Answer:
y = 6h h = hour
Step-by-step explanation:
lim
T-44
√x+5-7
x - 44
[tex]\displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\hspace{5em}\stackrel{\textit{L'Hopital's rule}}{\lim_{x\to 44}~\cfrac{ ~~ \frac{d}{dx}[\sqrt{x+5}-7] ~~ }{\frac{d}{dx}[x-44]}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{dx}[\sqrt{x+5}-7]\implies \cfrac{1}{2}(x+5)^{-\frac{1}{2}}(1)\implies \cfrac{1}{2\sqrt{x+5}} \\\\\\ \cfrac{d}{dx}[x-44]\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\implies \lim_{x\to 44}~\cfrac{ ~~ \frac{1}{2\sqrt{x+5}} ~~ }{1}\implies \lim_{x\to 44}~\cfrac{1}{2\sqrt{x+5}}\implies \cfrac{1}{2\sqrt{44+5}} \\\\\\ \cfrac{1}{2\sqrt{49}}\implies \cfrac{1}{2(7)}\implies \cfrac{1}{14}[/tex]
Can you solve two questions for me? Please dont use fancy words!
QUADRILATERALS PROPERTY ONLY
Answer:
6. ∠PVU = 58°
7. y = 74°
Step-by-step explanation:
Question 6Angles on a straight line sum to 180°.
⇒ ∠USP + ∠PSV = 180°
⇒ 148° + ∠PSV = 180°
⇒ 148° + ∠PSV - 148° = 180° - 148°
⇒ ∠PSV = 32°
The interior angle of a rectangle at each vertex is 90°.
⇒ ∠VPS = 90°
Interior angles of a triangle sum to 180°.
⇒ ∠PVS + ∠PSV+ ∠VPS = 180°
⇒ ∠PVS + 32° + 90° = 180°
⇒ ∠PVS + 122° = 180°
⇒ ∠PVS + 122° - 122° = 180° - 122°
⇒ ∠PVS = 58°
From inspection of the given diagram:
⇒ ∠PVU = ∠PVS
⇒ ∠PVU = 58°
Question 7Opposites sides of a rectangle are parallel.
Therefore, GF is parallel to AB:
⇒ ∠CFG = ∠CBA = 32°
Interior angles of a triangle sum to 180°.
⇒ ∠FGC + ∠GCF + ∠CFG = 180°
⇒ y + 74° + 32° = 180°
⇒ y + 106° = 180°
⇒ y + 106° - 106° = 180° - 106°
⇒ y = 74°
Can someone please help me this is geometry
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\boxed {M_{AB}=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2} ) }[/tex]
1) E(-5,-3) F(3,7) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-5+3}{2} ),\frac{-3+7}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{4}{2} )\\\\ M(x,y)=(-1,2)\\\\Thus, \ M(-1,2)[/tex]
2) L(-8,11) N(-3,12) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-8+(-3)}{2} ,\frac{11+12}{2} )\\\\M(x,y)=(\frac{-11}{2},\frac{23}{2})\\\\ M(x,y)= (-5.5,11.5)\\\\Thus, M(-5.5,11.5)[/tex]
3) A(-4,6) B(2,4) M(x,y)=?
[tex]\displaystyle\\M(x,y)=(\frac{-4+2}{2},\frac{6+4}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{10}{2})\\\\ M(x,y)=(-1,5)\\\\ Thus,\ M(-1,5)[/tex]
A linear function, f(x)+2x+3, is transformed to g)x)=2x-5 . What transformation occurred?
Step-by-step explanation:
The function f was shifted 8 units to the right to obtain g.
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
By using geometry we answer this question.
Geometry is nothing but the branch of mathematics which deals with measurements of shapes.
Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".
First, we see the scale from a playground to this drawing.
[tex]\frac{a}{l}= \frac{1}{5}[/tex]
[tex]l=5a[/tex]
Now we see the scale from the same playground to another drawing.
[tex]\frac{b}{l} =\frac{1}{8}[/tex]
[tex]b=\frac{l}{8}\\[/tex]
Here, l=5a then
[tex]b=\frac{5a}{8}[/tex]
Therefore, the side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
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Choose the symbol that makes the statement true
A. >
B. <
C. =
PLEASE HELP THANK YOU :)))
Answer:
C. =
Step-by-step explanation:
This is because 18% is 18/100. You could find the answer one of two ways. Divide by two or multiply by 2.
slove please and thanks
Express the inequality using interval notation.
161 6.)
Interval Notation:
-7 < x < -4
8
The inequality using interval notation are (-7, -4).
What is defined as the interval notation?An interval is represented on a number line using interval notation.
In those other sayings, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two specific data set.For instance, the set of digits x satisfying 0 ≤ x ≤ 8 is an interval containing 0, 8, as well as all numbers between 0 and 8.Open intervals: The endpoints of a inequality are not included in this type of interval. This is written in open interval notation: (-3, 1).closed intervals: The endpoints of a inequality are included in this type of interval. This is written in closed interval notation as [-3,1].For the given expression;
-7 < x < -4
As, x > -7; x is not equal to -7.
x < -4; here also x is not equal to -4.
So, the is a condition of open interval where both vales are not taken.
Thus, the intervals are written as; (-7, -4).
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On a spring day the temperature outside is 68 degrees F. What is this in Celsius? (Write your answer
as a whole number.)
3 kg of diced lamb costs £45 Elvis buys 2 kg of diced lamb. Work out how much Elvis pays.
Answer:
£30
Step-by-step explanation:
Elvis is paying for 2/3 of 3 kg, so the cost is:
[tex]\frac{2}{3}(45)=30[/tex]
Choose a real number uniformly at random in the interval [2,6] and call it X. Find the CDF of X, FX(x). Find EX.
Every point in the interval [2, 6] has an equal probability of occurring, 1/(6 - 2) = 1/4. So the PDF of X is
[tex]f_X(x) = \begin{cases} \frac14 & \text{if } 2 \le x \le 6 \\ 0 & \text{otherwise} \end{cases}[/tex]
Compute the CDF by integrating the PDF.
• If [tex]x<2[/tex], we have
[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^x 0 \, dt = 0[/tex]
• If [tex]2\le x< 6[/tex], we have
[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^x \frac{dt}4 \\\\ ~~~~~~~~~~~~~~~~~ = 0 + \frac14 \int_2^x \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \frac{x-2}4[/tex]
• If [tex]x\ge6[/tex], we have
[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^6 f_X(t) \, dt + \int_6^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^6 \frac{dt}4 + \int_6^x 0 \, dt \\\\ ~~~~~~~~~~~~~~~~~ = 0 + 1 + 0 \\\\ ~~~~~~~~~~~~~~~~~ = 1[/tex]
Putting the pieces together, we find the CDF to be
[tex]\boxed{F_X(x) = \begin{cases} 0 & \text{if } x < 2 \\\\ \dfrac{x-2}4 & \text{if } 2\le x < 6 \\\\ 1 & \text{if } x\ge6 \end{cases}}[/tex]
Compute the expectation of X.
[tex]\Bbb E[X] = \displaystyle \int_{-\infty}^\infty x\,f_X(x)\,dx \\\\ ~~~~~~~ = \int_{-\infty}^2 0 \, dx + \int_2^6 \frac x4 \, dx + \int_6^\infty 0 \, dx \\\\ ~~~~~~~ = 0 + \frac{6^2 - 2^2}8 + 0 \\\\ ~~~~~~~ = \boxed{4}[/tex]
A car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
Answer:
The mean will move to the left as more affordable vehicles are introduced.
Step-by-step explanation:
It is given that a car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
We need to find how will the distribution be affected if he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years.
Now, let us understand what is meant by mean;
What is the Mean ?
The mean of a set of data is its average value.
Further, It is given that the car salesman sells cars with prices ranging from $5,000 to $45,000.
Additionally, the salesperson has noticed that a lot of students are searching for vehicles around $5,000.
If he chooses to sell vehicles as well and anticipates selling 200 of them over the following ten years,
The histogram will deviate from its mean if cards with values less than $5,000 are also included in the data set.
The mean will move to the left as more affordable vehicles are introduced.
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Given right triangle ABC, what is the value of tan(A)?
5/13
12/13
12/5
13/12
Answer: 13/12 times 12/4 is the answer
Even counting numbers less than 10
Answer:
2, 4 6, 8
Step-by-step explanation:
The counting numbers are the set of numbers: 1,2,3,4,... It follows that pattern forever. No, 1/2 or .0745.
Answer:
2 4 6 8 is the answer for your question
A truck can be rented from Company A for $120 a day plus $0.50 per mile. Company B charges $80 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
There are 52 candies in a packet, about how many packets would 22 packets contain? Estimate the answer by rounding off the numbers to the nearest ten.
After rounding, we can say that there are about 1,140 candles in the 22 packets.
About how many packets would 22 packets contain?First let's get the exact number, and then round it as we need to do.
We know that each packet contains 52 candles, and there are 22 packets, so the total number of candles is given by the product between these two values, which gives:
C = 52*22 = 1,144 candles.
Now we want to round it to the nearest ten, to do so, we need to look at the digit at the right of the tens unit (in this case the ones digit) and see, if it is 5 or more, we round up, if it is 4 or less, we round down.
We can see that it is a 4, so we round down here:
C = 1,140
There are about 1,140 candles in the 22 packets.
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Please help me with this problem please. I will give a Brainly and bunch of extra points. Please please help me. I will give a Brainly and a bunch of extra points.
Answer:
see attached
Step-by-step explanation:
You want the truth table for a logical implication that involves other logical expressions with up to three variables.
Truth tableA truth table is conveniently produced using the logical operations available on a spreadsheet. The AND (∧), OR (∨), and NOT (¬) functions are built-in to the spreadsheet. The implication (→) function must use the equivalent:
p → q ≡ ¬p∨q
If p, q, and r are in columns A, B, C, respectively, then the formulas in columns D through G are ...
D: =OR(B2, NOT(C2))E: =AND(A2, D2)F: =AND(NOT(A2), B2)G: =OR(NOT(E2), F2)The formulas are filled to the following rows.
The values of p, q, and r are entered manually. The spreadsheet computes the truth values for the formulas.
The table shows the balance in dollars of a bank account each month for three months. What is the average balance of the account
The average balance of the account is $1126.37.
An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
Consider the table that shows the balance (in dollars) of a bank account for three months.
Months Account Balance
1 $1285.12
2 $961.36
3 $1132.63
As we are aware, the following formula for the mean or average of any set of data:
Mean, [tex]\overline X=\frac{\sum X}{n}[/tex]
where, ∑X is the sum of all the observations in the data and n is the number of observations in the data
Therefore, the average balance in the account is:
[tex]Average{~}balance=\frac{1285.12+961.36+1132.63}{3}[/tex]
[tex]Average{~}balance=\frac{3379.11}{3}[/tex]
Average balance = $ 1126.37
So, the account's average balance is $1126.37.
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The complete question is mentioned below:
The table shows the balance (in dollars) of a bank account each month for three months. What is the average balance of the account?
Table:
Month 1, account balance: $1285.12
Month 2, account balance: $961.36
Month 3, account balance: $1132.63
The average balance of the account is $1126.37
What is an average?Average: An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
Consider the table that shows the balance (in dollars) of a bank account for three months.
Months Account Balance
1 $1285.12
2 $961.36
3 $1132.63
As we are aware, the following formula for the mean or average of any
set of data,
Mean,
where, ∑X is the sum of all the observations in the data and n is the number of observations in the data
Therefore, the average balance in the account is,
Average balance of the account = $ 1126.37
So, the account's average balance is $1126.37
The complete question is mentioned below,
The table shows the balance (in dollars) of a bank account each month for three months.
Table:
Month 1, account balance: $1285.12
Month 2, account balance: $961.36
Month 3, account balance: $1132.63
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please help!! thank you
Step-by-step explanation:
when a line intersects with 2 (or more) parallel lines, the angles at the intersection points are the same for each parallel line.
therefore,
5 + 10x = 85
10x = 80
x = 8
so, B is the right answer option.
what is the equation for the line with slope (rate of change) 2/3 and y-intercept 9
Answer:
y = 2/3x + 9
Step-by-step explanation:
The equation of a line is defined as y = mx + b
with m being the slope, and b being he intercept.
So to figure out the equation for the line with a slope of 2/3 and an intercept of 9, we can just plug those values into our line equation!
So take y = (slope)*x + *(intercept)
and plug your values in and you get...
y = 2/3 * x + 9
Answer: the answers for the quiz are
1. What is the slope (rate of change) of the line in the graph show below? Answer is A. -2
2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). Answer is D. 4/3
3. constant of variation of -4y=8x answer is B. -2
4 the value of y when x=10 answer is B. 30
5. the equation for the line with slope 2/3 and y-intercept 9 answer is C. y=2/3x+9
6 is the equation in slope intercept form for the line that passes through the points (1, -3) and (3, 1) answer is D. y=2x-5
Step-by-step explanation:
Question
Find the rate if a principal of $5,875 earned $1,645 interest in 4 years. Round to the nearest whole percent.
The yearly interest rate percentage is 7%
The rate of interest can be found dividing the interest and the product of the principal and time period which can be written as
R = I / PT
where R is the Rate of interest
I is the Interest
P is the Principal amount
T is the time period.
Given values are
P = $5,875
I = $1,675
T = 4 years
Then,
R = I/PT
= 1,645/(5,875 x 4)
= 1645 / 23500
= 0.07
The Yearly interest rate percentage is
=0.07 x 100
= 7%
Therefore, the yearly rate percentage is 7%
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F(x)=x-5 and g(x)=x2 - 1 find
The value of the given functions are:
(i) f + g = x² + x - 6
(ii) f - g = -x² + x - 4
(iii) f . g = x³ - 5x² - x + 5
(iv) f/g = ( x - 5)/(x +1)(x - 1)
(v) g(f(x)) = x² - 10x + 24
The two functions are given that
f(x) = x - 5
g(x) = x² - 1
We have to find
(i) f + g
f(x) + g(x) = ( x-5) + (x² - 1)
= x² + x -5 -1
= x² + x -6
(ii) f - g
f(x) - g(x) = (x-5)- (x² - 1)
= -x² + x -5 +1
= -x² + x -4
(iii) f . g
f(x) . g(x) = (x-5)(x²-1)
=x(x² - 1) -5(x² - 1)
= x³ - x - 5x² + 5
= x³ - 5x² - x + 5
(iv) f/g
f(x) / g(x) = (x-5) / ( x² - 1)
= (x - 5) / (x+1)(x-1)
(v) g(f(x)) = - 1 + ( -5 + x )²
= -1 + 25 + x² - 10x
= x² - 10x + 24
Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.
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The complete question is:
F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).
7) Shelby is making cookies. She uses cups of
sugar for every 2 cups of flour. How many cups of
sugar does she need when she uses 3 cups of flour?
Show your work.
If a cat went 7/16 actoss the yard how much further does it have to go to reach the gate
Using proportions, it is found that the cat has to go 9/16 further to reach the gate.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
An entire distance is represented by the proportion of 1 = 100%. The cat has gone 7/16 of the distance, hence the fraction corresponding to the remaining distance that he has to go is given by:
1 - 7/16 = 16/16 - 7/16 = 9/16.
Hence the cat has to go 9/16 further to reach the gate.
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Round down to the nearst thousand if it is 30,000
Answer:
30 000
Step-by-step explanation:
30 000 if underlined digit is >= 5 round thousands up 1 ...o/w leave as is
30 000
I need help on this question and how to solve and get the answer thank you if anyone helps me
Answer:
its 4
Step-by-step explanation:
6.139 rounded to the nearest hundredth?
Answer:
Step-by-step explanation: 6.140
Find the area of the circle.
Use 3.14 for π. Do not round your answer.
Hint: A = πr²
6 inches
Area = [?] inches²
Enter the number that
belongs in the green box.
Answer:
28.26 inches^2
Step-by-step explanation:
The area of a circle is given by the formula [tex]A = \pi r^2[/tex].
We know that the diameter of the circle is 6 inches, therefore, its radius 3 inches (the radius is exactly one half of the circle's diameter).
Substituting into the formula
[tex]A = \pi r^2 \\ \\\to A = \pi \times 3^2 \\ \\\to A = \pi \times 9 = 28.26[/tex]
hello help me with question b
[tex] \bf\longrightarrow \large\frac{ \frac{ \frac{a( {r}^{4} - 1)}{ \cancel{r - 1}} }{a( {r}^{2} - 1) } }{ \cancel{r - 1}} = 10 \\ [/tex]
[tex]\bf\longrightarrow {r}^{4} - 1 = {10r}^{2} - 10[/tex]
[tex]\bf\longrightarrow {r}^{4} - {10r}^{2} + 9 = 0[/tex]
Put a = r²[tex]\bf\longrightarrow \: {a}^{2} - 10 {a}^{2} + 9 = 0[/tex]
[tex]\bf\longrightarrow \: a = \frac{10± \sqrt{100 - 36} }{2} = \frac{10±8}{2} [/tex]
a = 9 or a = 1r = 3 or r = 1 but r ≠ 1
[tex]\therefore[/tex] r = 3
[tex]\bf\longrightarrow \: a_3 = 54 \\ \bf\longrightarrow \: a {r}^{2} = 54 \\ \bf\longrightarrow \: a = \frac{54}{9} = 6[/tex]
Which of the functions below could have created this graph?
+
OA. F(x)=x2
OB. F(x)=-¹-4
O C. F(x)=x²+2x-2
OD. F(x)=3x³ +2x²
Answer:
only D is negative on the leading term
Step-by-step explanation:
even roots bounce at (0,0)
negative leading coefficient: initial graph descending to right, curve up
4 local extremes means remaining 5 degree of the function