Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = x - 1 ( add 1 to both sides )
y + 1 = x
change y back into terms of x, hence
[tex]f^{-1}[/tex] (x ) = x + 1 → A
the correct (answer)
is A f1(x)=x+1
A coin is tossed 5 times. Find the probability that all are heads. Find the probability that at most 2 are heads.
Answer:
1/32
15/32
Step-by-step explanation:
For a fair sided coin,
Probability of heads, P(H) = 1/2
Probability of tails P(T) = 1/2
For a coin tossed 5 times,
P( All heads)
= P(HHHHH),
= P (H) x P(H) x P(H) x P(H) x P(H)
= (1/2) x (1/2) x (1/2) x (1/2) x (1/2)
= 1/32 (Ans)
For part B, it is easier to just list the possible outcomes for
"at most 2 heads" aka "could be 1 head" or "could be 2 heads"
"One Head" Outcomes:
P(HTTTT), P(THTTT) P(TTHTT), P(TTTHT), P(TTTTH)
"2 Heads" Outcomes:
P(HHTTT), P(HTHTT), P(HTTHT), P(HTTTH), P(THHTT), P(THTHT), P(THTTH), P(TTHHT), P(TTHTH), P(TTTHH)
If we count all the possible outcomes, we get 15 possible outcomes representing "at most 2 heads)
we know that each outcome has a probability of 1/32
hence 15 outcomes for "at most 2 heads" have a probability of
(1/32) x 15 = 15/32
Elisa decides to walk home from her favorite restaurant. The restaurant is 5 miles from her home, and she can walk at a steady pace of 2 miles an hour. Which equation models Elisa's distance from home based on the time spent walking
Elisa's distance from home (in miles) equals her walking speed (2 mph) multiplied by time spent walking (t hours).
To model Elisa's distance from home based on the time spent walking, we can use the formula for distance, which is:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\\[/tex]
Given that Elisa walks at a steady pace of 2 miles per hour, her rate (or speed) is 2 miles per hour. Let's denote this rate as [tex]\( r = 2 \)[/tex] mph.
The time Elisa spends walking can vary, so let's denote it as [tex]\( t \)[/tex] (in hours).
Now, to find Elisa's distance from home, we'll substitute the values into the formula:
[tex]\[ \text{Distance} = r \times t \]\[ \text{Distance} = 2 \times t \][/tex]
Since Elisa's distance from home is what we're interested in, this equation models her distance from home based on the time spent walking. It shows that her distance from home increases linearly with time as she walks at a steady pace.
I NEED HELP PLEASEE
[tex]\bf \cfrac{1+cot^2(\theta )}{1+csc(\theta )}=\cfrac{1}{sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\implies \cfrac{1+\frac{cos^2(\theta )}{sin^2(\theta )}}{1+\frac{1}{sin(\theta )}}\implies \cfrac{~~\frac{sin^2(\theta )+cos^2(\theta )}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}\implies \cfrac{~~\frac{1}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}[/tex]
[tex]\bf \cfrac{1}{\underset{sin(\theta )}{~~\begin{matrix} sin^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}\cdot \cfrac{~~\begin{matrix} sin(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{sin(\theta )+1}\implies \cfrac{1}{sin^2(\theta )+sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\ne \cfrac{1}{sin(\theta )}~\hfill[/tex]
I need bad can someone help
Answer:
6x + 8y
Step-by-step explanation:
Distribute 2:
Note: This means to multiply 2 with the numbers inside the parentheses.
2 * 3x = 6x
2 * 4y = 8y
Our answer would be 6x +8y
Answer:
I think A and C are because they all go back to the original equation.
Step-by-step explanation:
Hope my answer has helped you and if not i'm sorry.
Figure ABCD is translated down by 6 units:
Which of the following best describes the sides of the transformed figure A'B'C'D'?
A'D' || A'B'
A'B' || B’C’
D’C’ || A'D'
A'D' || B’C’
Answer:
jjjjjj
Step-by-step explanation:
it would be the same as before because translated means it stays the same
Line l passes through the point of intersection,A, of the lines 4x-3y+4=0 and x+2y=5. Without finding A,find the equation of line l if its y-intercept is 1.5
Answer:
[tex]\large\boxed{y=\dfrac{15}{14}x+1.5}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
------------------------------------------------------------------------
You must solve the system of equations:
[tex]\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ[/tex]
[tex]\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}[/tex]
Does 3 to the 2 power plus 3 to the 3 power equal 3 to the 5 power?
Please Explain!
3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. In actuality, 3^2 + 3^3 = 36, while 3^5 = 243.
Explanation:No, 3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. This is a common misconception when dealing with exponents. To clear this up, let's look at what these expressions actually mean:
3 to the 2nd power (3^2) = 3*3 = 9
3 to the 3rd power (3^3) = 3*3*3 = 27
So, 3^2 + 3^3 = 9 + 27 = 36
However, 3 to the 5th power (3^5) = 3*3*3*3*3 = 243
So, as you can see, 36 does not equal 243.
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what are the solutions to the quadratic equation x^2=7x+4
Answer:
x = 7/2 ±sqrt(65)/ 2
Step-by-step explanation:
x^2=7x+4
Subtract 7x from each side
x^2-7x=7x-7x+4
x^2 -7x =4
Complete the square
Take the coefficient of x and divide by 2
-7/2
Then square it
(-7/2)^2 = 49/4
Add this to each side
x^2 -7x +49/4 =4+49/4
(x-7/2)^2 = 4 +49/4
(x-7/2)^2 = 16/4 +49/4
(x-7/2)^2 =65/4
Take the square root of each side
sqrt((x-7/2)^2) =±sqrt(65/4)
x-7/2 = ±sqrt(65)/ sqrt(4)
x-7/2 = ±sqrt(65)/ 2
Add 7/2 to each side
x-7/2 +7/2=7/2 ±sqrt(65)/ 2
x = 7/2 ±sqrt(65)/ 2
The solutions to the quadratic equation x^2 = 7x + 4 are x = 3 and x = -7, found using the quadratic formula and verified by substitution into the original equation.
To solve the quadratic equation x^2 = 7x + 4, we first need to bring all terms to one side of the equation to get it into the standard form ax^2 + bx + c = 0. This gives us x^2 - 7x - 4 = 0. We can then apply the quadratic formula, which is x = (-b \/- sqrt(b^2 - 4ac)) / (2a), where a, b, and c are coefficients from the equation ax^2 + bx + c = 0.
For our equation, a = 1, b = -7, and c = -4. Substituting these values into the quadratic formula gives us two solutions, which result in x = 3 and x = -7 as the solutions to the problem. To verify these solutions, we can substitute them back into the original equation and confirm they satisfy the equation, thus proving they are correct.
A study determined that there is a strong correlation between getting less than 8 hours of sleep a day and lower test scores. Can it be determined that the low test scores are caused by sleep deprivation? Explain.
A) Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.
B)Causation cannot be proven because all students get less than 8 hours of sleep.
C)Causation can be proven because it is well known that less sleep lowers test scores.
D)Causation can be proven because an experiment was used to prove this hypothesis.
Answer:
Option A (Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance).
Step-by-step explanation:
Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. It is important to note that correlation shows a relationship between the two variables but it cannot determine the causation i.e. it cannot be concluded that one variable caused the other variable to occur. Even though having a strong correlation does not mean causal relationship. Therefore, correlation does not prove causation. This is because there are several other lurking and unobserved variables which affect the observed variables. The former class of variables are not accounted for in the correlation. Therefore, the exact magnitude of the causal relationship cannot be determined. Therefore, Option A is the correct choice!!!
Answer:
OPTION A: Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.
Step-by-step explanation: I got it right on the test.
Which linear inequality is represented by the graph?
A. y < x + 3
B. y > x + 3
C. y > x + 3
D. y < x + 3
Answer:
The correct answer option is C. [tex]y>\frac{2}{3}x+3[/tex].
Step-by-step explanation:
We are given a graph and we are to determine whether which linear inequality is represented by the graph.
We know that the grey part on the graph represents the the region which is not included in the inequality.
Also, when x = 0, the values of y can only be less than 3.
So we choose two points on the graph and we find the slope.
For example, we take the points [tex](0,3)[/tex] and [tex](3,5)[/tex].
Slope = [tex]\frac{5-3}{3-0} =\frac{2}{3}[/tex]
which makes the equation of the line [tex]y=\frac{2}{3}x+3[/tex] and inequality [tex]y>\frac{2}{3}x+3[/tex].
One solution to the problem below is 5. What is the other solution? c^2 - 25 = 0
Answer:
c = -5
Step-by-step explanation:
Plug in -5 to c in the equation:
c² - 25 = 0
(-5)² - 25 = 0
Simplify. First, solve the power, then solve the subtraction:
(-5)² - 25 = 0
(-5 * -5) - 25 = 0
(25) - 25 = 0
0 = 0 (True)
~
Answer:
c=-5
Step-by-step explanation:
c^2-25=0
I'm going to solve this by using square root after I get the square termed by itself.
[tex]c^2-25=0[/tex]
Add 25 on both sides:
[tex]c^2=25[/tex]
Square root both sides:
[tex]c=\pm \sqrt{25}[/tex]
[tex]c=\pm 5[/tex]
Check!
[tex](5)^2-25=0 \text{ and } (-5)^2-25=0[/tex]
12. Determine the area of the given parallelogram with length 11 and altitude 5.
A. 55
B. 110
C. 27.5
D. 75
Complete the table for the given rule y=x+3
Answer:
x= 1 when y =4 , x= 5 when y = 8 , x=2 when y = 5.
Step-by-step explanation:
y=x+3
Through this rule we have to find out the values of x when values of y are given:
y=x+3
y = 4
Substitute the value in the rule:
4=x+3
Combine the constants:
4-3=x
x= 1 when y =4
y=x+3
y = 8
8= x+3
Combine the constants:
8-3= x
5=x
x= 5 when y = 8
y=x+3
y = 5
5=x+3
Combine the constants:
5-3=x
2=x
x=2 when y = 5....
find the sum of these polynomials (x^2+x+9)+(7x^2+5)
Answer:
The correct option is A
Step-by-step explanation:
(x^2+x+9)+(7x^2+5)
Open the parenthesis:
=x²+x+9+7x²+5
Now add the like terms:
=8x²+x+14
Therefore the correct option is A...
Answer:
A
Step-by-step explanation:
Choose the equation that represents the line that passes through the point (−1, 6) and has a slope of −3.
Answer:
y = - 3x + 3
Step-by-step explanation:
The equation of a line in slope intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3, hence
y = - 3x + c ← is the partial equation of the line
To find c substitute (- 1, 6 ) into the partial equation
6 = 3 + c ⇒ c = 6 - 3 = 3
y = - 3x + 3 ← equation of line
Answer: A
Step-by-step explanation:
FLVS Question, the answer is A !!
Solve the equation by factoring.
4x2 + 12x + 5 = 0
The solutions to the quadratic equation are x = -1/4 and x = -5.
First, we look at the coefficient of x², which is 4 in this case. We need to find two numbers whose product is 4 times 5 (the constant term) and whose sum is the coefficient of x (12 in this case). These numbers are 1 and 20, as 1 * 20 = 20 and 1 + 20 = 21.
Next, we rewrite the middle term (12x) of the quadratic expression as the sum of these two numbers:
4x² + 1x + 20x + 5 = 0.
Now, we group the terms in pairs:
(4x² + 1x) + (20x + 5) = 0.
Next, we factor out the greatest common factor from each group:
x(4x + 1) + 5(4x + 1) = 0.
Notice that we have a common binomial factor, (4x + 1), which we can factor out:
(4x + 1)(x + 5) = 0.
Now, we apply the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor to zero and solve for x:
1. 4x + 1 = 0 => 4x = -1 => x = -1/4.
2. x + 5 = 0 => x = -5.
Answer: x = -1/4, -5.
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What is the sum of the measures, in degrees, of the interior angles of a 16- sided polygon?
Answer: So the sum of all of the measures of the interior angles of a 16-sided polygon is 2520 degrees.
The sum of the interior angles of a 16-sided polygon is 2520 degrees.
The sum of the interior angles of a 16-sided polygon, or hexadecagon, is 2520 degrees, which can be calculated using the formula (n-2) x 180 degrees.
The sum of the interior angles of any polygon can be found using the formula (n-2) imes 180 degrees, where n is the number of sides of the polygon. A 16-sided polygon is known as a hexadecagon. Using the formula, we have:
Sum of interior angles = (16-2) imes 180 degrees
Sum of interior angles = 14 imes 180 degrees
Sum of interior angles = 2520 degrees
Therefore, the sum of the interior angles of a 16-sided polygon is 2520 degrees.
An aquarium measures 11 feet wide, 10 feet long and 7 feet deep. Approximately how many gallons of water does it hold if there are 7.48 gallons per cubic foot of water?
The aquarium, which has a volume of 770 cubic feet, can hold approximately 5,760 gallons of water when taking into consideration the conversion rate of 7.48 gallons per cubic foot.
Explanation:To calculate the volume of water an aquarium can hold, we need to first calculate the volume of the aquarium itself, which is determined by multiplying the length, width, and height together. In this case, we have an aquarium that measures 11 feet wide, 10 feet long and 7 feet deep, so multiplying these dimensions together gives us a volume of 770 cubic feet.
Next, we need to convert this volume into gallons. We're given the conversion rate of 7.48 gallons per cubic foot of water, so we multiply our previously obtained volume by this rate. This gives us: 770 cubic feet * 7.48 gallons per cubic foot, which equals 5,759.6 gallons.
So, the aquarium can hold approximately 5,760 gallons of water.
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which ordered pair is a solution to the inequality 3x - 4y < 16 ?
Answer:
C.
Step-by-step explanation:
You are given 3x-4y<16 and we want to see which of the ordered pairs is a solution.
These ordered pairs are assumed to be in the form (x,y).
A. (0,-4) ?
3x-4y<16 with (x=0,y=-4)
3(0)-4(-4)<16
0+16<16
16<16 is not true so (0,-4) is not a solution of the given inequality.
B. (4,-1)?
3x-4y<16 with (x=4,y=-1)
3(4)-4(-1)<16
12+4<16
16<16 is not true so (4,-1) is not a solution of the given inequality.
C. (-3,-3)?
3x-4y<16 with (x=-3,y=-3)
3(-3)-4(-3)<16
-9+12<16
3<16 is true so (-3,-3) is a solution to the given inequality.
D. (2,-3)?
3x-4y<16 with (x=2,y=-3)
3(2)-4(-3)<16
6+12<16
18<16 is false so (2,-3) is not a solution to the given inequality.
20 PTS! PLEASE HELP ME T^T!! Using complete sentences, explain which function has the greatest y-intercept.
Step-by-step explanation:
The y-intercept is the value of the function at x = 0.
f(0) = -3(0) + 2 = 2
g(0) = -3
h(0) = 4 sin(0 + π) + 3 = 3
h(x) has the greatest y-intercept.
Answer:
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
Step-by-step explanation:
The given function is
[tex]f(x)=-3x+2[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]f(0)=-3(0)+2[/tex]
[tex]f(0)=0+2[/tex]
[tex]f(0)=2[/tex]
The y-intercept of the function f(x) is 2.
From the given graph it is clear that the graph of g(x) intersect the y-axis at y=-3.
Therefore the y-intercept of the function g(x) is -3.
The given function is
[tex]h(x)=4\sin (2x+\pi)+3[/tex]
Substitute x=0, to find the y-intercept of the function.
[tex]h(0)=4\sin (2(0)+\pi)+3[/tex]
[tex]h(0)=4\sin (0+\pi)+3[/tex]
[tex]h(0)=4\sin (\pi)+3[/tex]
[tex]h(0)=4(0)+3[/tex]
[tex]h(0)=3[/tex]
The y-intercept of the function h(x) is 3.
The y-intercept of functions f(x), g(x) and h(x) are 2,-3 and 3 respectively. Therefore the function h(x) has the greatest y-intercept.
A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the remaining seats to be recliners. If x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities? x + y ≤ 50 x ≥ 20
The system of inequalities x + y ≤ 50 and x ≥ 20 can be graphically represented as two intersecting regions in a two-dimensional space, showing the possible combinations of stools (x) and recliners (y) the new coffee shop could have.
Explanation:The subject of the question is a system of inequalities which is a common topic in high school level algebra. In this case, the system of inequalities presented is x + y ≤ 50 and x ≥ 20, where 'x' represents the number of stools and 'y' represents the number of recliners in the new coffee shop.
In order to represent this system graphically, firstly, we draw two lines that correspond to the equations x + y = 50 and x = 20. The area of intersection between the two regions defined by these lines represents the solution to the system of inequalities.
For the inequality x + y ≤ 50, we shade the area below the line because the sign is 'less than or equal to', and for x ≥ 20, we shade to the right because of the 'greater than or equal to' sign. The overlap region satisfies both inequalities and represents the possible combinations of stools and recliners the coffee shop can have according to the owner's preferences.
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Find the value of x and Lj
Answer:
x = 4.2, LJ = 14.2
Step-by-step explanation:
When 2 chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is
10x = 6 × 7 = 42 ( divide both sides by 10 )
x = 4.2
Hence LJ = 10 + x = 10 + 4.2 = 14.2
michelle and rosa are researching the deepest lakes in the united states for a school project. lake tahoe has a depth of 1,644 feet. michelle believes the lake has a depth of 548 meters. rosa believes the lake has a depth of 498 meters. who do you agree with ?
Answer:
Rosa is closer to the correct depth.
Step-by-step explanation:
To show that two measurements are nearly equivalent, we must convert one of the measurements to the other unit.
1 m = 3.281 ft
[tex]\text{Depth } = \text{1644 ft} \times \dfrac{\text{1 m}}{\text{3.281 ft}} = \textbf{501.1 m}[/tex]
Neither is correct but Rosa is closer to the correct depth.
If Jackie were to paint her living room alone, it would take 8 hours. Her sister Patricia could do the job in 9 hours. How long would it take them working together? If needed, submit your answer as a fraction reduced to lowest terms.
Answer:
(72/17) hours
Step-by-step explanation:
Time Jackie would take alone , J = 8 hrs
Time Patricia would take alone , P = 9 hrs
Let the time they will take together be T
use the formula for shared unit rate
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{J}[/tex] + [tex]\frac{1}{P}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{1}{8}[/tex] + [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{T}[/tex] = [tex]\frac{17}{72}[/tex]
T = [tex]\frac{72}{17}[/tex] hours (or 4.24 hours)
It takes them to work together for 4 hours and 14 minutes.
Ratio and proportionA ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
Jackie was to paint her living room alone. It would take 8 hours.
Her sister Patricia could do the job in 9 hours.
To findHow long would it take them to work together?
How to get the solution?We know the work is inversely proportional to the time. And formula we have
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{T_1} +\dfrac{1}{T_2}[/tex]
We have
[tex]\rm T_1 = 8, \ \ \ and\ \ T_2 = 9[/tex]
Then by the formula.
[tex]\rm \dfrac{1}{T_f} = \dfrac{1}{8} +\dfrac{1}{9}\\\\\rm \dfrac{1}{T_f} = \dfrac{8+9}{8*9} \\\\\rm \dfrac{1}{T_f} = \dfrac{17}{72} \\\\T_f \ = \dfrac{72}{17}\\\\T_f \ = 4.24[/tex]
Then the time 4.24 will be 4 hours and 14 minutes.
Thus, it takes them to work together for 4 hours and 14 minutes.
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factor the given expression x squared + 16x +64
Answer:
(x + 8)^2.
Step-by-step explanation:
x^2 + 16x + 64
8 + 8 = 16 and 8^2 = 64 so the factors are
(x + 8)(x + 8) or (x + 8)^2
If you travel 720 miles in 12 hours, which of the following is the amount of time it would take you to travel 360 miles?
Answer:
6 Hours
Step-by-step explanation:
360 is half of 720, so it would take half the time to travel. half of 12 is 6
At a constant speed of 60 miles per hour, it would take 6 hours to travel 360 miles, which is a reasonable answer since the time required is halved when the distance is halved.
Explanation:The question involves calculating the time it would take to travel a certain distance given a constant speed which is a basic concept in mathematics, more specifically in the topic of rates and ratios.
If you travel 720 miles in 12 hours, you are traveling at a speed of 720 miles / 12 hours = 60 miles per hour. Now, to find out how long it would take to travel 360 miles at this constant speed, you divide the distance by the speed to get the time: 360 miles / 60 miles per hour = 6 hours. So, it would take 6 hours to travel 360 miles if you maintain the same speed.
When you check if the answer is reasonable, consider if the distance is halved, the time should also be halved if the speed remains constant. Since 360 miles is half of 720 miles, and 6 hours is half of 12 hours, the answer is indeed reasonable.
What is the type of two-dimensional solid created by a vertical cross section of the cone that passes through the apex? What is the area of the cross section? triangle; area = 45 ft2 triangle; area = 90 ft2 circle; area = 36π ft2 circle; area = 144π ft2
Answer:
The answer is B on edge
Step-by-step explanation:
The area of the cross section is equal to 90 ft²
Looking at the diagram we would see that the two dimensional solid that passed the point is a triangle.
The formula for area of a triangle[tex]\frac{1}{2} bh[/tex]
Where b = bas
h = height
The radius of the cone = 6
The diameter of the cone = 2*radius
= 2*6
= 12
We have to put d = b = 12
When we put the values into the area of a triangle
= [tex]\frac{1}{2} 12*15\\\\= \frac{180}{2} \\\\= 90 ft^2[/tex]
The area of the cross section is therefore 90 ft²
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In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump
for women was 70.0 inches, while the winning jump for men was 86.5 inches. Since then, the winning jump for
women has increased by about 0.48% per year, while the winning jump for men has increased at a slower rate,
0.4%. If these rates continue, when will the winning jump for women be higher than the winning jump for men?
after 110 years
after 248 years
after 265 years
after 270 years
Answer:
D) After 270 years
Answer:
Step-by-step explanation:
Given that in 1928, f(x) = the winning jump
for women was 70.0 inches and g(x) = the winning jump for men was 86.5 inches.
Increase = 0.48% for women and 0.4% for men
i.e. after x years [tex]f(x) =70(1.0048)^x \\\\g(x) = 86.5(1.004)^x[/tex]
Let us find when these two values would be equal.
That is at point of intersection
Solving we get x =244 years
Hence approximately after 248 years women will exceed men.
Evaluate -7a – 2b, if a = -1 and b = 2
Answer:
3
Step-by-step explanation:
Plug in the values for a and b= -7(-1)-2(2)
Multiply= 7-4
Subtract= 3
Hope this helps ^-^
Answer:
3
Step-by-step explanation:
We'd just substitute the value provided to us with the variable.
-7(-1) - 2(2)
-7 * -1 = 7
-2(2) = -4
7-4 = 3
Our answer is 3
Please help ASAP this is all due today
Answer:
x = 7.5
Step-by-step explanation:
Given
- 15 = [tex]\frac{x}{-0.5}[/tex]
Multiply both sides by - 0.5
- 0.5 × - 15 = x, hence
x = 7.5
Answer:
7.5.
Step-by-step explanation:
-15 = x / -0.5
Cross multiplying:
x = -15 * -0.5
= 7.5.