Answer:
The first option (5.7km)
Step-by-step explanation:
Since we have a right angle triangle and we know two of its sides we can easily find out the thirds side (the value of d) by using the Pathagoras Theorem. In our case 7 and d are our legs and the hypotenuse is equal to 9, so...
(Based on the Pathagoras Theorem)
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]9^{2} = 7^{2} + d^{2}[/tex]
[tex]d^{2} = 9^{2} - 7^{2} \\d^{2} = 81 - 49\\d^{2} = 32\\d = \sqrt{32}\\[/tex]
d ≈ 5.7km
There for aproximate distance across the lake is equal to 5.7km
Answer:
A
Step-by-step explanation:
The tomato plants in Ms. Lang's
garden grow 2 inches every 3 days. How much will they grow in 15 days?
Answer:
10 inches
Step-by-step explanation:
15 days/3 days =5
5 x 2 =10
Which of the following are solutions to the quadratic equation? Check all that apply. x² + 10x + 25 = 7
A. 5
B. -5
C. √7-5
D. -√7-5
E. √7 +5
F. √7
Answer: C, D
Step-by-step explanation:
[tex]x^2 +10x+18=0\\\\x=\frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2}\\\\x=\frac{-10 \pm \sqrt{28}}{2}\\\\x=-5 \pm \sqrt{7}[/tex]
Emily purchased a bond valued at $20,000 for highway construction for $10,460. If the bond pays 7.2%
annual interest compounded monthly, how long must she hold it until it reaches its full face value?
...
Answer:
26.556192
Step-by-step explanation:
7.2×10460÷100
20000÷(7.2×10460÷100)
a brave knight traveled on his horse from one kingdom to another in 2 days the first day he rode at a speed of 10 mph and the second day he rode at a speed of 8 mph if he traveled exactly the same amount of time each day and went 180 miles find how many hors it took the knight to travel from one kingdom to another
Using the relation between velocity, distance and time, it is found that it took the knight 20 hours to traveled from one kingdom to another.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
v = d/t
On the first day, he traveled at a speed of 10 mph, a distance of d, hence:
10 = d/t
t = d/10
On the second day, he traveled at a speed of 8 mph, a distance of 180 - d, hence:
8 = (180 - d)/t
t = (180 - d)/8
Equaling both equations for t, we find the distance on the first day, hence:
d/10 = (180 - d)/8
8d = 1800 - 10d
18d = 1800
d = 100 miles.
The time on the first day was:
t = 0.1d = 0.1 x 100 = 10 hours.
On the second day he traveled the same amount of time, hence, in total, he traveled 20 hours.
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In ΔOPQ, m∠O = 107° and m∠P = 28°. Which statement about the sides of ΔOPQ must be true?
QO > OP > PQ.
QO > PQ > OP.
PQ > OP > QO.
OP > QO > PQ.
PQ > QO > OP.
OP > PQ > QO.
Answer:
QO < OP < QP
Step-by-step explanation:
The third angle, angle Q, must measure 45° since angles in a triangle add to 180°.
So, OQ < OP < QP.
Answer:
PQ>OP>QO
Greater than symbol goes from largest to smallest
Write the equation of the line.
(Check image)
Options:
a. y = -2/3x + 4
b. y = 2/3x + 4
c. y = 3/2x + 4
d. y = -3/2x + 4
please show step by step
what does 21/10 divided by 2 4/5 represent in this situation
In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between ________and_________ miles.
The level of confidence for this estimate is ________%
Using the interpretation of the confidence interval, it is found that:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
Considering the mean and the standard error, the bounds of the interval are:
a = 9.72 - 0.22 = 9.50 miles.b = 9.72 + 0.22 = 9.94 miles.Hence:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.More can be learned about confidence intervals at https://brainly.com/question/25890103
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The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation () of 0.5 hours.
What is the probability that a randomly selected cyclist will take at least 2.45 hours to complete the race?
Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.5, \sigma = 0.5[/tex]
The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
1 - 0.4602 = 0.5398.
0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
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At the movie theater, child admission is $5.50 and adult admission is $9.00. on Thursday, 148 tickets were sold for a total sales of $992.50. how many adult tickets were sold that day
Answer:
51 Adult tickets were sold that day.
Step-by-step explanation:
Let c = child and a = adult
c + a = 148 5.50c + 9.00a = 992.50
Change the first equation so that it is either in the form c = or a =and then plug that number into the second equation.
I am going to change the first equation to c = by subtracting a from both sides
c = 148 - a
Now I am going to plug 148 -a for c in the second equation.
5.5(148 - a) + 9a = 992.5 Next distribute the 5.5
814 - 5.5a + 9 a = 992.5 Add the a terms together
814 + 3.5a = 992.5 Subtract 814 from both sides
3.5a = 178.5 Divide both sides by 3.5
a = 51
Which list below shows the fractions in order from greatest to least?
A. 3/6, 4/9, 3/7, 3/10
B. 3/10, 3/7, 4/9, 3/6
C. 3/10, 4/9, 3/7, 3/6
D. 3/6, 4/7, 4/9, 3/10
Answer:
Step-by-step explanation:
Assume that the function f is a one
-to-one function.
(a) If f (7)
= 5, find f-1 (5)
Your answer is
(b) 18 f-1 (-3) = -2, find f(-2).I
Your answer is
For the given inverse functions we have:
a) f⁻¹(5) = 7
b) f(-2) = -3
How to work with inverse functions?
Remember that if f(x) and g(x) are inverse functions, then:
[tex]f(x) = y\\then\\g(y) = x[/tex]
a) Now we know that:
f(7) = 5
Then if f⁻¹(x) is the inverse, we have:
f⁻¹(5) = 7
b) Now we know that:
f⁻¹(-3) = -2
Again, using the rule for inverse functions, we will have:
f(-2) = -3
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Now suppose b stays the same. Then, a must be its previous value to satisfy the new inequality.
When the coordinate satisfies the original inequality, if a stays the same, b must be greater than its previous value to satisfy the new inequality.
How to illustrate the information?It should be noted that inequality provides an interval to the solution.
This is illustrated graphically. Let's illustrate this with an example, suppose a =1, b = 3
a - b < 0.
1 - 3 < 0
-2 < 0
If a stays the same value, b will be greater than 1.
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For the inequality y−x>−x2−1, where is the graph shaded and is the curve solid or dotted?
The curve will be dotted and upper portion of the graph will be shaded.
Inequality expressionInequality are expressions not separated by an equal sign Given the following inequality
y−x>−x2−1
Equate to zero
y > x^2 + x -1
Since the inequality sign in the given expression is a less than sign, hence the curve will be dotted.
Also, since the inequality sign is a "greater than", hence upper portion of the graph will be shaded.
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Your students have been working on algebra equations involving inequalities. The rule for learning the > sign is:
The rule for learning the > sign is demonstrating eating with the right hand.
InequalityThe inequality signs are;
Greater than >Let was than <Equal to =Greater than or equal to ≥Less than or equal to ≤The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.
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Blossom company , a machinery dealer leased manufacturer equipment to Mays corporation on January 1, 2017. The lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year . The first payment is received on January 1, 2017 . Blossom had purchased the machine during 2016 for $75000 collectibility of lease payments is reasonable predictable, and no important uncertainties surround the amount of cost yet to be incurred by blossom se the annual rentel to ensure a 8% rate of return . The machine has an economic life of 8 years with no resiidaul value and reverts to blossom at the termination of the lease.A. Compute the amount of the lease receivable
The amount of the lease receivable will be $146999.
What are lease receivable?It should be noted that lease receivables means all the payments under the operative documents in respect of:
(i) the Purchaser Basic Rent,
(ii) the Maximum recourse amount,
(iii) the Purchaser Balance and
(iv) any purchase by the Lessee of the Properly up to the amount of the Capital then outstanding.
In this case, the lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year and the first payment is received on January 1, 2017.
The lease receivable will be:
= PVAD8%,7 × Lease payment
= 5.62288 × 26143
= $146999
In conclusion, the lease receivable is $146999.
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If
xn = (n−1)cos(n2 +n+1) 2n−1
EXERCISES
then xn has a convergence subsequence.
The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
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14) Write the scientific notation.
12 million
Answer:
1.2 × 107 this is the sciencetific notation for 12 million
..
Our peak time this week will be 8:00 AM to 12:00 PM, which requires 32% more agents than the afternoon requirements of 473 agents.” Representative: “So, you will need to have __________ in the morning shift.
The number of agents required in the morning shift 8:00 AM to 12:00 PM is 624.36 agents
PercentagePeak time = 8:00 AM to 12:00 PMAgent required in the afternoon = 473 agentsAgent required in the morning = (32% of 473) + 473
= (32/100 × 473) + 473
= (0.32 × 473) + 473
= 151.36 + 473
= 624.36 agents
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What is the following product 3 root 24 • 3 root 45
Answer:
54sqrt(30)
Step-by-step explanation:
3sqrt(24) can be simplified to 6sqrt(6) as 24 can be written as 4 * 6 and 4 is a perfect square
3sqrt(45) can also be written as 9sqrt(5) as 45 can be written as 5 * 9 and 6 is a perfect square
you can multiply 6sqrt(6) * 9sqrt(5) as though the square roots were variables
so
54sqrt(30)
this is your final answer
the rounded answer is 295.770181
This is so confusing please help asap !
Which equation is the inverse of y = 9x² - 4?
0y= ± √x+4
9
O y = ±₁
+4
9
Oy= 2√x+4
3
INX
+√√√x 2
Oy= 3 3
[tex]y=9x^2-4\\9x^2=y+4\\x^2=\dfrac{y+4}{9}\\x=\pm\sqrt{\dfrac{y+4}{9}}=\pm\dfrac{\sqrt{y+4}}{3}\\\\\text{inverse: }y=\pm\dfrac{\sqrt{x+4}}{3}[/tex]
The inverse of the function y = 9x² - 4 is y = ±√((x + 4)/9). The correct option is A.
What is the inverse of the function?To find the inverse of a function, we need to swap the positions of the input variable (usually x) and the output variable (usually y), and then solve for y. The resulting equation will be the inverse function.
To find the inverse of the function y = 9x² - 4, we need to swap the positions of x and y and then solve for y.
So, starting with y = 9x² - 4:
y = 9x² - 4
x = 9y² - 4 (swapping x and y)
x + 4 = 9y² (adding 4 to both sides)
y² = (x + 4)/9 (dividing both sides by 9)
y = ±√((x + 4)/9) (taking the square root of both sides, plus or minus)
So the inverse of the function y = 9x² - 4 is:
y = ±√((x + 4)/9)
Note that since we have a plus or minus sign in the expression, this means that the inverse is actually two functions: one that gives the positive square root, and one that gives the negative square root.
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A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?
Answer:
0.4
Step-by-step explanation:
4+3+2+1 =10
5m÷10 =0.5
(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)
2 : 1.5 : 1 : 0.5
longest piece= 2 (2m)
4+1= 5
2÷5= 0.4
(0.4×4=1.6, 0.4×1=0.4)
1.6 : 0.4
so the shortest piece is 0.4!
A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road sign is about 38.2 inches tall The road sign is about 38.2 inches tall The road sign is about 23.5 inches tall The road sign is about 23.5 inches tall The road sign is about 41.6 inches tall The road sign is about 41.6 inches tall The road sign is about 43.7 inches tall
The height of the equilateral triangle is 41. 6 inches. Option C
How to determine the height
The formula for finding the height of an equilateral triangle is given as;
h = (a√3)/2
we have a = 48 inches
Let's substitute the value
Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]
Height = [tex]\frac{48 * 1. 732}{2}[/tex]
Height = [tex]\frac{83. 14}{2}[/tex]
Height = [tex]41. 6[/tex] Inches
Thus, the height of the equilateral triangle is 41. 6 inches. Option C
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The width of a rectangular house is 22 feet. What is the perimeter of this house if it has the same area as a house that is 33 ft wide and 50 ft long
1) 184 feet
2) 200 feet
3) 194 feet
4) 206 feet
Answer:
3) 194 feet
Step-by-step explanation:
The other house:
"a house that is 33 ft wide and 50 ft long"
area = LW = (33 ft)(50 ft) = 1650 ft²
This house:
LW = A
L × 22 ft = 1650 ft²
L = 75 ft
P = 2(L + W)
P = 2(75 ft + 22 ft)
P = 194 ft
Answer: 3) 194 feet
Answer:
3) P = 194 ft.
Step-by-step explanation:
[tex]A=wl[/tex]
[tex](30)(50)=22l[/tex]
[tex]1650=22l[/tex]
[tex]l=1650/22=75[/tex]
the dimensions of the house are: (22 × 75)
Perimeter:
[tex]p=2(22)+2(75)=44+150=194[/tex]
Hope this helps
HELP ASAPPPP PLEASE!!!!
Answer:
(c) 45°
Step-by-step explanation:
A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.
ApplicationHere, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.
The measure of angle ABC is 45°.
C. 45°
Step-by-step explanation:When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.
Clockwise
This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.
Acute vs Obtuse
There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.
Which of the following best describes both the domain and range of the distance function d=55t
Answer: All real numbers
Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
If the function is:
What is f(-4)?
Answer:
D. -11
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]
[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]
[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]
f(-4) means to substitute x = -4 into the function.
As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:
[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]
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Answer is D. -11
Answer:
Solution Given:
f(-4) depends on the condition x≤-4,
so
f(-4)=2*-4-3=-8-3=-11
Which of the following best represents the linear regression equation for the
×-values and log(y)-values of the data shown below?
By using Microsoft excel to plot the data on a scatter plot, the linear regression equation can best be represented by: A. y = 12.11.1.36^x
What is a regression line?A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that linear regression equation for the x-values and log(y)-values is given by:
y = 12.11.0.30^x
Thus, it can best be represented by: y = 12.11.1.36^x
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Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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