Using permutations and combinations, The number of different ways this can be done is 316250 ways.
What exactly are combinations and permutations?A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.
We will solve it using permutations and combinations
a. The number is ²⁵P₄= 25! / (25 - 4)!
25! / 21! = 25 × 24 × 23 × 22 = 303600 ways.
b. The number is ²⁵C₄= 25! / 4! . (25 - 4)!
= 25! / 4! . 21! = 25 × 24 × 23 × 22 / 4 × 3 × 2
= 12650 ways
Total number of ways to select persons are =
303600 + 12650
= 316250
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Rewrite the following quadratic function in vertex form and graph it F(x)=2x^2+8x+4
In vertex form, the quadratic function F(x) = 2x² + 8x + 4 is given by:
y = 2(x + 2)² - 4
The graph of the function is given at the end of the answer.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.What is the vertex of a quadratic equation?A quadratic equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]For the function F(x) = 2x² + 8x + 4, the coefficients are given as follows:
a = 2, b = 8, c = 4.
Hence the coordinates of the vertex are:
h = -8/4 = -2.k = -(8² - 4(2)(4))/8 = -4.Hence:
y = 2(x + 2)² - 4
As the leading coefficient is of a = 2.
The graph of the function is given at the end of the answer.
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C=0.4m+68C, equals, 0, point, 4, m, plus, 68 Lúcia hires a truck driver to deliver the food for her catering company. For a delivery that is mmm miles away, the total cost, CCC, in dollars, is given by the above equation. What is the meaning of the 0.4m0.4m0, point, 4, m in this equation?
The meaning of the 0.4m in this equation is the additional cost of hiring the delivery truck for m number of miles.
EquationGiven equation:
C = 0.4m + 68
Where
m = number of miles
C = total cost of hiring the delivery truck
68 = Fixed cost of hiring the delivery truck
0.48 = Additional cost per mile of hiring the delivery truck
For instance,
If the truck is hired for 10 miles
C = 0.4m + 68
= 0.4(10) + 68
= 4 + 68
C = $72
Therefore, the meaning of the 0.4m in this equation is the additional cost of hiring the delivery truck for m number of miles.
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Consider these graphed number lines. 4 number lines going from negative 5 to positive 5. Graph A: points are at 1 and 4. Everything between the points is shaded. Graph B: Points are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded. Graph C: Open circles are at 1 and 4. Everything between the points is shaded. Graph D: Open circles are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded. Which number line represents the solution for the inequality |2x – 5| Greater-than-or-equal-to 3? graph A graph B graph C graph D
The graph of the inequality |2x - 5| ≥ 3 represents 4 ≤ x ≤ 1 which is
B: Points are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded.
What is inequality?Inequality is a comparison between two nonequal quantities and they are of four types.
We know |2x - 5| ≥ 3 is,
2x - 5 ≥ 3.
2x ≥ 3 + 5.
2x ≥ 8.
x ≥ 4.
OR
-(2x - 5) ≥ 3.
-2x + 5 ≥ 3.
-2x ≥ - 2.
-x ≥ 1.
x ≤ 1. ( Think of moving the terms on other sides to make x positive)
So, the graph of the inequality |2x - 5| ≥ 3 is 4 ≤ x≤ 1.
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Convert 29 days to weeks and days.
Answer:
4 weeks and 1 day
Step-by-step explanation:
7 x 4 = 28
28 + 1 = 29
Answer:
4weeks and 1 day
7X4=28
28+1=29
Step-by-step explanation:
hope this helps (❁´◡`❁)
a scuba diver is swimming at the depth -46 feet and then swims 0.5 foot toward the surface every 3 seconds. what is the location of the scuba diver relative to the surface after 15 seconds
Answer:
-43.5
Step-by-step explanation:
After 15 second he would have swam to a level of -43.5.
1. find three consecutive integers such that twice the least integer is 12 more than the greater integer.
2. The perimeter of a rectangle is 150 cm the length is 15cm greater than the width. Find all of the dimensions, please.
Answer: offf
Step-by-step explanation:off
1. A rectangle has a length that is three feet more than twice its width.
(a) If the width of the rectangle is represented
by the variable w, give an expression for
the length of the rectangle in terms of w.
(b) What would the perimeter of this
rectangle be if the width was 10 feet?
(c) The perimeter of the rectangle is 78 feet. Set up an equation using w that models this
situation. Solve it and state the values for both the width and the length of the rectangle.
Part a: Expression for length; l = 2w + 3.
Part b: Perimeter equation; P = 2(l + 10).
Part c: Length of rectangle = 29 feet.
What is defined as the rectangle?A rectangle is a the kind of quadrilateral, a two-dimensional shape with four sides as well as four vertices. The rectangle's four angles are all right angles as well as equal to 90 degrees.The given conditions are-
Let 'l' be the length of the rectangle.
Let 'w' be the width of the rectangle.
Part a: expression for the length of a rectangle in the terms of w.
Length is three feet more than twice its width.
l = 2w + 3
Thus, the expression of l in terms of w is: l = 2w + 3.
Part b: Perimeter equation.
The width is given as 10 feet.
The formulae of perimeter if rectangle is;
P = 2(l + w)
Put the value;
P = 2(l + w)
P = 2(l + 10)
Thus, the equation for perimeter is P = 2(l + 10)
Part c: Length of rectangle.
perimeter of rectangle = 78 units.
P = 2(l + w)
w = 10 feet.
78 = 2(l + 10)
l + 10 = 39
l = 29
Thus, the length of the rectangle is found as 29 feet.
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What is the answer to 0.772 times 0.06
Answer: 0.04632
Step-by-step explanation:
30-12 (mod 6) pls I need solution class ss1
Answer:
30
Step-by-step explanation:
Divide
[tex]\frac{12}{6}\\\\\bold{Long\:division}\\6 \times 2 = 12\\= 2[/tex]
[tex]\mathrm{2\:remainder\:0}[/tex]
Simplify the rest of the expression
[tex]= 30 - 0\\= 30[/tex]
Hope this helps!
help!!!!!!!!!!! plsssssssssss
Answer:
1st image: -14, 4
2nd image: -0.7, 1.7
3rd image: -5/8, 7/8
Step-by-step explanation:
What I came up with...
What is the equation of the line that passes through the point (-8,-8)(−8,−8) and has a slope of 0?
Answer:
[tex]y=-8[/tex]
Step-by-step explanation:
Recall the slope formula:
[tex]m=\frac{x_{2} -x_{1}}{y_{2} -y_{1}}[/tex]
Since all of the x and y values are -8, we can easily plug in the values.
[tex]m=\frac{-8+8}{-8+8}=0[/tex]
(The second -8 on the top and bottom is positive because adding when subtracting negatives, you must add. For example -1-(-1) would become -1+1=0)
Recall the point-slope formula:
[tex]y-y_{1} = m(x-x_{1} )[/tex]
Now substitute and solve.
[tex]y-(-8)=0(x-(-8)[/tex] Substitute
[tex]y+8=0(x+8)[/tex] Simplify
[tex]y+8=0[/tex] Distributive Property
[tex]y=-8[/tex] Subtraction Property
Therefore the answer is [tex]y=-8[/tex].
Find the y-intercept of the line on the graph
Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.
As per question statement, we are supposed to determine the y-intercept of the line on the graph, but no equation of the line, or graph is provided. Hence, we considered the equation of a random line, say,
[3x +4y = 12] and then, determine it's y-intercept.
To solve this question, we can use two methods:
One method is by converting the given equation into the format of the standard equation of a line, and then comparing it to the standard equation to determine the y-intercept, i.e.,
The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,
[tex]3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)[/tex]
Now comparing (i) to the standard equation of line, we can identify that
(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.
Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".
Y-Intercept: The y-intercept is the point on a cartesian plane, where a graph crosses the y-axis, i.e., the value of y when (x = 0).To learn more about Y-Intercepts, click on the link below.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the point where the maximum value occurs for this function:
hxx) = -(x + 2)² +8.
Drawing Tools
Select
Mark Feature
Line
+
Click on a tool to begin drawing.
-10
-8
-6
-4
10-
00
Delate Undo
2
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8
Reset
10
Maximum value occurs at the vertex, given by (h,k)=(-2,8)
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The given function is: h(x) = -(x + 2)² +8.
This function is in the form: a[tex](x-h)^{2}[/tex]+k
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object. The word symmetry implies balance.
The axis of symmetry is given by x = h
By comparison, we have -h=2.
This implies h=-2
Therefore the axis of symmetry is x = -2
The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. If your quadratic equation has a negative term, it will also have a maximum value.
The maximum value occurs at the vertex, given by (h,k)=(-2,8)
See attachment for the axis of symmetry and maximum point.
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Given that lines A and B are parallel, if angle 1 measures 48 degrees and angle 2 measures 51 degrees, what is the measure of angle 3?
Answer:
81°
Step-by-step explanation:
m∠1 + m∠2 + m∠3 = 180° because they add to form a straight angle.
7 is divided by the sum of a number and 8
Answer:
n + 8 ÷ 7
Step-by-step explanation:
I think that's the answer, but I could be wrong- lol.
Janet rents a booth at the farmers market
that costs $150 a day. She sells jars of fresh
honey from her family farm for $8 each. At
the end of the day, she splits all the
money she brings home with her mom
who takes care of the bees. If j is the
number of jars of honey sold, write a
function f(j) representing how much
money Janet makes each day.
HELP PLEASEEEEEEE!!!!!!!!
It should be noted that two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5 include 0.2025 and 0.2209.
How to illustrate the information?It should be noted that based on the information, we want to find two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5.
In this case, it should be noted that 0.45 × 0.45 = 0.2025. It should be noted also that 0.47 × 0.47 = 0.2209.
As a result, 0.2025 and 0.2209 are two perfect squares such that the square root will lie between consecutive numbers of 0.4 and 0.5.
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The average amount of money spent by students in the cafeteria last week was $2.75. The actual amount spent varied by no more than $0.50. Write and solve an absolute value inequality to represent the range of possible amounts.
The average amount of money spent by students in the cafeteria last week was between $2.25 to $3.25
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let x represent the average amount of money spent by students.
The absolute value inequality is given by the equation:
|x - 2.75| = 0.5
Hence:
x - 2.75 = 0.5 or -(x - 2.75) = 0.5
x = 3.25 or x = 2.25
The average amount of money spent by students in the cafeteria last week was between $2.25 to $3.25
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8 more than negative 10
8 is greater than -10, because 8 is farther to the right than -10 in a number line.
Peeling 8 potatoes in 5 minutes
Answer:
1.6 potatoes per minute
Step-by-step explanation:
8 divided by 5 is 1.6
Helllp 20 points plus brainliest
Answer: Maxwell jogs faster.
Step-by-step explanation:
Haley jogs 3/4 miles in 10 minutes.
Maxwell jogs 2/3 miles in 8 minutes.
3/4 = .75
2/3 = .6 repeating
Add. Pllssssssss help
[tex] \bf \implies \: ( - \frac{9}{4}) \: or \: (- 2 \frac{1}{4} )\: or \: ( - 2.25 )\\ [/tex]
Step-by-step explanation:Step-by-step explanation is in attachment see and go through it
2. Let f(x) = x4 + 2x3 - x² - 2x + 10. Given that one root of f(x) is 1 + i find all other roots.
All the roots of equation x⁴ +2x³ -x² -2x +10 are: (1 + i), (1 - i), -2i, 2i
In the given question, we have to find out all the roots or solutions for the equation x⁴ +2x³ -x² -2x +10. One of the roots given for this equation is 1+i
According to the 'Complex Conjugate' pairs, if an equation has a complex number as a root then its conjugate will also be a root of the equation.
So, we get z = 1 + i as a root then z* = 1 - i which is the conjugate of z, and z* will also be a root of the equation.
Also, the product of two roots will also be a root of the equation. So,
we know that, x = 1 + i, x = 1 - i, we get their product:
(x -(1 + i))*(x - (1 - i)) => by solving we get => x² -2x +2 = 0
=> x² -2x +1 = 1 => x² -x -x +1 = 1 (by middle term split)
=> x(x-1) -1(x-1) = 1 => we get (x - 1) as a factor
So, (x - 1) = 1 => x = 2
=> x = -2i, we get x = -2i
Again, by Complex conjugate pairs if x = -2i is a factor then it's conjugate x = 2i is also a factor.
Hence, the roots of the equation are: (1 + i), (1 - i), -2i, 2i
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Which step in the construction of copying a line segment ensures that the new line segment has
the same length as the original line segment?
Answer:
Fill in the blanks to declare sum equal to a + b (int _ = a __b
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PLSSSSSS Will records the wins and losses for his high school basketball team each year. He notices that the ratio of wins to losses has been consistent each year. Wins Losses 18 2 45 5 36 4 27 x Using the information in the table, how many losses should he predict for next year if the number of games won is 27? Group of answer choices 9 1 3 6
Do the ratios 2 1 and 14 9 form a proportion?
No the given two ratios not form a proportion.
Any relationship that has a constant ratio is said to be proportional. For instance, the ratio of proportionality is the average number of apples per tree, and the number of apples in a crop is proportional to the number of trees in the orchard.
Two equivalent fractions are typically used to represent a proportion. For instance: The ratios on either side of the equal sign can be seen in the equation. Because inches and feet are consistent units, each ratio compares the same units, and as a result, all ratios are equivalent. Two quantities are compared to form a ratio. An equality of two ratios is a proportion.
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Solve for m.
m – 6.82 = 9.24
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer:
Hi
Step-by-step explanation:
Diego is actually and totally wrong
because √4 divide 2= 2 divide 2 =1
and 4/2=2
pls rate as brainliest
Need help with #9! Intermediate Algebra.
Answer:12.35 = t
Step-by-step explanation:
95 + t + 3.5 = 110.85
where t = tax
12.35 = t
The table below shows the cost of gasoline based on the number of gallons purchased. Gallons Purchased Cost of Gasoline 5 $16.25 8 $26.00 11 $35.75 14 $45.50 Which equation represents the cost, y, of x gallons of gasoline? Responses
The equation that represents the cost, y, of x gallons of gasoline, is expressed as: y = 3.25x.
How to Create a Linear Equation for a Table?To create an equation in slope-intercept form, y = mx + b, for a table of values, use two pairs of values from the table to find the slope (m) and determine the y-intercept (b).
Using (5, 16.25) and (8, 26.00) find the slope (m):
Slope (m) = change in y / change in x = (26.00 - 16.25) / (8 - 5)
Slope (m) = (9.75) / (3)
Slope (m) = 3.25
Find the y-intercept (b) by substituting m = 3.25 and (8, 26.00) into y = mx + b:
26.00 = 3.25(8) + b
26.00 = 26.00 + b
26.00 - 26.00 = b
0 = b
b = 0
Substitute m = 3.25 and b = 0 into y = mx + b:
y = 3.25x + 0
y = 3.25x
Therefore, the equation that represents the cost, y, of x gallons of gasoline, is expressed as: y = 3.25x.
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