Answer:
16.1 cm (nearest tenth)
Step-by-step explanation:
Pythagoras’ Theorem
[tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = 16 cmb = 2 cmSubstitute the given values into the formula and solve for c:
[tex]\implies 16^2+2^2=c^2[/tex]
[tex]\implies 256+4=c^2[/tex]
[tex]\implies c^2=260[/tex]
[tex]\implies c=\sqrt{260}[/tex]
[tex]\implies c=2\sqrt{65}[/tex]
[tex]\implies c=16.1 \sf \: cm\:(nearest\:tenth)[/tex]
16.1 is rounded to the nearest tenth
Which function has the greatest x-intercept?
Et
f(x) = 3x - 9
g(x) = (x + 31)
h(x) = 2x – 16
j(x) = -5(x - 2)2
Answer:
g(x) = (x + 31)
f(x)= 3x-9
3×x-9= -9+3×x
=-6x
g(x)=(x+31)
1×x+31=32+1×x
=32x
h(x)=2x-16
2×x-16= 16+2×x
=18x
j(x)= -5(x-2)2
(-5x+10)2
-10x+20= 10×x+20
=20-10×x
=10x
How many cubes with side lengths of 1/2 cm does it take to fill the prism.
Answer:
24 cubes
Step-by-step explanation:
You can figure this a couple of ways.
I usually find it easiest to figure in terms of the number of cubes each dimension represents. The vertical dimension (3/2 cm) is the length of 3 cubes; the front-back dimension (2 cm) is the length of 4 cubes, and the width (1 cm) is the length of 2 cubes.
The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.
I need some help solving this problem as soon as possible please!
Choose the correct ordered pairs represented in the table. The following table gives per unit costs for furniture and
shows selling prices. The numbers represent hundreds of dollars.
Step-by-step explanation:
an ordered pair is always the combination of an input value and the corresponding output value.
so, it is all already written in the table :
(1, 1)
(2, 4)
(3, 9)
(4, 16)
(5, 25)
Answers:
The ordered pairs are:
(1,1)(2,4)(3,9)(4,16)(5,25)================================================
Explanation:
The top row represents the inputs, while the bottom row is the outputs.
Each ordered pair is of the form (input, output)
Each column represents a different ordered pair.
For example, the last column has the input 5 and output 25 to give the ordered pair (5,25)
Extra Notes:
Usually x is the input and y is the output. In this case, we have c as the input and f(c) as the outputThe function rule in this case is f(c) = c^2How many different three-digit numbers can be written using digits from the set {3, 4, 5, 6, 7}
without any repeating digits?
Answer:
should be about 60
Step-by-step explanation:
What is the range of the following numbers: 2, 5, 5, 8, 4, 3
Answer: range is 6
Step-by-step explanation:
Smallest number is 2
largest number is 8
8-2=6
Factor the polynomial completely. 2x^2-9x+7
The polynomial is a quadratic function, and the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
How to factor the polynomial?The polynomial expression is given as:
2x^2 - 9x + 7
Expand
2x^2 - 9x + 7 = 2x^2- 2x - 7x + 7
Factorize the above expansion
2x^2 - 9x + 7 = 2x(x - 1) - 7(x - 1)
Factor out x - 1
2x^2 - 9x + 7 = (2x -7)(x - 1)
Hence, the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
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45.348 to two decimal places
Answer:
45.35
Step-by-step explanation:
Because there are 3 numbers to the right of the decimal point, this number has 3 decimal places. This question wants you to alter the number so that it has only 2 numbers to the right of the decimal. You can't just totally ignore the numbers you want to eliminate, so rounding rules need to be applied.
First, identify the number in the second decimal place position. If the number to the right of this position (the third decimal position) is in the range of 5 - 9, you must add 1 to the second decimal place value. Then, you can drop the numbers after the second decimal place. If the number to the right is 0 - 4, you can simply drop it the value and all the other values to the right.
In this case, the second decimal place has a value of 4. The number to the right is 8. Because 8 is within the 5 - 9 range, add 1 to 4 to get a new decimal value of 5. Finally, drop all the numbers to the right of the new second decimal place value. This leaves you with your answer: 45.35.
9. Two fair dice are rolled. Find the odds of rolling the following sums.
(a) 2
(b) 6
(c) 9
(d) Between 5 and 8 (exclusive; that is, not including 5 or 8)
(e) Not more than 5
Find the missing number in the ratio table below.
11 22 33 44
9 18 27 ?
A: 38
B: 36
C: 35
D: 37
NO LINKS
Answer:
answer is B
Step-by-step explanation:
33/27 = 44/x
33x = 1188
x = 36
NEED HELP URGENTLY!!!!!
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 3x - 5 and g(z) = ²5 to
determine iff (z) andg(z) are Inverses of each other.
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 3x - 5
Here, g(x) is not given clearly.
But we can identify the given function as an inverse of each other.
Let's suppose the ordered pairs are:
[x, f(x)] and [x, g(x)]
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
f(0) = -5 so for (0, -5) on the f(x) list then (-5,0) must be on the g(x) list
f(1) = -2 so for (1, -2) on the f(x) list then (-2, 1) must be on the g(x) list
f(2) = 1 so for (2, 1) on the f(x) list then (1, 2) must be on the g(x) list
Let's suppose:
g(x) = (x+5)/3
g(-5) = 0
g(-2) = 1
g(1) = 2
So the ordered pair (-5, 0), (-2, 1), and (1, 2) are in the list of g(x).
Thus, the functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
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In a class of 25 students, 13 have a brother and 9 have a sister. There are 7 students who do not have any siblings. What is the probability that a student chosen randomly from the class has a brother and a sister?
Answer:
Step-by-step explanation:
Discussion
9 with a sister
13 with a brother
7 with neither.
The total is 29 so you are counting some siblings twice. There are 29 - 25 students that have both, so 4 students have both.
P(brother and sister) = 4/25
P(brother and sister) = 0.16
Answer
P = 0.16
If for a particular one-to-one function f(2) = 13, what are the corresponding input and output
values for the inverse function?
Answer:
[tex]f^{-1}(13) = 2[/tex].
Step-by-step explanation:
For function [tex]f[/tex], the notation [tex]f(2) = 13[/tex] means that when the input to the function is [tex]2[/tex], the output would be [tex]13[/tex].
The inverse function of a one-to-one function [tex]f[/tex] is commonly denoted as [tex]\!f^{-1}[/tex].
The inverse function undoes the action of the original function. In this question, [tex]f[/tex] maps [tex]2[/tex] to [tex]13[/tex]. Thus, [tex]f^{-1}[/tex] would need to map [tex]13\![/tex] back to [tex]2\![/tex]. Therefore, [tex]f^{-1}(13) = 2[/tex] should be the corresponding input and output values.
x2 + y2 – 2y – 99 = 0
What is the center of this circle ?
],
What is the radius of this circle ?
units
Answer:
The center is at (h, k) : (0, -1) and the radius is 10. ... The radius is 10. That is, since r^2 = 100, r must be 10.
Step-by-step explanation:
hope this helps you!
Solve the system using elimination.
Answer:
This equation has no solution
Step-by-step explanation:
if the same equation equals 2 different numbers then therefore there is no solution.
Easy math pls help quick will give brainlest
Answer:
Problem 9: h(1/8) = 5/8
Problem 10: k = -5
Step-by-step explanation:
Problem 9:
[tex]h( \frac{1}{8} ) = 3( \frac{1}{8} ) + \frac{1}{4} = \frac{3}{8} + \frac{2}{8} = \frac{5}{8} [/tex]
Problem 10:
[tex] \frac{k - 3}{2} = - 4[/tex]
[tex]k - 3 = - 8[/tex]
[tex]k = - 5[/tex]
Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income in the fi rst year after retirement?
Answer:
$1000
Explanation:
If the employee has worked there for 20 years and for every year its 50 dollars. That would mean its 50x20 which eqauls 1000.
The monthly income in the first year after retirement is $1000.
What is monthly income?Average monthly income is the amount you earn each month. Depending on your source of income, you can subtract insurance payments, rent allowances and other costs, such as federal and state taxes, from your total income every month. Net worth is your debt subtracted from your total assets.
Given that, Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service.
After working for 20 years, Janet has decided to retire from her job at a major department store.
The company has offered her a flat monthly retirement benefit of $50 for each year of service, which means that her monthly income in the first year after retirement would be $50 multiplied by 20, which is equal to $1000.
Hence, the monthly income in the first year after retirement is $1000.
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the circumference of a circle is 110 cm . find its area
Answer:
It's about 962.89 cm^2
Answer:
962.89cm^2
Step-by-step explanation:
So, in this question, you have to find the radius of the circle because the area of a circle = πr^2. So first, you find r^2, and to do that, you divide 110 by π and you get 35.0140874802, now divide that by two and you get 17.5070437401 and that is your radius. Now, you do 17.5070437401 to the power of 2 (17.5070437401^2) and you get 306.496580518. Now multiply that by π and you get 962.89.
brainliest p l z
Hello, help me please))
Answer:
691/8-10/11Step-by-step explanation:
You can rewrite the given log expressions to express them in terms of ln(a), ln(b), and ln(c). Then substituting the given values will produce the value of the expression.
Or, you can define the variables 'a', 'b', and 'c' and let your calculator compute these directly.
__
1.[tex]\ln\left(\dfrac{a^4}{b^4c^{-2}}\right)=4\ln(a)-(4\ln(b)-2\ln(c))=4\cdot2-4\cdot3+2\cdot5=\boxed{6}[/tex]
2.[tex]\ln\left(\sqrt{b^{-2}c^4a^2}\right)=\dfrac{1}{2}\left(-2\ln(b)+4\ln(c)+2\ln(a)\right)=\ln(a)-\ln(b)+2\ln(c)\\\\=2-3+2\cdot5=\boxed{9}[/tex]
3.[tex]\dfrac{\ln(a^1b^2)}{\ln(bc)^2}=\dfrac{\ln(a)+2\ln(b)}{(\ln(b)+\ln(c))^2}=\dfrac{2+2\cdot3}{(3+5)^2}=\dfrac{8}{64}=\boxed{\dfrac{1}{8}}[/tex]
4.[tex]\ln(c^{-2})\left(\ln\dfrac{a}{b^{-3}}\right)^{-1}=\dfrac{-2\ln(c)}{\ln(a)-(-3)\ln(b)}=\dfrac{-2(5)}{2+3\cdot3}=\boxed{-\dfrac{10}{11}}[/tex]
_____
The applicable rules of logarithms are ...
ln(ab) = ln(a) +ln(b)ln(a/b) = ln(a) -ln(b)ln(a^b) = b·ln(a)ln(a) = b ⇔ a = e^bOf course, a square root is the same as a 1/2 power.
Based on the work provided, write the dividend as a product of two factors
Answer:
x4+2x3+x2+5x+b=x-2x3+x+3
Step-by-step explanation:
a ball is kicked 26 m
ball starts at 26m
1st bounce = 13 m
2nd bounce = 6.5 m
3rd bounce = 3.25 m
4th bounce = 1.625 m
5th bounce = 0.8125 m
6th bounce = 0.40625 m
7th bounce = 0.203125 m
answer: 0.203125 meters
There are 12 servings in a box of cereal. Each day, Ryan eats 2 servings of cereal. What fraction of the full box of cereal has Ryan eaten after 5 days?
Find the mean, median, mode, and range of the data set after you perform the given operation on each data value.
14, 7, 34, 29, 14, 6; multiply by 6
A. mean: 17.33, median: 14, mode: 14, range: 168
B. mean: 104, median: 84, mode: 84, range: 168
C. mean: 17.33, median: 84, mode: 84, range: 66
D. mean: 104, median: .4, mode: 14, range: 66
Answer:
A
Step-by-step explanation:
Median is the middle
Mode is the number you see the most
Add and divide for the mean
Subtract the lowest value from the highest value for the range
The Venn diagram shows the number of employers who ranked skills important for careers in their field.
C represents communication, T represents technical skills, and M represents the ability to handle money.
Circles C, T, and M overlap. Circle C contains 9, circle T contains 7, and circle M contains 19. The overlap of C and M contains 22, the overlap of M and T contains 21, and the overlap of T and C contains 18. The overlap of all 3 circles contains 25.
How many employers ask that employees be skilled in communication and handling money?
47
50
67
86
=======================================================
Explanation:
C = set of people skilled at communication
M = set of people skilled at handling money
Refer to the Venn Diagram shown below.
The blue region refers to the set of employees that are in circle C and in circle M.
Add up the numbers in the blue region to get 22+25 = 47
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents the cost for (P) people to attend the movies.
The function m(t) represents the miles driven over t hours.
The function t(m) represents the average high temperature for a given number of months.
The function p(w) represents the profit of a farmer who sells (w) whole watermelons.
The function (n) represents the number of person-hours it takes to assemble (n) engines in a factory.
Answer: The function c(p) represents the cost for (P) people to attend the movies.
The function t(m) represents the average high temperature for a given number of months.
Step-by-step explanation:
What is area of the irregular figure below? 6in 4in 12in
Composite figures can be subdivided into standard shapes. The area of the considered composite shape is 112 sq. cm
How to calculate the area of a composite figure?Area of some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc is already derived.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
The missing image is attached below.
We can split this composite figure in two parts by extending the line CG to meed AE on the point D. It makes a square (top) and a rectangle(bottom) as shown in the right sided image.
Area of the figure = Area of the top square + Area of the bottom rectangle.
Finding area of the top figure ABCD:Length of AE = |AE| = 16 cm
|AE| = |AD| + |DE| = 16
|DE| = |GF| = 8 cm
Thus, we get:
|AD| + 8 = 16
|AD| = 8 cm
Assuming the sides AD and BC are parallel, and so as the pair of sides AC and BD, and adjacent sides are perpendicular, its a rectangle with length = width = 8 cm, so its a square of side length 8 inches.
Area of square ABCD of side length 8 inches = [tex]\rm side^2 = 8^2 = 16 \: cm^2[/tex]
Finding area of the bottom figure DEFG:Assuming opposite sides of DEFG are parallel to each other and adjacent ones are perpendicular, we get:
|DE| = |GF| = 8 cm
|EF| = |DG| = |DC| + |CG| = |AB| + |CG| = 8+8 = 16 inches
Thus, its a rectagle with dimensions of 8 cm by 16 cm.
Thus, its area is: [tex]\rm Length \times width = 8 \times 12 = 96 \: \rm cm^2[/tex]
Thus, area of the composite figure = 16 + 96 = 112 sq. cm.
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Inflation is causing prices to rise at a rate of 10% per year. For an item that costs $300 today, what will be in 4 years?
Answer:
I'd say 439.3!
Step-by-step explanation:
I'm so sorry if this is wrong!
Elizabeth started cutting the
grass at 1:05. She finished
cutting the grass at 2:27. How
long did it take Ellzabeth to cut
the grass?
Answer:
1 hour and 22 minutes
Step-by-step explanation:
2:27 finished and started at 1:05
Find the mean of each distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answer:
See below ~
Step-by-step explanation:
a)
Mean = 3(21) + 1(22) + 2(23) + 5(24) + 1(25) / 12Mean = 63 + 22 + 46 + 120 + 25 / 12Mean = 276/12Mean = 23b)
Mean = 4.3 + 4.8 + 5.1 + 5.1 + 5.2 + 5.5 + 5.7 + 6.6 + 6.9 + 7.3 + 7.4 / 11Mean = 63.9/11Mean = 5.81Answer:
a) 23 °C
b) 5.81 m² (2 dp)
Step-by-step explanation:
Part (a)This set of data is presented as a Dot Plot.
The frequency (how often a data value occurs) is represented by the number of dots above each data value.
For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.
To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.
[tex]\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}[/tex]
Part (b)This set of data is presented as a stem and leaf diagram, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.
Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8
To find the mean, sum the data values, then divide by the total frequency.
To find the total frequency, simply count the number of values in the leaf part of the diagram.
Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4
Total frequency = 11
[tex]\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}[/tex]
Can someone help me with this
Answer:
95% = Within two standard deviations from the mean
99.7% = Within three standard deviations from the mean
68% = Within one standard deviation from the mean
Step-by-step explanation:
I hope this helped! If it did, please click "Thanks" to help me out!
You have a career and are given a salary of 45,000. If you have to pay 15% of your income in Federal and State taxes, how much money do you make after paying taxes? What is your monthly income?
Answer:
after taxes: $38,250monthly: $3,187.50Step-by-step explanation:
Your after-tax income is the gross pay less the amount that is paid to taxes. The monthly income is 1/12 of the annual amount.
__
The tax is the taxed amount multiplied by the tax rate.
taxes = $45,000 × 15% = $6,750
The after-tax income is the income less the taxes:
after-tax income = $45,000 -6,750 = $38,250
The monthly income is 1/12 of this amount:
monthly income = annual income/12 = $38,250/12 = $3,187.50
