{2}[/tex]
⇒ [tex](cx+\frac{1}{2} )=\frac{33}{8}[/tex]
⇒ [tex]cx = \frac{33}{8} -\frac{1}{2}[/tex]
⇒ [tex]cx = \frac{33-4}{8}[/tex]
⇒ [tex]cx=\frac{29}{8}[/tex]
⇒ [tex]x=\frac{29}{8c}[/tex]
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What is the rate of change for the interval between A and B?
The slope of this graph is rise over run which means how much your distance x has between the 2 points and how much y increased between those 2 points. So it starts at (1,-2) and ends at (2,1). So x had a run of 1 and y had a rise of 3 we have 3/1 which is equivalent to 3, so the answer would be B.
Please I really need help with this one
Answer:
C
Step-by-step explanation:
Given the complex number a ± bi, then the complex conjugate is
a ∓ bi
Note the real part remains unchanged while the sign of the imaginary part is reversed, thus
The conjugate of 7 - i is 7 + i → C
Answer:
○ C 7 + i ohms
Step-by-step explanation:
Conjugates are expressions with OPPOSITE operation symbols, so the conjugate of 7 - i is 7 + i.
I am joyous to assist you anytime.
Sara bought 4 pounds
of coffee beans for
$3,20 per pound.
What was the total
cost, before tax?
Answer:
$12.80
Step-by-step explanation:
Sara bought 4 pounds of coffee.
Each pound (lb) costs $3.20
To find the total cost, multiply the cost per pound ($3.20) with the amount of pounds Sara is going to buy (4):
4 x 3.20 = $12.80
$12.80 would be the total cost before tax.
~
Answer:
12.8
Step-by-step explanation:
Its proportions: 1 pound equals 3.20, 4 poundes equals x.
3.20 (cost per pound) x 4 (how many pounds) = 12.8 (answer)
Can you make a triangle with the following side lengths: 1 in, 2 in, 5 in ?
Answer:
No, because the two shorter sides added must be longer than the longest side.
Also 1 squared plus 2 squared is not equal to 5 squared.
emily and how are selling wrapping paper for a school fundraiser. customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. emily sold 14 rolls of plain wrapping paper and 6 rolls of holiday wrapping paper for a total of $248. joe sold 10 rolls of plain wrapping paper and 12 rolls of holiday wrapping paper for a total of $316. find the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper.
The cost of one roll of plain wrapping paper is found to be $10, and one roll of holiday wrapping paper is $18.
We have two equations based on the given information:
Emily's sales: 14 rolls of plain wrapping paper + 6 rolls of holiday wrapping paper = $248
Joe's sales: 10 rolls of plain wrapping paper + 12 rolls of holiday wrapping paper = $316
Using algebra to solve the system, we represent the cost of one roll of plain wrapping paper as p, and the cost of one roll of holiday wrapping paper as h. Thus, the equations become:
14p + 6h = 248
10p + 12h = 316
We use the method of substitution or elimination to find the value of p and h. For instance, using elimination, we can multiply the first equation by 2 to make the coefficients of h the same:
(14p + 6h) * 2 = 248 * 2
28p + 12h = 496
Then we subtract the second equation from this new equation:
(28p + 12h) - (10p + 12h) = 496 - 316
18p = 180
p = $10
With the cost of plain wrapping paper found, substitute p = $10 into one of the original equations to find h:
10 * 10 + 12h = 316
12h = 216
h = $18
The cost of one roll of plain wrapping paper is $10, and the cost of one roll of holiday wrapping paper is $18.
what is the answer to (3n-4)5
15n -20
Good luck!! :)
Answer:2
Step-by-step explanation:
At a home improvement store, you
decide to purchase a hammer and
a pack of nails. The hammer costs
$8.53. The pack of nails costs $0.87.
What is the total cost? How much
change will you receive if you pay
with a $10 bill? a $20 bill?
Answer:
$9.40, $0.60, $10.60
Step-by-step explanation:
$8.53 + $0.87 = $9.40
$10 - $9.40 = $0.60
$20 - $9.40 = $10.60
Answer:
8,53+0,87=$9,40
if you pay $10 - 9,40 = $0,60 ( you will get $0,60 back )
if you pay $20 -9,40 = $10,60 ( you will get $10,60 back )
Step-by-step explanation:
27. Isiah is 3 years younger than twice Jack's age. Kaleb is 4 times Isiah's age. Write a variable expression to represent Isiah's age and then another to represent Kaleb's age.
To represent Isiah's age, the variable expression is I = 2J - 3. To represent Kaleb's age, the variable expression is K = 4I.
Explanation:To write a variable expression for Isiah's age, we start by defining a variable. Let's call Isiah's age 'I'. We are given that Isiah is 3 years younger than twice Jack's age, which can be written as 2J - 3. So, the variable expression for Isiah's age is I = 2J - 3.
To write a variable expression for Kaleb's age, we know that Kaleb is 4 times Isiah's age. Therefore, Kaleb's age can be represented by the variable expression K = 4I, where 'K' represents Kaleb's age and 'I' represents Isiah's age.
Let Jack's age be represented by a variable, let's say j. To express Isiah's age in terms of Jack's age, we use the information given in the question. Isiah is 3 years younger than twice Jack's age, so we can write the expression for Isiah's age as 2j - 3. Following that, we can represent Kaleb's age as being 4 times Isiah's age, which can be expressed as 4(2j - 3).
What is the cofunction of cos 2pi/ 9
The cofunction of cos is sin(90-x)
90 degrees is equal to PI/2
The cofunction becomes sin(PI/2 - 2PI/9)
Rewrite both fractions to have a common denominator:
PI/2 = 9PI/18
2PI/9 = 4PI/18
Now you have sin(9PI/18 - 4PI/18)
Simplify:
Sin(5PI/18)
The cofunction of cos 2pi/9 is sin(pi/2 - 2pi/9), which is a basic concept in trigonometry.
Explanation:The student is asking about the cofunction of
cos 2pi/9
. In trigonometry, the cofunction of a function is basically the complementary function of 90 degrees minus the original function. In this case, the cofunction of cos is sin, so to find the cofunction of cos 2pi/9, you need to find sin(90 - 2pi/9). However, since we are dealing with radians here, rather than degrees, we will be using pi/2 instead of 90 degrees. Therefore, the cofunction of cos 2pi/9 is
sin(pi/2 - 2pi/9)
.
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How does the value of the digit 2 in the number 32,000 compare with the value of the digit 2 in the number 26,000?
*Explain ur answer*
Answer:
the second value is ten times higher then the refference one
The value of the digit 2 in the number 32,000 is greater than the value of the digit 2 in the number 26,000 by a factor of 10.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The value of a digit in a number depends on its place value.
In the number 32,000, the digit 2 is in the ten thousands place, which has a value of 20,000.
In the number 26,000, the digit 2 is in the thousands place, which has a value of 2,000.
Therefore,
The value of the digit 2 in the number 32,000 is 10 times greater than the value of the digit 2 in the number 26,000.
This is because the ten thousands place is 10 times greater than the thousands place.
In other words,
The digit 2 in the number 32,000 represents 20,000 while the digit 2 in the number 26,000 represents only 2,000.
Thus,
The value of the digit 2 in the number 32,000 is greater than the value of the digit 2 in the number 26,000 by a factor of 10.
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-1/7(14+28p)-13=4(1/2p-3)-6p
Answer:
No Solution
Step-by-step explanation:
-1/7(14+28p)-13=4(1/2p-3)-6p
-2-4p-13=2p-12-6p
rearrange the question so like terms are next to each other
-2-13-4p=2p-6p-12
-15-4p=-4p-12
add 12 to both sides
-3-4p=-4p
add 4p to both sides
-3=0
No solution
Answer:
something is wrong in the equation
Step-by-step explanation:
Can someone tell me how to do number 15 please!!!
Answer:
x = 90
c = 11
d = 11
Step-by-step explanation:
For this, we just need to use algebra to solve for x.
(x / 3) - 4 = 26 | First we add 4 to both sides
x / 3 = 30 | Then we multiply both sides by 3
x = 90.
For the others, it's the same.
-8 + 10c = 102 | Subtract -8 from both sides, or add 8
10c = 110 | Divide both sides by 10
c = 11
2.5d + 7.5 = 20 | Subtract 7.5 from both sides
2.5d = 27.5 | Divide both sides by 2.5
d = 11
Find a solution to the linear equation y=−4x+36 by filling in the boxes with a valid value of x and y.
A solution would be:
[tex](1,32)[/tex]
Step-by-step explanation:This is a linear equation written in Slope-Intercept form. Recall that this form, in general, is written as follows:
[tex]y=mx+b \\ \\ \\ Where: \\ \\ m:slope \\ \\ b:y-intercept[/tex]
In this case, we have the following equation:
[tex]y=-4x+36 \\ \\ \\ Where: \\ \\ m=-4 \\ \\ b=36[/tex]
In order to find a solution, let's set [tex]x=1[/tex], so the y-value will be:
[tex]y=-4(1)+36 \\ \\ y=-4+36 \\ \\ y=32[/tex]
So, a solution to the linear equation is the point [tex](1,32)[/tex]
Final answer:
The solutions to y = -4x + 36 are x = 3 resulting in y = 24, and x = -7 resulting in y = 64, both of which have been verified to be correct by substitution back into the original equation.
Explanation:
To find a solution to the linear equation y = -4x + 36, we can substitute any value for x and solve for y, or vice versa. Let's use the given solutions x = 3 and x = -7 to find the corresponding values for y.
Substitute x = 3 into the equation: y = -4(3) + 36, which simplifies to y = -12 + 36, resulting in y = 24.
Substitute x = -7 into the equation: y = -4(-7) + 36, which simplifies to y = 28 + 36, resulting in y = 64.
To check the validity of these solutions, we back-substitute them into the original equation. For x = 3, the equation becomes 24 = -4(3) + 36, which simplifies to 24 = 24, confirming the first solution. Similarly, for x = -7, the equation becomes 64 = -4(-7) + 36, simplifying to 64 = 64, confirming the second solution. Both substitutions lead to an identity, verifying the correctness of the solutions.