Given Data:
The upstream speed is, 25 miles/hr.
The downstream speed is, 35 miles/hr.
The total time is, 12 hr.
Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,
[tex]t=\frac{d}{25}[/tex]He can travel 35 miles/ hr in upstream, so the time taken will be,
[tex]t^{\prime}=\frac{d}{35}[/tex]Total time is, 12 hr. So we have,
[tex]\begin{gathered} 12=\frac{d}{25}+\frac{d}{35} \\ 12=\frac{d}{5\times5}+\frac{d}{7\times5} \\ 12=\frac{1}{5}(\frac{d}{7}+\frac{d}{5}) \\ 12\times5=\frac{d}{7}+\frac{d}{5} \\ 60\times35=5d+7d \\ 2100=12d \\ d=\frac{2100}{12}=175 \end{gathered}[/tex]Therefore the total distance is, 350 mile
Determine the probability of flipping a heads, rolling a number less than 5 on a number cube and picking a heart from a standard deck of cards.
1/12
16/60 or 4/15
13/156
112
The probability of flipping a heads is 1/2, probability of rolling a number less than 5 is 2/3, and probability of picking a heart from a standard deck of cards is 1/4.
What is probability?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is always a number b/w 0 and 1, with 0 approximately says impossibility and 1 says surity.
We can find probability using the formula:
P = required out comes/ total outcomes
In first case the required out come is only one which is heads and total outcomes include both heads and tails,
Therefore, required outcome = 1
total outcome = 2
Probability = 1/2
In second case the required out come are number less than five which are 1, 2, 3, 4 and a number cube have numbers till 6.
Therefore, required outcome = 4
total outcome = 6
Probability = 4/6 = 2/3
In third case the required out come hearts card and there are 13 hearts card in a card deck and total outcomes include all types of cards which are 52,
Therefore, required outcome = 13
total outcome = 52
Probability = 13/52 = 1/4
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thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following function:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, in order to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(More to know: when a number is multiplied with 0 then the result is always 0 even the number being multiplied with zero is in lakhs.)
f(0) = 0+0-0+12
f(0) = 12
Now, in order to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, in order to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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An empty rectangular tank measures 60 cm by 50 cm by 56 cm. It is being filled with water flowing from a tap at rate of 8 liters per minute. (a) Find the capacity of the tank (b) How long will it take to fill up (1 liter = 1000 cm
(a) The capacity of the tank is its volume, which we can calculate by multipling its sides:
[tex]V=abc=60\cdot50\cdot56=168000[/tex]This is, 168000 cm³. It is equivalent to 168 L.
(b) If the tank is being filled at a rate of 8 liters per minute, we can find the time to fill ir by dividing its capacity by the rate:
[tex]t=\frac{168}{8}=21[/tex]That is, it will take 21 minutos to fill it up.
Determine whether the arc is a minor arc, a major arc, or a semicircle of R. Questions 25 nd 27
We can find the missing angles using the drawing below.
Then,
[tex]\begin{gathered} 360=60+60+55+x+y \\ \text{and} \\ 55+y=x \\ \Rightarrow240=2(55+y) \\ \Rightarrow120=55+y \\ \Rightarrow y=65 \\ \Rightarrow x=120 \end{gathered}[/tex]Therefore
25)
Arc JML covers an angle equal to 65+55+60=180; thus, ArcJML is a semicircle of R.
27)
Which phrase best describes the translation from the graph y = 2(x-15)² + 3 to the graph of y = 2(x-11)² + 3?O4 units to the left4 units to the rightO 8 units to the leftO 8 units to the rightMark this and returnSave and ExitNextSubmit
Given:
it is given that a graph of the function y = 2(x-15)^2 + 3 is translated to the graph of the function y =2(x - 11)^2 + 3
Find:
we have to choose the correct option for the given translation.
Explanation:
we will draw the graphs of both the functions as following
The graph of the function y = 2(x - 15)^2 + 3 is represented by red colour and the graph of the translated function y = 2(x - 11)^2 + 3 is represented by blue colour in the above graph.
From, the graphs of both functions, it is concluded that the graph of the translated function is shifted 4 units to the left.
Transform AABC by the following transformations:• Reflect across the line y = -X• Translate 1 unit to the right and 2 units down.87BА )5421-B-7-6-5-4-301245678- 1-2.-3-5-6-7-8Identify the final coordinates of each vertex after both transformations:A"B"(C"
SOLUTION
A reflection on the line y = -x is gotten as
[tex]y=-x\colon(x,y)\rightarrow(-y,-x)[/tex]So, the coordinates of points A, B and C are
A(3, 6)
B(-2, 6)
C(3, -3)
Traslating this becomes
[tex]\begin{gathered} A\mleft(3,6\mright)\rightarrow A^{\prime}(-6,-3) \\ B(-2,6)\rightarrow B^{\prime}(-6,2) \\ C(3,-3)\rightarrow C^{\prime}(3,-3 \end{gathered}[/tex]Now translate 1 unit to the right and 2 units down becomes
[tex]\begin{gathered} A^{\prime}(-6,-3)\rightarrow A^{\doubleprime}(-5,-5) \\ B^{\prime}(-6,2)\rightarrow B^{\doubleprime}(-5,0) \\ C^{\prime}(3,-3\rightarrow C^{\doubleprime}(4,-5) \end{gathered}[/tex]So, I will attach an image now to show you the final translation.
I need help finding the area of the sector GPH?I also have to type a exact answer in terms of pi
Let us first change the 80° to radians.
[tex]\text{rad}=80\cdot\frac{\pi}{180}=\frac{4\pi}{9}[/tex]so we get that the area is
[tex]\frac{2}{9}\pi\cdot12^2=144\cdot\frac{2}{9}\pi=32\pi[/tex]so the area is 32pi square yards
(c) Given that q= 8d^2, find the other two real roots.
Polynomials
Given the equation:
[tex]x^5-3x^4+mx^3+nx^2+px+q=0[/tex]Where all the coefficients are real numbers, and it has 3 real roots of the form:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]It has two imaginary roots of the form: di and -di. Recall both roots must be conjugated.
a) Knowing the sum of the roots must be equal to the inverse negative of the coefficient of the fourth-degree term:
[tex]\begin{gathered} \log _2a+\log _2b+\log _2c+di-di=3 \\ \text{Simplifying:} \\ \log _2a+\log _2b+\log _2c=3 \\ \text{Apply log property:} \\ \log _2(abc)=3 \\ abc=2^3 \\ abc=8 \end{gathered}[/tex]b) It's additionally given the values of a, b, and c are consecutive terms of a geometric sequence. Assume that sequence has first term a1 and common ratio r, thus:
[tex]a=a_1,b=a_1\cdot r,c=a_1\cdot r^2[/tex]Using the relationship found in a):
[tex]\begin{gathered} a_1\cdot a_1\cdot r\cdot a_1\cdot r^2=8 \\ \text{Simplifying:} \\ (a_1\cdot r)^3=8 \\ a_1\cdot r=2 \end{gathered}[/tex]As said above, the real roots are:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]Since b = a1*r, then b = 2, thus:
[tex]x_2=\log _22=1[/tex]One of the real roots has been found to be 1. We still don't know the others.
c) We know the product of the roots of a polynomial equals the inverse negative of the independent term, thus:
[tex]\log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-q[/tex]Since q = 8 d^2:
[tex]\begin{gathered} \log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-8d^2 \\ \text{Operate:} \\ 2\log _2a_1\cdot\log _2(a_1\cdot r^2)\cdot(-d^2i^2)=-8d^2 \\ \log _2a_1\cdot\log _2(a_1\cdot r^2)=-8 \end{gathered}[/tex]From the relationships obtained in a) and b):
[tex]a_1=\frac{2}{r}[/tex]Substituting:
[tex]\begin{gathered} \log _2(\frac{2}{r})\cdot\log _2(2r)=-8 \\ By\text{ property of logs:} \\ (\log _22-\log _2r)\cdot(\log _22+\log _2r)=-8 \end{gathered}[/tex]Simplifying:
[tex]\begin{gathered} (1-\log _2r)\cdot(1+\log _2r)=-8 \\ (1-\log ^2_2r)=-8 \\ \text{Solving:} \\ \log ^2_2r=9 \end{gathered}[/tex]We'll take the positive root only:
[tex]\begin{gathered} \log _2r=3 \\ r=8 \end{gathered}[/tex]Thus:
[tex]a_1=\frac{2}{8}=\frac{1}{4}[/tex]The other roots are:
[tex]\begin{gathered} x_1=\log _2\frac{1}{4}=-2 \\ x_3=\log _216=4 \end{gathered}[/tex]Real roots: -2, 1, 4
What is the surfacearea of the cone?2A 225π in²B 375m in²C 600T in²D 1000 in 225 in.15 in.
We are given a cone whose radius is 15 inches and slant height is 25 inches. We need to solve for its surface area.
To find the surface area of a cone, we use the following formula:
[tex]SA=\pi rl+\pi r^2[/tex]where r = radius and l = slant height.
Let's substitute the given.
[tex]\begin{gathered} SA=\pi(15)(25)+\pi(15^2) \\ SA=375\pi+225\pi \\ SA=600\pi \end{gathered}[/tex]The answer is 600 square inches.
Select all of the expressions approval to c⁶/d⁶:
answers:
(cd-¹)⁶
c¹²d¹⁸/c²d³
c⁸d⁹/c²d³
c⁶d-⁶
c-⁶d⁶
(c‐¹d)-⁶
Answer:
is = c⁸d⁹/c²d³
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use Pythagoras rule to find the slant height of a cone a height of 8 and base radius of 6cm
The Pythagoras rule states that the square hypotenuse is equal to the sum of the squares of the other two sides
In this case, we are given both sides' measures and are asked about the hypotenuse. We leave the hypotenuse on the left side alone by applying the square root on both sides
L = √64+36
L= √100
L = 10
Junior's brother is 1 1/2 meters tall. Junior is 1 2/5 of his brother's height. How tall is Junior? meters
To determine Junior's height you have to multiply Juniors height by multiplying 3/2 by 7/5his brother's height by 1 2/5.
To divide both fractions, first, you have to express the mixed numbers as improper fractions.
Brother's height: 1 1/2
-Divide the whole number by 1 to express it as a fraction and add 1/2
[tex]1\frac{1}{2}=\frac{1}{1}\cdot\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using denominator 2, that way you will be able to add both fractions
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Junior's fraction 1 2/5
-Divide the whole number by 1 to express it as a fraction and add 2/5
[tex]1\frac{2}{5}=\frac{1}{1}+\frac{2}{5}[/tex]-Multiply the first fraction by 5 to express it using the same denominator as 2/5, that way you will be able to add both fractions:
[tex]\frac{1\cdot5}{1\cdot5}+\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{5+2}{5}=\frac{7}{5}[/tex]Now you can determine Junior's height by multiplying 3/2 by 7/5
[tex]\frac{3}{2}\cdot\frac{7}{5}=\frac{3\cdot7}{2\cdot5}=\frac{21}{10}[/tex]Junior's eight is 21/10 meters, you can express it as a mixed number:
[tex]\frac{21}{10}=2\frac{1}{10}[/tex]Check picture pls this is geometry work
Answer:
45
scalene
acute
Step-by-step explanation:
Answer: The triangle classified by the sides is 59 degrees. The triangle is classified by the angel is 1
Step-by-step explanation:
Allison earns $6,500 per month at her job as a principal the chart below shows the percentages of her budget. how much does Allison pay for her mortgage
Total earning for Allison is $6,500 per year
mortage = 24.6%
he spent 24.6% of his salary on mortgage
24.6 / 100 x 6500
0.246 x 6500
= $ 1599
He spent $1,599 on mortgage
solve by square roots: 16k^2-1=24
we have
[tex]16k^2-1=24[/tex]step 1
Adds 1 both sides
[tex]\begin{gathered} 16k^2-1+1=24+1 \\ 16k^2=25 \end{gathered}[/tex]step 2
Divide by 16 both sides
[tex]\begin{gathered} \frac{16}{16}k^2=\frac{25}{16} \\ \text{simplify} \\ k^2=\frac{25}{16} \end{gathered}[/tex]step 3
Applying square root both sides
[tex]k=\pm\frac{5}{4}[/tex]What is the domain of the function represented by the graph?
All real numbers (In interval form (-∞,∞) )
Given,
From the graph,
To find the domain of the function.
Now,
We know that a domain of a function is the set of the all the x-values for which the function is defined.
By looking at the graph of the function we see that it is a graph of a upward open parabola and the graph is extending to infinity on both the side of the x-axis this means that the function is defined all over the x-axis i.e. for all the real values.
Also, we know that the function will be a quadratic polynomial since the equation of a parabola is a quadratic equation and as we know polynomial is well defined for all the real value of x.
The domain of the function is:
Hence, All real numbers (In interval form (-∞,∞) )
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Answers asap please
x ≥ 1 or x ≥ 3 is inequality of equations .
What do you mean by inequality?
The allocation of opportunities and resources among the people who make up a society in an unequal and/or unfair manner is known as inequality. Different persons and contexts may interpret the word "inequality" differently.The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. It is an illustration of inequity. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.9 - 4x ≥ 5
4x ≥ 9 - 5
4x ≥ 4
x ≥ 1
4( - 1 + x) -6 ≥ 2
-4 + 4x - 6 ≥ 2
4x ≥ 2 + 8
4x ≥ 10
x ≥ 10/4
x ≥ 5/2
x ≥ 2.5
x ≥ 1 or x ≥ 3
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Find the probability of getting 4 aces when 5 cards are drawn from an ordinary deck of cards
First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:
(a standard deck card has 52 cards)
[tex]C\left(52,5\right)=\frac{52!}{5!\left(52-5\right)!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48\operatorname{\cdot}47!}{5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}47!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48}{120}=2,598,960[/tex]Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.
Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:
[tex]P=\frac{48}{2598960}=\frac{1}{54145}[/tex]The probability is 1/54145.
The ratio of boys to girls in a school is 5:4. if there are 500 girls , how many boys are there in the school?
Answer:
The number of boys in the school is;
[tex]625[/tex]Explanation:
Given that the ratio of boys to girls in a school is 5:4;
[tex]5\colon4[/tex]And there are 500 girls in the school.
The number of boys in the school will be;
[tex]\begin{gathered} \frac{B}{G}=\frac{5}{4} \\ G=500 \\ B=\frac{5\times G}{4}=\frac{5\times500}{4} \\ B=625 \end{gathered}[/tex]Therefore, the number of boys in the school is;
[tex]625[/tex]A pair of parallel lines is cut by a transversal, as shown (see figure):Which of the following best represents the relationship between angles p and q?p = 180 degrees − qq = 180 degrees − pp = 2qp = q
we know that
In this problem
that means
answer isp=qIf the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?
Answer:
C(2,-2), D(-1,-2)
Explanation:
The area of a rectangle is calculated using the formula:
[tex]A=L\times W[/tex]• From the graph, AB = 3 units.
,• Given that the area = 12 square units
[tex]\begin{gathered} 12=3\times L \\ L=\frac{12}{3}=4 \end{gathered}[/tex]This means that the distance from B to C and A to D must be 4 units each.
Count 4 units vertically downwards from A and B.
The coordinates of C and D are:
• C(2,-2)
,• D(-1,-2)
The first option is correct.
A)State the angle relationship B) Determine whether they are congruent or supplementary C) Find the value of the variable D) Find the measure of each angle
Answer:
a) Corresponding
b) Congruent, since they have the same measure.
c) p = 32
d) 90º
Step-by-step explanation:
Corresponding angles:
Two angles that are in matching corners when two lines are crossed by a line. They are congruent, that is, they have the same measure.
Item a:
Corresponding
Item b:
Congruent, since they have the same measure.
Item c:
They have the same measure, the angles. So
3p - 6 = 90
3p = 96
p = 96/3
p = 32
Item d:
The above is 90º, and the below is the same. So 90º
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. (Let b = 5.1.)
Given:-
An image with triangle.
To find:-
The value of B,a,c.
So the laws of sines are,
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]So now we substitute the known values. we get,
[tex]\frac{\sin16}{a}=\frac{\sin B}{5.1}=\frac{\sin125}{c}[/tex]Now we find the value of B,
Since the sum of angles of the triangle is 180. we get,
[tex]\begin{gathered} A+B+C=180 \\ 16+B+125=180 \\ B+141=180 \\ B=180-141 \\ B=39 \end{gathered}[/tex]So substituting the value we get,
[tex]\frac{\sin16}{a}=\frac{\sin 39}{5.1}=\frac{\sin125}{c}[/tex]Now we find the value of a. we get,
[tex]\begin{gathered} \frac{\sin16}{a}=\frac{\sin 39}{5.1} \\ \frac{0.2756}{a}=\frac{0.6293}{5.1} \\ a=\frac{0.2756\times5.1}{0.6293} \\ a=2.2335 \end{gathered}[/tex]Now we find c. we get,
[tex]\frac{0.2756}{2.2335}=\frac{\sin 125}{c}[/tex]So
use the number line to find the distance between -3 and -9
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
use the point slope formula and the given points to choose the correct linear equation in slope intercept form (0,7) and (4,2)
We have to write the equation of the line that passes through (0,7) and (4,2) in point-slope form.
We start by using the points to calculate the slope m:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-7}{4-0}=-\frac{5}{4}[/tex]Then, if we use point (0,7), we can write the equation in point-slope form as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-\frac{5}{4}(x-0) \\ y=-\frac{5}{4}+7 \end{gathered}[/tex]Answer: the equation is y = -(5/4)*x + 7
Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
In general, a function f(x) means that the input is x and the output is f(x) (or simply f).
Therefore, in our case, the input is the length of the race and the outcome is the time.
The better option is Time(length), option A.Parallel to x = -4 and passing through the point (-3,-5)find the equation of the line
A line of the form x = a, where "a" is a number is a VERTICAL LINE. The graph of the line x = - 4 is shown below:
The line that is parallel to this will also be a vertical line of the form x = a.
The line parallel passes through (-3, -5). So, this will have equation
x = - 3
Answer[tex]x=-3[/tex]
keith lives 5/6 mile north of the school Karen lives 2/3 Mile North of the school what is the distance from Keith's house to Karen's house?
The distance from Keith's house to Karen's house is
= 5/6 - 2/3
= 5/6 - 4/6
= 1/6 miles
Which expression is equivalent to ( 43.4-2)-2 ?
EXPLANATION
The expression that is equivalent to (43,4 - 2)-2 is given appyling the distributive property as follows:
-86.8 + 4 = -82.8
3. Solve using the Laws of Sines Make a drawing to graphically represent what the following word problem states. to. Two fire watch towers are 30 miles apart, with Station B directly south of Station A. Both stations saw a fire on the mountain to the south. The direction from Station A to the fire was N32 W. The direction from Station B to the fire was N40 ° E. How far (to the nearest mile) is Station B from the fire?
Let's make a diagram to represent the situation
The tower angle is found by using the interior angles theorem
[tex]\begin{gathered} 50+58+T=180 \\ T=180-50-58=72 \end{gathered}[/tex]It is important to know that the given directions are about the North axis, that's why we have to draw a line showing North to then find the interior angles on the base of the triangle formed.
To find the distance between the fire and Station B, we have to use the law of sines.
[tex]\frac{x}{\sin58}=\frac{30}{\sin 72}[/tex]Then, we solve for x
[tex]\begin{gathered} x=\frac{30\cdot\sin 58}{\sin 72} \\ x\approx26.75 \end{gathered}[/tex]Hence, Station B is 26.75 miles far away from the fire.