Answer:
60/5=12
Step-by-step explanation:
each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of the table. if a tile is picked up at random, what is the probability that the number on the tile is multiple of 7 or a multiple of 8?
The probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.
To find the probability that a tile picked at random has a number that is a multiple of 7 or a multiple of 8, we need to count the number of tiles that satisfy this condition and divide it by the total number of tiles.
First, let's find how many numbers from 1 to 50 are multiples of 7 and multiples of 8 separately.
Multiples of 7:
7, 14, 21, 28, 35, 42, 49
There are 7 multiples of 7 between 1 and 50.
Multiples of 8:
8, 16, 24, 32, 40, 48
There are 6 multiples of 8 between 1 and 50.
However, we need to be careful not to count the numbers that are multiples of both 7 and 8 (multiples of 56). There's only one such number in the range (56).
So, the total number of tiles with numbers that are multiples of 7 or multiples of 8 is 7 + 6 - 1 = 12.
The total number of tiles from 1 to 50 is 50.
Now, we can find the probability:
Probability = [tex]\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
Probability = [tex]\frac{12}{50}[/tex]
Probability = 0.24
So, the probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.
Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4
explain how you can compare two different mixed numbers that have the same whole number part ?
The graph below shows the solution set of which inequality?
The ratio of areas between two similar triangles is 1:4. if one side of the smaller triangle is 2 units, find the measure of the corresponding side of the other triangle.
What is 16 divided by 4/9
The result of 16 times 9/4 is 36.
The original question appears to be asking how to divide 16 by the fraction 4/9, but it also contains an error in stating the mathematical expression. To divide 16 by 4/9, you need to multiply 16 by the reciprocal of 4/9, which is 9/4. Here's the step-by-step calculation:
Find the reciprocal of 4/9, which is 9/4. Reciprocal means exchanging the numerator and denominator.
Multiply 16 by the reciprocal (16 * 9/4).
Come up with the solution: (16 * 9) / 4 = 144 / 4 = 36.
Therefore, 16 divided by 4/9 equals 36.
the jeans you would like to buy are on sale for $28. write an equation that will help you determine how much you save by getting the jeans on sale. p= regular price and c= cost savings
the answer would be p-28=c
Mark Me Brainliest !
Answer:
P - 28 = C
Step-by-step explanation:
P (Regular Price )
C ( Cost Savings )
You Noticed These Jeans You Liked.
You Couldn't Afford Them So You Waited Til The Price Dropped.
When Prices Drop Its Either 1 of 2 Reasons
Holiday Seasons Or Price Elasticity
So These Jeans Become $28 On The Market.
Simply You Figure Out How Much You'll Save By Comparing The Original Price To The Discounted Price.
There For Your Answer Will Be The Following :
Regular Price - Discounted Price = Cost Savings
Which function is the inverse of f(x) = 2x + 3? f-1(x) = –2x + 3 f-1(x) = 2x + 3
The inverse function is [tex]f^{-1}(x) = \frac{x - 3}{2}[/tex].
To find the inverse of the function [tex]f(x) = 2x + 3[/tex], follow these steps:
Replace [tex]f(x)[/tex] with [tex]y[/tex]:
[tex]y = 2x + 3[/tex]
Interchange the variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x = 2y + 3[/tex]
Solve for [tex]y[/tex]:
[tex]x - 3 = 2y[/tex]
[tex]y = \frac{x - 3}{2}[/tex]
Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x - 3}{2}[/tex]
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation
(-2,3) ; y= 1/2x-1
A. y=1/2x+1
B. y=-2x-1
C. y=1/2x-1
D.y=-1/2x-1
Based on the graph, what is the initial value of the linear relationship?
A. -4/5
B. 0
C. 4
D. 5
What is f(x) = 2x2 + 28x – 5 written in vertex form?
Answer:
b
Step-by-step explanation:
When dividing both sides of an inequality by an integer we must reverse the inequality symbol
In the equation 6x – 2 = –4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.
Answer:
Spencer and Jeremiah both are correct
Step-by-step explanation:
We have given an equation 6x-2 = -4x+2
In this case spencer and jeremiah both are correct whether we first subtract 6x from both sides or we add 4x to both sides will not lead to any incorrection we will get the same result after simplification from both the methods
If we subtract 6x from both sides we will get 6x-6x-2= -4x-6x+2 after simplification we will get -2 = -10x+2
After further simplification we will get x=4/10=2/5
And if we add 4x on both sides we will get 6x+4x-2= -4x+4x+2 after simplification we will get 10x -2 =2 which eventually gives the result
x=4/10=2/5
Therefore, Both are correct
Quadrilateral ABCD is a square.
BC = 10
What is the length of AC?
the sum of 3 less than 5 times a number and tge number is increased by 9 is 24. what is the number ?
which of the following is the sum of 16 4/7+3 3/7 reduced to lowest terms?
Math. Will Upvote. Please help
A function is a relation in which each element of the domain has exactly one element of the range assigned to it.
True Or False?
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A function can only be represented by a straight line on the coordinate plane.
True Or False?
in which of the following are 1/2,5/6,and 5/8 arranged in order
If the probability of a win is 0.24 and the probability of a draw is 0.16, what is the probability of a loss
the probability of a loss is 0.6.
To find the probability of a loss, we first need to understand that in this context, the sum of all possible outcomes (win, draw, and loss) must equal 1.
Given:
- Probability of a win = 0.24
- Probability of a draw = 0.16
Let's denote the probability of a loss as [tex]\( P(\text{loss}) \).[/tex]
We know that:
[tex]\[ P(\text{win}) + P(\text{draw}) + P(\text{loss}) = 1 \][/tex]
So, to find [tex]\( P(\text{loss}) \),[/tex] we rearrange the equation:
[tex]\[ P(\text{loss}) = 1 - (P(\text{win}) + P(\text{draw})) \][/tex]
[tex]\[ P(\text{loss}) = 1 - (0.24 + 0.16) \][/tex]
[tex]\[ P(\text{loss}) = 1 - 0.4 \][/tex]
[tex]\[ P(\text{loss}) = 0.6 \][/tex]
Therefore, the probability of a loss is 0.6.
d(n)=3(−2)^ n−1
What is the 4th term in the sequence?
Answer: -24
Step-by-step explanation:
3(-2)^(4-1)=3*-8=-24
Find x and y so that the ordered data set as a mean of 42and a median of 35.
17,22,26,29,34,x,42,67,70,56,y soln: 17+22+26+29+34+x+42+67+70+56+y= 363+x+y (363+x+y)/11=42 y=99/x x is median
What is the inverse of the function f(x) = 4x + 8?
h(x) = x – 2
h(x) = x + 2
h(x) = x – 2
h(x) = x + 2
we have
[tex]f(x)=4x+8[/tex]
Step 1
Let
[tex]y=f(x)[/tex]
[tex]y=4x+8[/tex]
Step 2
exchanges the variable x for y and the variable y for x
[tex]x=4y+8[/tex]
Step 3
Isolate the variable y
[tex]4y=x-8[/tex]
[tex]y=\frac{1}{4}x-2[/tex]
Step 4
Let
[tex]h^{-1}(x)=y[/tex]
[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex] ------> the inverse function
therefore
the answer is
[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex]
The inverse of the function f(x) = 4x + 8 is h(x) = (x - 8) / 4.
Explanation:The inverse of the function f(x) = 4x + 8 can be found by switching the x and y variables and solving for y. So, we have:
x = 4y + 8
Now, we rearrange the equation to isolate y:
x - 8 = 4y
y = (x - 8) / 4
Therefore, the inverse function is h(x) = (x - 8) / 4.
If max drives 25 miles per hour, how many minutes will it take him to drive 15 miles
Solve for x
6x + 3 - 1/2 x = -2x +5
A laboratory technician needs to make a 72-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?
Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined
Step-by-step explanation:
According to the dilution law,
[tex]C_1V_1+C_2V_2=C_3V_3[/tex]
where,
[tex]C_1[/tex] = concentration of pure acid solution = 100 %
[tex]V_1[/tex] = volume of pure acid solution = x L
[tex]C_2[/tex] = concentration of another acid solution= 10%
[tex]V_2[/tex] = volume of another acid solution= (72-x) L
[tex]C_3[/tex] = concentration of resulting acid solution = 20 %
[tex]V_1[/tex] = volume of resulting acid solution = 72 L
Putting the values in the equation:
[tex]100\times x+10\times (72-x)=20\times 72[/tex]
[tex]x=8L[/tex]
Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72-liter batch of a 20% acid solution.
R=gs/g+s
solve for g
.
.
Final answer:
To solve for g in the equation R = gs/(g+s), you can isolate g by multiplying both sides by (g+s) and rearranging the equation. The final solution is g = -Rs/(R - s).
Explanation:
To solve for g in the equation R = gs/(g+s), we can start by isolating g on one side of the equation. We can do this by multiplying both sides of the equation by (g+s), which cancels out the denominator on the right side:
R(g+s) = gs
Next, distribute the R to both terms on the left side of the equation:
Rg + Rs = gs
Now, we can rearrange the equation to isolate g on one side:
Rg - gs = -Rs
Factor out g on the left side:
g(R - s) = -Rs
Finally, divide both sides of the equation by (R - s) to solve for g:
g = -Rs/(R - s)
If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.
AB and BC are tangent to circle D. Find x if AB=3x+2 and BC=x+12. Find x.
Answer:
The value for x will be 5.
Step-by-step explanation:
As the segment AB and BC are tangent to the circle D, it will have the same long. Due to segment longitude is written as function of the variable x, it requires to solve the following equation:
[tex]long(AB)= 3x+2= long(BC)= x+12[/tex]
[tex]3x+2=x+12[/tex]
[tex]3x-x= 12-2[/tex]
[tex]2x= 10[/tex]
[tex]x= 5[/tex]
The rabbit population on a small island is observed to be given by the function P(t) = 130t − 0.4t^4 + 1200 where t is the time (in months) since observations of the island began.
(a) When is the maximum population attained (Round your answer to one decimal place.)
What is the maximum population? (Round your answer to the nearest whole number.)
(b) When does the rabbit population disappear from the island? (Round your answer to one decimal place.) ...?
Answer:
Step-by-step explanation:
P(t)=130t -0.4t^4 +1200
The population will be max when first differential of p(t) =0
So p'(t) =130-1.6t^3=0
1.6t^3=130
t^3 =130/1.6
t^3 =81.25
t = cube root of 81.25
t =4.3 months
P(max) =130(4.3) -0.4(4.3)^4 +1200
= 559-136.75+1200
=1622
Population will disappear when p(t) =0
Which is the graph of f(x)=(x-1)(x+4)
The quadratic function is described by the standard equation [tex]\boxed{ \ f(x) = ax^2 + bx + c \ }.[/tex]
We have the quadratic function [tex]\boxed{ \ f(x) = (x - 1)(x + 4) \ }.[/tex]
Let us configure it to obtain a standard equation.
[tex]\boxed{f(x) = (x - 1)(x + 4)}[/tex]
[tex]\boxed{f(x) = x^2 + 4x - x - 4}[/tex]
Hence, we get [tex]\boxed{\boxed{ \ f(x) = x^2 + 3x - 4 \ }}.[/tex]
We identify the coefficients a, b, and c. For this equation, [tex]\boxed{ \ a = 1, b = 3, and \ c = -4 \ }[/tex]The parabola opens upward because a > 0, resulting in a vertex that is a minimum.The y-intercept of the quadratic function f(x) = x² + 3x - 4 is (0, c), i.e., the point [tex]\boxed{ \ (0, -4) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - 1)(x + 4) \ }[/tex] we get the x-intercepts at [tex]\boxed{ \ (-4, 0) \ and \ (1, 0) \ }[/tex]The axis of symmetry is [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex], i.e., [tex]\boxed{ \ x = h = -\frac{3}{2(1)} \rightarrow h = -\frac{3}{2} \ }[/tex]The minimum value is [tex]\boxed{ \ k = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Finding the minimum value is as follows:
[tex]\boxed{ \ k = f (- \frac{3}{2}) = (- \frac{3}{2})^2 + 3(- \frac{3}{2}) - 4 = -\frac{25}{4} = -6\frac{1}{4} \ }, or[/tex][tex]\boxed{ \ k = \frac{3^2 - 4(1)(-4)}{-4(1)} = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]Notes:
The graph of a quadratic function is called a parabola.When a > 0, the parabola opens upward, resulting in a vertex that is a minimum.When a < 0, the parabola opens downward, resulting in a vertex that is a maximum.The value c is the y-intercept of the graph, because a y-intercept is a point on the graph where x is zero. In other words, the graph passes through the point [tex]\boxed{ \ (0, c) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - x_1)(x - x_2) \ }[/tex] we get x-intercepts at [tex]\boxed{ \ (x_1, 0) \ and \ (x_2, 0) \ }.[/tex] An x-intercept represents a point on the graph where y is zero.The axis of symmetry represent the line that passes through the vertex of parabola with equation [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Learn moreA line that is not parallel to either the x-axis or the y-axis https://brainly.com/question/4691222 Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) https://brainly.com/question/1332667The midpoint https://brainly.com/question/3269852Keywords: which is the graph of f(x) = (x - 1)(x + 4), the x-intercept, quadratic function, a standard equation, the y-intercept, the axis of symmetry, the vertex, parabola, upward, downward
The graph of f(x) = (x-1)(x+4) is an upward-opening parabola with roots at x = 1 and x = -4. It should be plotted carefully, labeling and scaling the axes to show maximum and minimum values, and ensuring it passes through the roots with the proper shape.
Explanation:The graph of the function f(x) = (x-1)(x+4) can be determined by finding the roots and the shape of the curve. The roots of the function can be found when f(x) = 0, which occurs at x = 1 and x = -4. Therefore, these are the points at which the graph will intersect the x-axis. Since it's a quadratic function, its graph will be a parabola.
Additionally, because the coefficient of x² is positive, the parabola opens upwards. To graph this function accurately, one needs to plot the roots and then sketch the parabola, ensuring that it intersects these points and opens upwards. The vertex of the parabola can also be found by averaging the roots, which gives us the x-value of the vertex as (-4 + 1)/2 = -1.5, with the corresponding y-value obtained by evaluating f(x) at x = -1.5.
The resulting graph would start above the x-axis for x < -4, pass through the x-axis at x = -4, reach a vertex at x = -1.5, pass through the x-axis again at x = 1, and continue upwards for x > 1.
The graph should be accurately scaled and labeled with the function f(x) and the variable x, and include the maximum and minimum values on the axes based on the calculated points and the behavior of the quadratic function.