Nora needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 478 forks. There are currently 286 forks. If each set on sale
contains 12 forks, write and solve an inequality which can be used to determine s, the
number of sets of forks Nora could buy for the restaurant to have enough forks.
Let
s -----> the number of sets of forks Nora could buy for the restaurant to have enough forks
so
the inequality that represent this situation is
[tex]286+12s\ge478[/tex]solve for s
[tex]\begin{gathered} 12s\ge478-286 \\ 12s\ge192 \\ s\ge16 \end{gathered}[/tex]the minimum number of sets is 16Angelina has 10 yards of fabric. She needs ⅓ yard of fabric for each purse she will sew. How many purses will she be able to make?
Divide the total amount of fabric by the amount needed to create a purse to find how many purses will she be able to make.
Since she has 10 yards of fabric and each purse requires 1/3 of a yard, then, divide 10 over 1/3:
[tex]10\div\frac{1}{3}=\frac{10}{1}\div\frac{1}{3}=\frac{10\times3}{1\times1}=\frac{30}{1}=30[/tex]Therefore, Angelina will be able to make 30 purses using 10 yards of fabric.
14. Given: JM bisects JL JM perpendicular to KLProve: TRIANGLE JMK congruent to TRIANGLE JML
1) is already written, so we start with the second line.
2)
JM is parallel to KL ----> Given
3) ∠KML = ∠JML ----> They are angles on two perpendicular lines, and Since JM bisects LK, they are equal.
4) ∠KJL=∠MKL ---> Since JM bisects ∠J, the angles KJL and MKL are equal
5) ∠JKM=∠JLM ----> Since 3) and 4), the angles JKM and JLM must also be equal so that the sum of internal angles of each triangle will be 180°
Thus: Triangle JMK is congruent to triangle JML
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
ANSWER:
Separate the quotient in two terms
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \tan x=\frac{1}{\cos x}\cdot\sin x \end{gathered}[/tex]Therefore, the step shown in the image is to separate the quotient in two terms
Determine the equation of the graphed circleReminder that the equation should look like the example I provided
The equation of a circle of radius r and center at (h, k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]The image provided shows a circle and we must find the radius and center by simple inspection.
The center is located at (-5, 3).
From that point, until I find a point of the circumference I can count 4 units. It is confirmed when I see the segment from (-9, 3) to (-1, 3) as a diameter of length 8. The radius is half the diameter, thus r = 4.
Substituting, we have the required equation:
[tex]\begin{gathered} (x+5)^2+(y-3)^2=4^2 \\ \boxed{\mleft(x+5\mright)^2+\mleft(y-3\mright)^2=16} \end{gathered}[/tex]2/5m = 1/2 what is the m stand for ?
we can interpret m as a constant of proportionality.
f(x) = 4x - 2 for x = 0
Substituting x = 0 into the function we get:
f(0) = 4(0) - 2
f(0) = 0 - 2
f(0) = -2
1c. Clue 1The number has three digits.Clue 2 The number is less than 140.Clue 3 The number has 7 as a factor.Clue 4 The number is even.Clue 5 The sum of the digits of the number is less than 9.
We have an even 3 digits number whose sum lie is less than 9, has got 3 digits and less than 140.
We will establish the inequalities that satisfies the conditions given and then figure out the number.
[tex]\begin{gathered} 100x+10y+z<140 \\ x+y+z<9 \\ 100x+10y+z=14a\text{ where a lies between 8 and 9} \end{gathered}[/tex]From our last inequality, we can easily see that the number in question is 14 x 8 or 14 x 9. Any multiple of 7 that is even is also a multiple of 14.
[tex]\begin{gathered} 14\times8=112\text{ AND} \\ 14\times9=126 \end{gathered}[/tex]From the above, it can be easily seen that 112 satisfies the conditions listed.
The number is 112
New Orleans is 2 feet below sea level. Salton City has an elevation that is lower than New Orleans. What is a possible elevation, in feet, of Salton City?
Answer:
-4 feet (4 feet below sea level)
Salton City's potential elevation is determined to be 3 feet below sea level by using a number line and the elevation of New Orleans, which is 2 feet below sea level.
What is meant by number line?A number line is a mathematical visual representation of numbers on a straight line. On a number line, the numbers are arranged in order at regular intervals along its length.It often appears horizontally and could extend indefinitely in either direction. A number line is a horizontal line with consistently spaced numerical increments.How the number on the line can be answered depends on the numbers that are present. Given, the elevation indicates that New Orleans is 2 feet below (lower than) sea level.The elevation of Salton City is lower than that of New Orleans. Required; potential rise of Salton CitySalton City's elevation can be calculated using the information below on a number line: We have;& |t; |-3 |-2 |0 > if SL stands for sea level, N for New Orleans, and S for Salton City. On the number line above, a S. N. SLA point to the right of the -2 mark denotes an elevation that is higher than New Orleans, and a point to the left of -2 denotes an elevation that is lower than New Orleans.Therefore,
Salton City should be located to the left of -2, which is a point, at a distance of x -2 feet.
Salton City's elevation, which is determined by the set x -2 feet, is less than 2 feet above sea level.
Since -3 feet is less than -2 feet, Salton City's elevation might be as low as x = 3 feet below sea level, which is less than () 2 feet below sea level.
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(-1,2) and (3,32)
For each of the following, find the formula for an exponential function that passes through the two points given.
The required exponential function f(x) = (4)(2)ˣ which is passes through the two points (-1,2) and (3,32).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Let the formula for an exponential function would be as
⇒ f(x) = abˣ
The exponential function passes through the two points (-1,2) and (3,32).
f(-1) = 2
f(3) = 32
2 = ab⁻¹
2b = a
32 = ab³
Substitute the value of a = 2b in the above equation,
32 = 2b×b³
32 = 2b⁴
b⁴ = 16
b⁴ = 2⁴
b = 2
Substitute the value of b = 2 in the equation a = 2b,
So a = 2×2 = 4
⇒ f(x) = (4)(2)ˣ
Therefore, the required exponential function f(x) = (4)(2)ˣ
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Solve y^3= −125.
y = −5
y = ±5
y = −25
y = ±25
Answer:
A. y=-5Step-by-step explanation:
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtractDo exponents first.
[tex]\sf{y^3=-125}[/tex]
[tex]\sf{x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\dfrac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\dfrac{-1+\sqrt{3}i}{2}}}[/tex]
[tex]\rightarrow \sf{y=\sqrt[3]{-125},\:y=\sqrt[3]{-125}\dfrac{-1+\sqrt{3}i}{2},\:y=\sqrt[3]{-125}\dfrac{-1-\sqrt{3}i}{2}}[/tex]
[tex]\sf{\sqrt[3]{-125}=\boxed{\sf{-5}}}[/tex]
Therefore, the correct answer is y=-5.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{y^3 = -125}[/tex]
[tex]\large\text{Solve/take the cube root}[/tex]
[tex]\mathsf{(-125)^{^\dfrac{1}{3}}}\mathsf{ = y}[/tex]
[tex]\mathsf{y = (-125)^{^\dfrac{1}{3}}}[/tex]
[tex]\large\text{Simplify it}[/tex]
[tex]\mathsf{y = -5}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{y = -5\ (\rm \bold{O}ption\ A.)}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The data for numbers of times per week 20 students at Stackamole High eat vegetables are shown below. A dotplot shows 4 points above 1, 4 points above 3, 5 points above 2, 3 points above 4, 3 points above 5, and 1 point above 9.
Considering the given dot plot for the distribution, it is found that:
a) The distribution is right skewed.
b) There is an outlier at 9.
c) Since there is an outlier, the best measure of center is the median.
Dot plotA dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:
1, 1, 1, 1, 2, 2, 2, 2, 2 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 9.
To find the skewness of the data-set, we need to find the mean and the median.
The mean is the sum of all values divided by the number of values of 20, hence:
Mean = (4 x 1 + 5 x 2 + 4 x 3 + 3 x 4 + 3 x 5 + 9)/20 = 3.1.
The median is the mean of the 9th and the 10th elements(even cardinality) of the data-set, hence:
Median = (2 + 3)/2 = 2.5.
The mean is greater than the median, hence the distribution is right skewed.
To identity outliers, we need to look at the quartiles, as follows:
First quartile: 0.25 x 20 = 5th element = 2.Third quartile: 0.75 x 20 = 15th element = 4.The interquartile range is:
IQR = 4 - 2 = 2.
Outliers are more than IQR from the quartiles, hence:
4 + 1.5 x 2 = 4 + 3 = 7 < 9, hence 9 is an outlier in the data-set, and hence the median will be the best measure of center.
Missing information
The questions are as follows:
Part A: Describe the dotplot. (4 points)
Part B: What, if any, are the outliers in these data? Show your work. (3 points)
Part C: What is the best measure of center for these data? Explain your reasoning. (3 points) (10 points)
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Find the length of the legs of a night triangle whose hypotenuse is 25cm and whose area is 84cm use phytagorean theorem.
Answer:
Explanation:
Here, we want to find the length of the legs of the right triangle given the area and the length of the hypotenuse
We have the sketch of the triangle as shown below:
According to Pythagoras' the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides
Thus, mathematically:
[tex]a^2\text{ + b}^2\text{ = 25}^2[/tex]Mathematically, we have the area calculated as:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times b\times h \\ \\ 84\text{ = }\frac{1}{2}\times a\times b \\ \\ a\text{ = }\frac{168}{b} \end{gathered}[/tex]Now, we have two equations to solve simultaneously
Substitute equation ii into i
We have that as:
[tex][/tex]there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation
According to the given data we have the following:
total households in the US=1.2*10^8. hence:
[tex]1.2*10^8=120000000[/tex]average household uses 400 gallons of water each day
let x=total number of gallons of water used by households in the US each day
Therefore x=total households in the US*average gallons of water households uses each day
x=120,000,000*400
x=48,000,000,000
The total number of gallons of water used by households in the US each day is 48,000,000,000
The wholesale price for a bookcase is 152$. A certain furniture marks up the wholesale price by 36%. find the price of the bookcase in the furniture store. round answer by the nearest cent, as necessary
The price of the bookcase in the funiture store is:
$206.72
Explanation:Given that the markup is 36% of $152
This is:
0.36 * 152 = $54.72
Therefore, the price of the bookcase in the funiture store is:
$152 + $54.72
= $206.72
Austin walks 3.5km every day. How far does he walk in 7 days?Write your answer in meters.
Answer:
24,500 meters
Step-by-step explanation:
i inserted a picture of the question, could you please take the short way.
Recall the following property of exponents:
[tex](a\cdot b)^x=a^x\cdot b^x\text{.}[/tex]Therefore:
[tex](14\cdot(-58))^{16}=14^{16}\cdot(-58)^{16}\text{.}[/tex]Answer: Option A.
48.001 to the hundredths
Since we want to express 48.001 to the hundredths, let's look at the places of the digits after the decimal point:
Therefore, 48.001 to the hundredths is 48.00
When nee, a standard tire has 10/32 inches of tread. When only 2/32 inches of tread remains, tire needs to be replaced. If this occurs after 40,000, what thickness of tire rubber is lost every 1,000 miles driven? Answer in fractions of an inch.
Given:
A standard tire has 10/32 inches of tread.
The tire needs to be replaced when only 2/32 inches of tread remains left.
Here the tire is needed to be replaced after 40,000 miles.
To find:
The thickness of tire rubber lost every 1,000 miles.
Step-by-step solution:
According to the question,
The tire is replaced when only 2/32 inches of tread remain left.
The new tire has 10/32 inches of tread.
Thus tire needs to loose:
10/32 - 2/32 = 8/32 inches of tread.
This means upon traveling for 40,000 miles, 8/32 inches of tread is lost.
So their ratio equals:
40,000 = k (8/32)
k = 40,000 × 32 / 8
k = 40,000 × 4
k = 1,60,000
So to calculate for 1000 miles:
1000/x = 1,60,000
1/x = 1,60,000 / 1000
1/x = 160
x = 1 / 160 inches
Thus we can say for every 1000 miles, 1 / 160 inches of tread is lost.
8.[–/1 Points]DETAILSALEXGEOM7 9.2.012.MY NOTESASK YOUR TEACHERSuppose that the base of the hexagonal pyramid below has an area of 40.6 cm2 and that the altitude of the pyramid measures 3.7 cm. A hexagonal pyramid has base vertices labeled M, N, P, Q, R, and S. Vertex V is centered above the base.Find the volume (in cubic centimeters) of the hexagonal pyramid. (Round your answer to two decimal places.) cm3
Solution
- The base is a regular hexagon. This implies that it can be divided into equal triangles.
- These equal triangles can be depicted below:
- If each triangle subtends an angle α at the center of the hexagon, it means that we can find the value of α since all the α angles are subtended at the center of the hexagon using the sum of angles at a point which is 360 degrees.
- That is,
[tex]\begin{gathered} α=\frac{360}{6} \\ \\ α=60\degree \end{gathered}[/tex]- We also know that regular hexagon is made up of 6 equilateral triangles.
- Thus, the formula for finding the area of an equilateral triangle is:
[tex]\begin{gathered} A=\frac{\sqrt{3}}{4}x^2 \\ where, \\ x=\text{ the length of 1 side.} \end{gathered}[/tex]- Thus, the area of the hexagon is:
[tex]A=6\times\frac{\sqrt{3}}{4}x^2[/tex]- With the above formula we can find the length of the regular hexagon as follows:
[tex]\begin{gathered} 40.6=6\times\frac{\sqrt{3}}{4}x^2 \\ \\ \therefore x=15.626947286066 \end{gathered}[/tex]- The formula for the volume of a hexagonal pyramid is:
[tex]\begin{gathered} V=\frac{\sqrt{3}}{2}b^2\times h \\ where, \\ b=\text{ the base} \\ h=\text{ the height.} \end{gathered}[/tex]- Thus, the volume of the pyramid is
[tex]\begin{gathered} V=\frac{\sqrt{3}}{2}\times15.626947286066^2\times3.7 \\ \\ V=782.49cm^3 \end{gathered}[/tex]Consider the following functions.S(x) = x2 - 4x + 4 and g(x) = x - 2Step 1 of 2: Find• ()a). simplify your answer.AnswerKeybo(*)(x) =Subn
Answer:
[tex]x-2[/tex]Explanation:
Here, we want to simplfy the given expression
From what we have:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex]Substituting the values, we have it that:
[tex]\frac{x^2-4x+4}{x-2}\text{ = }\frac{(x-2)(x-2)}{x-2}\text{ =x-2}[/tex]Line segment AB has a midpoint C.If AC=17 and AB = 5x-6, then find the value of x
From that diagram that is drawn above, C is the midpoint of the line AB:
AC = 17
AB = 5x - 6
Since C is the midpoint of AB;
AB = 2AC = 2CB:
5x - 6 = 2(17)
5x - 6 = 34
5x = 34 + 6
5x = 40
x = 40/5
x = 8
Solve. 0.25(60) + 0.10x = 0.15(60+x)
[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]
ATTACHED IS THE SOLUTION
Question 2 A recipe for homemade modeling clay requires 4 parts plain flour to 1 part cornstarch. Indicate whether each set of ingredients below is proportional to the recipe. Proportional Not Proportional 8 cups plain flour and 2 cups cornstarch 20 cups plain flour and 5 cups cornstarch 2 cups plain flour and 1 cup cornstarch Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Frequirements | Platform Status 2021 McGraw-HI Education. All Rights Reserved
The given ratio is 4 parts of plain flour to 1 part of cornstarch.
So, each recipe with the same ratio will be the answer.
As you can observe, the first choice is proportional because the plain flour is 4 times the cornstarch.
The second choice is proportional too because the plain flour is 4 times the cornstarch.
However, the last choice is not proportional because it has a ratio of double, which is not correct.
Really need help with this math assignment please help no
In a linear relationship, each step of x modifies the y value in the same way.
In the first table, when x = 1, y = 3 and when x = 2, y = 6. This is an increment of 3. If this is a linear relationship, we expect the next value of y to be the previous value plus 3, thus y = 9. But in the table shows x =3 and y = 12. We can rule out the first table.
With similar reasoning, in the second table, we see (1, 2) and (2, 5). This is an increase of the y value of 3. We expect the next value to be y = 8, but we see (3, 9). The second table is not a linear relationship.
In the third table, we see (1, -3) and (2, -5). This is a decrease of -2. We expect the next value of y to be y = -7, and we do see (3, -7). The next value should be y = -9, and the table shows (4, -9). Table 3 shows a linear relationship.
To be sure, let's see the 4th table. We see (1, -2) and (2, -4). This is a decrease of -2. The expected next value is y = -6, but the next point is (3, -2). Fourth table is not a linear relationship.
Thus, the correct answer is the top-right table.
help meeeeeeeeee pleaseee !!!!!
For the given functions, the two compositions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3*x² + 15
How to find the compositions of the functions?Here we have two functions which are:
f(x) = x² + 5
g(x) = 3x
Now we want to find the compositions:
(f o g)(x) = f( g(x) )
So we just need to evaluate f(x) in g(x), we will get:
f( g(x) ) = g(x)² + 5
f( g(x) ) = (3x)² + 5 = 9x² + 5
The other composition is:
(g o f)(x) = g(f(x))
And we can get this in a similar way:
g(f(x)) = 3*f(x) = 3*(x² + 5) = 3*x² + 15
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If joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was joey from home?
The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
It is known that East and West are the opposite of each other.
So, 15 2/3 towards the east let's take it positively.
And 21 3/4 towards left let's consider it negative.
So, the distance from the home
⇒ | ( 15 + 2/3) - (21 +3/4) |
⇒ | 15 -21 + 2/3 - 3/4 |
⇒ | -6 + (8 - 9)/12 |
⇒ | -6 - 1/12 |
⇒ | -(6 +1/12) |
⇒ 6 1/12
Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".
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I need help I need help I need help I need help I need help i need help I need help
Answer:
5) The midrange is 19.5ºF
6) The midrange is 67.5º
Explanation:
The problem tell us how to calculate the midrange.
In (5) the minimum and maximum values are given (-6ºF and 45ºF, respectively). Using the formula:
[tex]Midrange=\frac{-6+45}{2}=\frac{39}{2}=19.5ºF[/tex]In (6), we need to find the minimum and maximum values from a list of them. We can see that the minimum is 58º and the maximum 77º
Then:
[tex]Midrange=\frac{58+77}{2}=\frac{135}{2}=67.5º[/tex]Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y? 5y = 25y = 1011y = 211y = 10
Explanation:
The equation is given below as
[tex]8y+4=6+2y+1y[/tex]Step 1:
Collect similar terms, we will have
[tex]\begin{gathered} 8y+4=6+2y+1y \\ 8y+4=6+3y \\ 8y-3y=6-4 \\ 5y=2 \end{gathered}[/tex]Hence,
The simplified form of the equation will be
[tex]\Rightarrow5y=2[/tex]The graph of function f is shown. The graph of an exponential function passes through (minus 0.25, 10), (0, 6), (5, minus 2) also intercepts the x-axis at 1 unit. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 - 3 4 - 15 16 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept but different end behavior as x approaches ∞. C. They have the same x- and y-intercepts. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;
B. They have the same x–intercept but different end behaviours as x approaches ∞What is the end behaviour of a graph?The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.
The given points on the exponential function, f, are;
(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)
The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;
(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)
The coordinates of the x–intercept is given by the point where the y–value is zero.
The x–intercept for the exponential function, f, is therefore (1, 0)
Similarly, the x–intercept for the function, g, is (1, 0)
Therefore, both functions have the same x–intercept
However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.
The correct option is therefore;
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Help first one to get this correct will be marked
Answer:
1st one
Step-by-step explanation:
1st one
You have one input (x) with more than one output (y)
(-9, -9) and (-9, 6)
