Answer:
5
Step-by-step explanation:
This is quite some trial and error question.
Based on the question, the numbers we can use are 1,3,5,7 and 9.
We will start with the middle digit first.
Since the question has stated it is 3 times the last digit, the number has to be in multiples of 3.
So we are left with: 3 and 9.
Then, the question also states the middle digit is 4 more than the first digit. See, its a digit, so the value cannot be less than 1 (odd numbers only and no negative values), so if we subtract 4 to the middle digit to find the first, it should still be a Positive Single numerical value.
3 - 4 = -1
9 - 4 = 5
Therefore, this middle digit is = 9.
Since we know the middle digit = 9
The first digit will be 9 - 4 = 5
The whole value is now 593.
Verbal
3. Can a function be its own inverse? Explain.
Answer:
The function can have its own inverse, that is, [tex]$f^{-1}(x)=f(x)$[/tex] and this type of function is called an involution. Example f(x)=6-x.
Step-by-step explanation:
A statement that a function can be its own inverse is given.
It is required to explain whether a function has its own inverse. Then explain whether the given statement satisfies the condition.
Step 1 of 3
Consider a function is f(x)=6-x.
This function is a continuous function for all values of x. This function is also a linear function. So, every continuous linear function is a one-to-one function.
So, this function is one-to-one.
Step 2 of 3
Consider f(x) as y and rewrite the equation.
The equation becomes [tex]$y=6-x$[/tex]
Solve the rewritten equation.
Add -6 on both sides of the equation.
[tex]$$\begin{aligned}&y=6-x \\&y-6=6-x-6 \\&y-6=-x\end{aligned}$$[/tex]
Step 3 of 3
Multiply by -1 on both sides.
[tex]$$\begin{aligned}&y-6=-x \\&(-1)(y-6)=(-x)(-1) \\&-y+6=x \\&x=6-y\end{aligned}$$[/tex]
Interchange x and y in solved equation.
[tex]$$\begin{aligned}&x=6-y \\&y=6-x\end{aligned}$$[/tex]
So, the inverse of the given function is [tex]$f^{-1}(x)=6-x$[/tex].
The function and inverse of the function are the same, that is, [tex]$f^{-1}(x)=f(x)$[/tex]
So, a function can have its own inverse. This type of function is called an involution.
Given the legs of a right triangle are 8 and 4, what is the measure of the hypotenuse?
Answer:
Hypotenuse = 8.94
Step-by-step explanation:
Hey Guys! I need some help. This is the question... Sara travels often for her job. The miles she traveled for the last seven work days are shown.
88, 72, 91, 65, 86, 93, 97
Which is the interquartile range of Sara's daily miles?
Using the median concept, it is found that the interquartile range of Sara's daily miles is of 21 miles.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the quartiles.The ordered data-set is given as follows:
65, 72, 86, 88, 91, 93, 97
There are 7 elements, hence the median is the 4th element, of 88. Then:
The first half is 65, 72, 86.The second half is 91, 93, 97.Since the quartiles are the medians of each half, the have that:
The first quartile is of 72 miles.The third quartile is of 93 miles.The interquartile range is of 93 - 72 = 21 miles.More can be learned about the median of a data-set at https://brainly.com/question/3876456
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93a²xy - 124a²x - 62a²x³y²
Step-by-step explanation:
the ans is 19 a6 x5 y3
93-12-62×a2xy×a2x×a2x3y2
ans. 19 a6 x5 y3 add all the spuare and cube
Answer:
[tex]31a^2x(3y-4-2x^2y^2)[/tex]
Step-by-step explanation:
So the given equation is : 93a²xy - 124a²x - 62a²x³y². In this form you'll notice they all have a, and specifically a^2, and they also have x, but we only factor out x^1 since the first variable only has a degree of 1. So this gives us the equation: [tex]a^2x(93y-124-62x^2y^2)[/tex]. Now if we look at the coefficients you'll notice that they have a GCF of 31. So we can factor that out to. This gives you the equation: [tex]31a^2x(3y-4-2x^2y^2)[/tex] Which is your completely factored equation. You could also technically group 2xy^2 and 3y to get: [tex]31a^2x(y(3-2xy)-4)[/tex], although I'm not sure if that's considered "simplifying it"
Probabilities that can be estimated from long-run relative frequencies of events are called _____ probabilities.
Probabilities that can be estimated from long-run relative frequencies of events are called objective probabilities.
What is Objective Probability?In contrast to intuition or guessing, objective probability refers to the chances or odds that an event will occur based on the examination of certain measurements. Each metric is based on factual observation, a documented observation, or a long history of data collection.
Instead of being dependent on anecdotes, firsthand knowledge, or hunches, the objective probability is based on statistics, experiments, and mathematical measures. Using objective probability is crucial in the realm of finance to prevent making irrational investment decisions.
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solve:
-2(6)^x=-432
Answer:
x = 3
Step-by-step explanation:
1) Divide both sides by -2.
[tex]6^x=\frac{-432}{-2}[/tex]
2) Two negatives make a positive.
[tex]6^x=\frac{432}{2}[/tex]
3) Simplify [tex]\frac{432}{2}[/tex] to 216.
[tex]6^x=216[/tex]
4) Convert both sides to the same base.
[tex]6^x=6^3[/tex]
5) Cancel the base of 6 on both sides.
x = 3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{-2(6)^x = -432}[/tex]
[tex]\huge\textbf{DIVIDE -2 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{6^x = 216}[/tex]
[tex]\huge\textbf{Solve for the current exponent:}[/tex]
[tex]\mathbf{6^x = 216}[/tex]
[tex]\huge\textbf{Log them:}[/tex]
[tex]\mathbf{Log \ 6^x = log = 216}[/tex]
[tex]\huge\textbf{Take the log to both of the sides:}[/tex]
[tex]\mathbf{x \times log (6) = log(216)}[/tex]
[tex]\huge\textbf{Convert it:}[/tex]
[tex]\mathbf{x = \dfrac{log(216)}{log(6)}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = 3}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]What assumption do we need to make to find a valid 99% confidence interval for the mean number of all workplace homicides per year
We have to assume that the sample mean is given , distribution is normal and sample size is also given.
Given confidence level 99%.
We have to answer the assumptions that are needed to make a valid 99% confidence interval.
Confidence interval can be made by formula of margin of error.
Margin of error is the difference between actual values and the calculated values.
Upper level of confidence interval=Mean+ margin of error
Lower level of confidence interval= Mean - margin of error.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the corresponding z value for the confidence level given ,
σ is population mean and n is sample size.
Hence to calculate the confidence interval we need population mean, sample size.
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If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
The vertex U' is located at (-4, -5)
How to determine the location of U'?The vertices are given as:
U = (-4, 5)
V = (-6, 2)
The rule of transformation is given as:
Reflection across the x-axis
This is represented as:
(x, y) => (x, -y)
So, we have:
U' = (-4, -5)
Hence, the vertex U' is located at (-4, -5)
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Complete question
Quadrilateral UVWX is reflected over the x-axis to form quadrilateral U′V′W′X′. If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
(6+√-64)(3-√-16) Multiply. This is urgent, please explain this to me!
Answer:
50
Step-by-step explanation:
[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i
[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i
the factors can then be expressed as
(6 + 8i)(3 - 4i) ← expand using FOIL
= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]
= 18 - 24i + 24i + 32 ← collect like terms
= 18 + 32 + 0
= 50
which type of data would be best displayed in a box plot
The type of data that would be best displayed in a box plot is the number of votes received by each of four candidate.
What is a box plot?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
The whiskers represent the minimum and maximum scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
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help me find x please
Step-by-step explanation:
x² + (2x)² = (√180)²
x² + 4x² = 180
5x² = 180
x² = 180/5
x² = 36
x = √36 (and no - √36 because x ≥ 0)
x = 6
An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.
What is the largest possible volume of the box?
The largest possible volume of the given box is; 96.28 ft³
How to maximize volume of a box?Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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can someone answer this question for me pls n thanks
Answer:
Mean: 29.5; Median: 26; Modes: 25, 26
Step-by-step explanation:
Add 10+12+25+25+26+26+30+31+33+34+47+55 = 354
Then divide it by 12 354/12 = 29.5
Mode are numbers that appear most often which in this case are 2 numbers, 25 and 26.
In the following exercises, solve
635. The price that Tyler pays for gas varies directly with the number of gallons he buys. If 24 gallons cost him $59.76, what would 30 gallons cost?
Answer:
The cost of 30 gallons of gas is $74.7.
Step-by-step explanation:
Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.The cost 24 gallons is $59.76 to him.Now we need to find the cost of 30 gallons.To solve this problem use a direct variation formula.Solve for constant variation.Step 1 of 3
Here we need to find the cost of 30 gallons.
Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.
The cost of 24 gallons is $59.76 to him.
Let, x be the number of gallons and y be the cost or price for gas.
Use the formula for direct variation which is given by y=kx.
Step 2 of 3
Now substitute the value y=$59.76 and x=24.
Put value in y=kx, we get
[tex]$$\begin{aligned}&59.76=k \times 24 \\&k=2.49\end{aligned}$$[/tex]
Substitute value of k is y=kx, we get y=2.49x
Step 3 of 3
Now we need to find the value of y that is the cost for 30 gallons.
Again use direct variation formula y=kx and value of k and x, we get [tex]$y=2.49 \times 30$[/tex]
[tex]$$y=74.7$$[/tex]
^
Find (ff)(0).
f(x) = 3x - 2
a. 1
b. 0
Please select the best answer from the choices provided
ABCD
Answer:
a
Step-by-step explanation:
go it right on a mastery test
The length of a pencil, l cm, varies directly with its mass m g and inversely with its area of cross section A cm square when m=4 and A=0.4 l=18
The equation connecting L, m, A is L = [tex]\frac{1.8m}{A}[/tex]
What is a Variation?Variation is a mathematical relationship that shows how a certain variable behaves when other variables depending on it increase or decrease.
The types of variation are: Direct, indirect, joint and partial.
Analysis:
L ∝ [tex]\frac{m}{A}[/tex]
introducing a constant K to replace the proportionality sign,
L = [tex]\frac{Km}{A}[/tex]
when L = 18, m = 0.4, A = 0.4
18 = [tex]\frac{K(4)}{0.4}[/tex]
4K = 0.4 x 18
k = 1.8
Therefore the equation connecting the three variables is,
L = [tex]\frac{1.8m}{A}[/tex]
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For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.
37. y = | x − 1 |
The points used in plotting the graph of the absolute function as given are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).
What are the points to be used to plot the graph of the absolute function?The absolute function given is; y = | x − 1 |
Hence, by consider x-values; -2,-1,0,1,2....it follows that the corresponding y-values which are all positive by virtue of the absolute value symbol are; 3, 2, 1, 0, 1.
Hence, the points are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).
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find the product (t - sa) (9t + 6sa)
The product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a²
What is the product of two factors?The product of two factors of an expression results in a quadratic or polynomial expression depending on the degree to which their power is being raised.
From the information given, we have:
= (t - sa) (9t +6sa)
= 9t² + 6tsa - 9tsa - 6(sa)²
= 9t² - 3tsa - 6s²a²
Therefore, we can conclude that the product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a².
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Wendy keeps her hamster, Fluffy, in a cage shaped like a rectangular prism that is 20 inches long, 14 inches wide, and has a volume of 4,340 cubic inches. Kenneth keeps his hamster, Speedy, in a cage that is the same length, but is 15 inches wide and has a volume of 5,250 cubic inches.
Speedy cage is 2 inches taller than fluffy cage.
How to find the volume of a rectangular prism?The volume of rectangular prism = lwh
where
l =lengthh = heightw = weightTherefore,
height of fluffy cage can be calculate as follows:
4340 = 20 × 14 × h
4340 = 280h
h = 4340 / 280
h = 15.5 inches
height of Kenneth cage can be calculate as follows:
5250 = 20 × 15 × h
5250 = 300h
h = 5250 / 300
h = 17.5 inches
height difference = 17.5 - 15.5 = 2.0 inches
Hence, speedy cage is 2 inches taller than fluffy cage.
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2. The name of the 1500-meter gold medal winner for each of the Olympics
from 1896 to 2000 is placed in a jar. (If a man has won the race more than
once, his name will be included for each race he won.)
A. If one name is drawn from the jar, which country has the best chance
of having a name drawn?
B. Three names are drawn without replacing the name after it is drawn.
What is the probability that the three winners will be from either
New Zealand or Australia?
pLEASE HELP
The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.
How to calculate probability?It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.
Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.
The probability that the winners will be from either New Zealand or Australia will be:
= 3/29 + 2/29
= 5/29
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Answer
A. Great Britain
B. 3/29+2/29=5/29
please give me the brainliest.
A rectangle has a length of 6x-5y+1 if the perimeter of the rectangle is 16x-4y-4 determine an expression for its width
Answer:
Width = 3y - 3
Step-by-step explanation:
P = 2l + 2w
12x - 4y - 4 = 2(6x - 5y + 1) + 2w
12x - 4y - 4 = (12x - 10y + 2) + 2w
6y - 6 = 2w
w = 3y - 3
What is the degree of the polynomial?
The degree of the polynomial is 2
How to determine the degrees?The root of the polynomial is given as:
Root = x - 3i
The above expression is a complex root.
This means that the conjugate is also a root of the polynomial
So, we have
Roots = x - 3i and x + 3i
Multiply the roots
f(x) = (x - 3i)(x + 3i)
This gives
f(x) = x^2 + 9
The degree of the above equation is 2 i.e. the highest power
Hence, the degree of the polynomial is 2
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Can you answer my question please and thank you
Answer:
50
Step-by-step explanation:
I did this by inspection because {7, 24, 25} is a common trio, but ill just break it down for you.
Let the hypotenuse be x
Then [tex]14^2+48^2=50^2[/tex]
2500 = [tex]x^2[/tex]
x=50 or -50 (not applicable because you cannot have a negative length).
So the hypotenuse is 50.
Note: Common trios such as {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17} are worth remembering as you can often multiply them in such questions. Such as in this question, {7, 24, 25} times 2 is {14, 48, 50}.
Hope you have a nice day!
vA sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.
[0.3105, 0.3695] expect to buy a new car next year.
These are the answer choices -
A) [0.3074, 0.3726]
B) [0.3105, 0.3695]
C) [0.3140, 0.3660]
D) [0.3392, 0.3408]
It is given that a sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year.
For large random samples, a confidence interval for a population proportion is given by
[tex]sample proportion[/tex] ± [tex]z * \frac{\sqrt{sample proportion (1 - sample proportion)} }{n}[/tex]
where z* is a multiplier number that comes from the normal curve and determines the level of confidence (see Table 9.1 for some common multiplier numbers).
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How many solutions does the equation ||2x-3|-m|=m have if m>0?
There are three solutions of the equation ||2x-3|-m|=m have if m>0.
We have to estimate the number of solutions of the equation ||2x - 3| - m| = m where m > 0.
As we know in the modulus function
|x|= x if x>0
-x if x<0
0 if x=0
here given m > 0
if |2x-3|-m>0 then the modulus value will be ||2x-3|-m|= |2x-3|-m
Then, |2x - 3| - m = m
⇒|2x - 3| = m+m= 2m
⇒2x - 3 = 2m or -(2x-3)=2m
⇒2x - 3 = 2m or 2x-3=-2m
⇒2x = 3 ± 2m
⇒x = (3 ± 2m)/2
⇒x= (3 + 2m)/2 or (3 - 2m)/2
If |2x-3|-m<0 then then the modulus value will be | |2x-3|-m| = -(|2x-3|-m)
-(|2x-3|-m)=m
⇒m-|2x-3|=m
⇒-|2x-3|= m-m
⇒ |2x - 3| = 0
⇒2x = 3
⇒x = 3/2
Therefore The solution of the equation will be (3 + 2m)/2, (3 - 2m)/2, and 3/2.
Therefore there are three solutions of the equation ||2x-3|-m|=m have if m>0.
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In the xy-coordinate plane, point (1, 4) is on the line whose equation is y = 3x + b. What is the value of b ?
Answer:
b = 1
Step-by-step explanation:
since the point (1, 4 ) lies on the line then it satisfies the equation , that is
3(1) + b = 4
3 + b = 4 ( subtract 3 from both sides )
b = 1
15. Jeff packed tins in cartons standing upright and Sammy packed lying along the width of the carton. How many more tins are packed standing upright than lying along the width?
I think the answer is D
☆...hope this helps...☆
_♡_mashi_♡_
Find the image vertices for a dilation with center
Image vertices are mathematically given as:
A' = (-12 , 4) B' = (16 , -12) C' = (8 , 12) D' = (-4 , 16)What are the image vertices for dilation with the center?Generally, Multiplying the vertices by a scale factor of four is required in order for us to locate the picture vertices for dilation with center (0, 0).
In conclusion,, the image vertices are :
A' = (-12 , 4) B' = (16 , -12) C' = (8 , 12) D' = (-4 , 16)Read more about vertices
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Create a scatterplot displaying the data in the table. Be sure to include a linear trend line. (2 points)
The scatter plot is shown in the attached picture, and the line of best is also shown.
What is scatter plot?Scatter plots are graphs representing individual data points and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one on the y-axis for each point.
We have the data shown in the table.
We can plot the data on the coordinate plane such as:
(x, y) = (54, 92), (46, 80) and so on
We can find the equation of best fit:
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
y = mx + c
Thus, the scatter plot is shown in the attached picture, and the line of best is also shown.
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Consider a TV set that consumes 120 W of electric power when it is on, and is kept on for an average of 6 h per day. For a unit electricity cost of 23 cents per kWh, determine the cost of electricity this TV consumes per month (30 days). The cost of electricity the TV consumes per month is $
The cost of electricity consumed by the TV per month is $4.968.
In the question, we are given that a TV set consumes 120W of electric power when switched on. It is kept on for a daily average of 6 hours per day. The number of days in the month is given to be 30 days. The cost per unit of electricity is 23 cents per kWh.
We are asked to find the cost of electricity the TV consumes in the month.
The daily energy consumed by the TV = Power*Daily time = 120*6 Wh = 720 Wh.
The monthly energy consumed by the TV = Daily energy*Number of days in the month = 720*30 Wh = 21600 Wh = 21600/1000 kWh = 21.6 kWh.
Hence, the total cost of electricity the TV consumes = Monthly energy*Per unit cost = 21.6*23 cents = 496.8 cents = $496.8/100 = $4.968.
Therefore, the cost of electricity consumed by the TV per month is $4.968.
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