If two 6-sided number cubes are rolled, what is the probability that you will roll a 1 first and then roll a 5 with the second cube?
Final answer:
The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.
Explanation:
To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.
The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:
Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36
A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?
Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg
A segment has endpoints at (3,−4) and (3,−17). How many units long is the segment?
[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]
What is the value of X?
Sin64 degree= cos x
Enter your answer in the box.
Answer:
x = 26° is the answer.
Step-by-step explanation:
We have to find the value of x from the given equation.
sin 64° = cos x
since sin 64° = 0.8987
Therefore cos x = 0.8987
[tex]x = cos^{-1}(0.8987) = 26[/tex]
x = 26°
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4
Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)
A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2
Equation of parabola with focus at (0,-4) and directrix is y=4 .
As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is (x,y).
Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
→x²+y²+8 y +16 = y² - 8 y+16
→ x² = -8 y - 8 y= -16 y [ Cancelling y² and 16 from L.H.S and R.H.S ]
So , equation of parabola is , x²= - 16 y or f(x)= -x²/16
The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .
Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.
The parabola is opening downwards.
Let any point on parabola is [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]
[tex]d=\sqrt{x^2+(y+4)^2[/tex]
Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]
As these distances are equal.
[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]
[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]
[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]
[tex]x^2=-8y-8y[/tex]
[tex]x^2=-16y[/tex]
[tex]y=\dfrac{-x^2}{16}[/tex]
So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]
Learn more about parabola here:
https://brainly.com/question/21685473?referrer=searchResults
Two f-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60° angle. if each flies at a constant rate of 500 mph, after how many hrs will the fighters be 1200 mi apart?
Which are the solutions of this equation 4x2-7x=3x+24
Answer: x = -3/2 x =4
Answer:
3rd and last choice on ed
Step-by-step explanation:
10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.
Help please! Math Nation Section 6 Test Yourself Practice Tool.
Answer: D) [tex]y=-5(x-5)^2+1125[/tex]
Step-by-step explanation:
Let x be the number of $2 increases in price and y be the revenue.
By using the given table , lets check all the options
A) [tex]y=(x+5)^2-1125[/tex]
For x=1, y=1045
[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]
B) [tex]y=(x-5)^2+1125[/tex]
For x=1, y=1045
[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]
C) [tex]y=-5(x+5)^2-1125[/tex]
[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]
D) [tex]y=-5(x-5)^2+1125[/tex]
[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]
Hence, this is the quadratic equation that models the data.
Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]
In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:
[tex]y = a(x - h)^2 + k[/tex]
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).
Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:
[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]
A parallelogram has vertices E(−8, 3), F(2, −2), G(−1, 3), and H(−5, −2). What are the coordinates of the midpoint of each diagonal?
(3, −0.5)
(−4.5, 3)
(−3, 0.5)
(0.5, −1.5)
Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?
a horizontal compression by a factor 2
a vertical stretch by a factor of 2
a horizontal translation 2 units to the left
a vertical translation 2 units down
Consider the two functions shown here. What is the rate of change of each function?
Function 2: y = ½ x + 7
What is the value represented by the letter A on the box plot of data?
{5, 20, 40, 50, 50, 85}
Enter your answer in the box.
Which is the best estimate for (6.3x10^-2)(9.9x10^-3) written in scientific notation?
Answer:
[tex]6 \times 10^{-4}.[/tex]Step-by-step explanation:
We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].
In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.
On multiplying 6.3 by 9.9 , we get 62.37.
Now we would multiply [tex]10^{-2} \ by \ 10^{-3}.[/tex]
Therefore,
[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]
Therefore,
[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]
Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].
Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]
Therefore, correct answer is [tex]6 \times 10^{-4}.[/tex]
Solve the single variable equation for n.
4(-n + 4) + 2n = 2n
a. n = 4
b. no solution
c. infinitely many solutions
Translate shapes , pls help me with this
Answer:
A: (-4,-2)
B: (-3,-4)
C: (0,2)
D: (-2,-1)
Hope this helps! I'm not the best at math though, so it could be incorrect.
Suppose that 1% of the students in a school have head lice and the test for head lice is accurate 75% of the time. What is the probability that a student in the school has head lice, given that the test came back positive?,
If the test is positive, there is a 2.9% chance that the subject has head lice.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Assume that the school has 100 students. If 1 student has lice and 99 others don't, that means one student has lice.
Suppose that all students took the test. Only 0.75 of 1 people with lice would have a positive test result because it is only 75% accurate.
Because the test is only 75% accurate, out of the 99 students who do not have lice, 25% would test positive. 24.75 false positive tests are involved here!
So far, 25.50 of our students have had positive tests, although only 0.75 of them truly have lice. 2.9% is 0.75 out of 25.5.
learn more about conditional probability here :
https://brainly.com/question/30144287
#SPJ7
Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property
Answer:
subtraction property
Step-by-step explanation:
What is the relative minimum of the function?
Answer:
The required relative minimum is -5
Step-by-step explanation:
Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.
Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.
So, its relative minimum is -5.
35 points!
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
6. Angle ABC is congruent to which angle?
1. Angle CAB
2. Angle XYZ
3. Angle XZY
4. Angle YZX
~
7.
Side CA is congruent to which side?
1. ZX
2.YX
3.XY
4.YZ
Answer:
[tex]\angle ABC \cong \angle XYZ[/tex]
[tex]CA \cong ZX[/tex]
Step-by-step explanation:
According to the given figures:
[tex]\angle ABC \cong \angle XYZ[/tex]
Also,
[tex]CA \cong ZX[/tex]
Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.
You can deduct these answers by observing the number of line that match each pair of congruent elements.
What are the x and y intercepts of the line? 2x - 3y = 12
Javier is 175% heavier than his brother. If Javier’s brother weighs 80 pounds, how much does Javier weigh?
Let us say weight of Javier is x pounds.
Weight of his bother = 80 pounds
Javier is 175 % or 1.75 times heavier than his brother.
So Javier's weight = x pounds= 1.75 *80 = 140 pounds.
Answer: Javier's weight is 140 pounds.
The cake store is having a 25\%25%25, percent off sale on all of its cakes. If the cake you want regularly costs \$9$9dollar sign, 9, how much would you save with the discount?
Answer:
$2.25.
Step by step explanation:
We have been given that the cake store is having a 25% off sale on all of its cakes.
To find our savings with the discount we will find 25% of $9 (regular cost of cake).
[tex]\text{Savings with the discount}=9\times\frac{25}{100}[/tex]
[tex]\text{Savings with the discount}=9\times\frac{1}{4}[/tex]
[tex]\text{Savings with the discount}=\frac{9}{4}=2.25[/tex]
Therefore, we will save $2.25 with the given discount.
Val rented a bicycle while she was on vacation. A paid a flat rental fee of $55 plus $8.50 each day the total cost was 123 dollars write an equation you can use to find the number of days when she rented to bicycle
Determine the 10th term 0.1,0.5,2.5
Line segment AC has endpoints A (-1,-3.5) and C (5,-1). Point B is on line segment AC and is located at (0.2,-3). What is the ratio of AB/BC
Answer:
AB/BC = (1.3) / (5.2). Hope this helps :)
Step-by-step explanation:
will give brainlist
what is the approximate area of the figure
Answer:
the answer is 137.1
Step-by-step explanation:
Divide the figure into recognizable shapes. Find the area of each shape and add them together.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP