Rachel is correct because Rachel ran farther than Beth .
In the question ,
it is given that ,
Rachel ran 115 yards and Beth ran 327 yards ,
For comparing both the distance , we need to convert both the distance in the same unit ,
So , we convert yards to feet ,
we know that,
1 yard = 3 foot ,
So, 115 yard = 3*115 = 345 feet ,
Rachel ran 345 feet and Beth ran 327 feet .
hence , we can conclude that Rachel ran 345 feet which is greater than Beth , who ran only 327 feet .
Therefore , Rachel is correct because Rachel ran farther than Beth .
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Determine the minimum and maximum value for f(x) = -5x²-3x+7 over interval [-1, 3].
The maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. A number that can be entered for the variable to produce a true number statement is the solution to an equation. 3(2)+5=11, which states that 6+5=11, is accurate. The answer is 2, then. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the minimum and maximum values when x are -1 and 3:
(1) When x = -1:
f(x) = -5x²-3x+7f(x) = -5(-1)²-3(-1) +7f(x) = -5(1) + 3 +7f(x) = -5 + 10f(x) = 5(2) When x = 3:
f(x) = -5x²-3x+7f(x) = -5(3)² -3(3)+7f(x) = -5(9) -9 +7f(x) = -45 -9 +7f(x) = - 54 + 7f(x) = - 47Therefore, the maximum and minimum value of the equation "f(x) = -5x²-3x+7" over the interval [-1, 3] is 5 and -47.
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Simplify. -(-6w + x - 3y)
Answer: 6w - x + 3y
Step-by-step explanation:
identify the terms ,coefficients constants in 5c2 + 7d
Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.
In the given expression:
[tex]5c^2+7d[/tex]There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.
With the information given, find the lenght of the prism
Answer:
The lenght of the prism is 22 cm.
Step-by-step explanation:
From the given drawing, we can conclude that a one-unit line measures 2 cm. Since the prism is 11 unit lines long, we can conclude that it is 22 cm.
A population of a certain species of bird is 22,000 animals and is decreasing by 700 birds per year..Write an equation for y, the population at time t (in years), representing the situation.y= How many birds are in the population after 7 years?
We can solve that problem using a linear function, we know that
[tex]y=mx+y_0[/tex]Where y0 is the initial population and m is the rate of decreasing, we know that for each "x" years we have -700 birds, therefore
[tex]y=-700x+22000[/tex]Let's use t instead of x
[tex]y=-700t+22000[/tex]That's the equation that represents the population at time t
[tex]\begin{gathered} y=-700t+22000\text{ \lparen t = 7\rparen} \\ \\ y=-700\cdot(7)+22000 \\ \\ y=-4900+22000 \\ \\ y=17100 \end{gathered}[/tex]Therefore after 7 years, the population will be 17100 birds.
how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Determine whether the ratios are equivalent.
2:3 and 24:36
O Not equivalent O Not equivalent
We can conclude that the given ratios 2:3 and 24:36 are equivalent.
What are ratios?A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ratios are equivalent or not:
2:3 and 24:362/3 = 24/362/3 = 2/3 (Divide by 12)Then, 2:3 :: 2:3
Therefore, we can conclude that the given ratios 2:3 and 24:36 are equivalent.
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Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 milesfrom city B, how far is city A from city B?City Ais 20 miles due east of city B.City A is 35 miles due east of city B.City A is 42 miles due east of city B.City A is 122 miles due east of city B.
Given:
City A is due east of city B.
City C is located 35° west of north from city B.
Distance between city C and city A is 100 miles.
Distance between city C and city B is 70 miles.
The objective is to find the distance between city A and city B.
The above situation can be represented as,
Thus the total angle of ∠B = 90°+35° = 125°.
Now the measure of angle A can be calculated by law of sines.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{100}{\sin125\degree}=\frac{70}{\sin A} \\ \sin A=70\cdot\frac{\sin 125\degree}{100} \\ \sin A=0.573 \\ A=\sin ^{-1}(0.573) \\ A\approx35\degree \end{gathered}[/tex]By the angle sum property of triangle the value of angle C can be calculated as,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 35\degree+125\degree+\angle C=180\degree \\ \angle C=180\degree-35\degree-125\degree \\ \angle C=20\degree \end{gathered}[/tex]Now, the distance between A and B can be calculated by,
[tex]\begin{gathered} \frac{AB}{\sin C}=\frac{BC}{\sin A} \\ \frac{AB}{\sin20\degree}=\frac{70}{\sin 35\degree} \\ AB=\sin 20\degree\cdot\frac{70}{\sin 35\degree} \\ AB\approx42\text{ miles} \end{gathered}[/tex]Thus, the distance of city A is 42 miles due east of city B.
Hence, option (C) is the correct answer.
two parallel lines are intersected by a transversal one angle is 100 degrees, more info on the picture
Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.
Explain about the obtuse angle?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.
Hence obtuse angle is one of the angle which is not correct 100 degree angle
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On a recent survey, students were asked if they ice skate, snowboard, or ski. The Venn diagram below shows the results of the survey
The number of students who took the survey was 47 (option B).
How to identify the number of students who took the survey?To identify the number of students who took the survey, we must look at the number of students in each of the Venn diagram spaces. In this case, the number of students who practice each sport are:
Ice Skate: 7 students.Snowboarding: 10 students.Ski: 13 students.Ice Skate and Snowboard: 4 students.Ski and Snowboard: 8 students.Ice Skate and Ski: 2 students.Ice Skate, Snowboard and Ski: 3 students.To know the number of students who took the survey, we must add the number of students in each space as shown below:
7 + 10 + 13 + 4 + 8 + 2 + 3 = 47According to the above, the correct answer is option B, since 47 students took the survey.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
How many students took the survey?
Options
A.32
b.47
c.53
D.56
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Describe where the function has a hole and how you found your answer.
Step 1:
Write the function
[tex]f(x)\text{ = }\frac{x^2+\text{ 7x + 10}}{x^2\text{ + 9x + 20}}\text{ }[/tex]Step 2:
Factorize both the numerator and the denominator.
[tex]\begin{gathered} f(x)\text{ = }\frac{x^2\text{ + 2x + 5x + 10}}{x^2\text{ + 4x + 5x + 20}} \\ f(x)\text{ = }\frac{x(x\text{ + 2) + 5(x + 2)}}{x(x\text{ + 4) + 5 (x + 4)}} \\ f(x)\text{ = }\frac{(x\text{ + 5)(x +2)}}{(x\text{ + 5)(x + 4)}} \end{gathered}[/tex]Step 3:
A hole is a common factor between the numerator and the denominator.
Hole: x + 5 = 0
x = -5
Final answer
Hole is -5
Which of the following is the horizontal asymptote for the graph below?10A x=-7B. X=0ООC. y - 0C D. y = -7
A horizontal like y = k, where k is not part of the graph, but guides the function for x-values “far” to the right and/or “far” to the left.
The horizontal asymptote can be observed in the figure below:
Answer: y = 0.
Add the complex numbers 3 + 11i and -3 - 11i.6 + 0i0 + 0i0 + 22i- 9 + 121i
SOLUTION
The given complex unbers are:
[tex]3+11i,-3-11i[/tex]Add the complex numbers:
[tex]3+11i+(-3-11i)[/tex]Simplify the expression:
[tex]\begin{gathered} 3+11i-3-11i \\ =3-3+11i-11i \\ =0+0i \end{gathered}[/tex]Therefore the required answer is: 0+0i
Roberts Company has the following sales budget for the first four months and the year:
January February March April
Budgeted units to sell
200
400
800
950
Total - 2,350
Sales price per unit
$25
$25
$25
$25
Total-$25
Total sales
$5,000
$10,000
$20,000
$23,750
Total - $58,750
What is the new amount of budgeted total sales for March if the budgeted number of units is expected to be 1,100 units instead of 800 units?
A. $27,500
B. $10,000
C. $47,500
D. $66,250
Using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, new amount of budgeted total sales for March:
So, we know that:
2350 × 25 = $58,750And 2350 is further:
2350 = 200 + 400 + 800 + 950.Let's replace 800 with 1100.
Now, solve as follows:
200 + 400 + 1100 + 950 = 2,6502,650 × 25 = $66,250Therefore, using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.
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you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]Solve. Your answer should be in simplest form. 2/5 (−3/7)
Answer:
2/5 (-3/7) = -6/35 ≅ -0.1714286
Step-by-step explanation:
and that’s how you do it
Add: 2/5 + 3/7 = 2 · 7/5 · 7 + 3 · 5/7 · 5 = 14/35 + 15/35 = 14 + 15/35 = 29/35.
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 7) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two fifths plus three sevenths is twenty-nine thirty-fifths.
Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
The net of a cone is shown below. What is the surface area of the cone rounded to the nearest tenth of a square inch? Use π = 3.14.A. 125.6 in²B. 1,256.6 in²C. 175.8 in²D. 251.3 in²
ANSWER
[tex](C)175.8in^2[/tex]EXPLANATION
The surface area of a cone can be found using the formula:
[tex]A=\pi r^2+\pi rl[/tex]where l = slant height
r = radius
The diameter of the cone is given, but we can find the radius since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{8}{2} \\ r=4\text{ units} \end{gathered}[/tex]From the figure, the slant height of the cone is 10 units.
Hence, its surface area is:
[tex]\begin{gathered} A=(\pi\cdot4^2)+(\pi\cdot4\cdot10) \\ A=50.24+125.6 \\ A\approx175.8in^2 \end{gathered}[/tex]The answer is option C.
Kaylee drove 160 miles in 5 hours. If she continued at the same rate, how far would she travel in 17 hours?
The distance covered by Kaylee in 17 hours at the same rate is 544 miles.
According to the question,
We have the following information:
Distance covered by Kaylee = 160 miles
Time taken by Kaylee = 5 hours
We know that the following formula is used to find the speed:
Speed = distance/time
Speed = 160/5 mile/hour
Speed = 32 miles/hour
Now, we have to find the distance when time taken is 17 hours and the speed is the same.
Now, from the formula of speed, we can find the distance:
Distance = speed*time
Distance = 32*17
Distance = 544 miles
Hence, the distance covered by Kaylee in 17 hours is 544 miles.
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4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6
To find the value of y
4(y – 4) = 8
Divide both-side of the equation by 4
y - 4 = 2
Add 4 to both-side of the equation
y = 2 + 4
y = 6
D is the correct option
How many solutions does the system formed by x − y = 4 and ay − ax + 4a = 0 have for a nonzero number a? Give your answer and complete the explanation.
Given system of equations have no solutions that is nonzero.
We have been given the system of equations formed by x − y = 4 and ay - ax + 4a = 0
We need to find the number of non-zero solutions the system have for a nonzero number 'a'
x - y = 4 ............(1)
ay - ax + 4a = 0 ............(2)
From equation (1),
x = 4 + y
Substitute x = 4 + y in equation (2),
ay - a(4 + y) + 4a = 0
ay - 4a - ay + 4a = 0
-4a + 4a = 0
0 = 0
This means that the system have no solutions that is nonzero.
Therefore, given system of equations have no solutions that is nonzero.
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Ishaan started a toy car collection. His grandfather gave him 15 cars to start his collection. He can use his allowance to add 4 cars to his collection every month. Which equation can be used to find y, the total cars in his collection after x months?
The equation that he can use to find y, the total cars in his collection after x months is y = 15 + 4x.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of months be x.
Let the number of cars be y.
The equation will be:
y = 15 + (4 × x)
y = 15 + 4x
This illustrates the equation.
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I need help with my algebra
We have the next equation line:
[tex]3x-y\text{ = 5}[/tex]We need to solve the equation for y to get the equation form
[tex]-y\text{ =5-3x}[/tex]Multiply the equation by -1
[tex](-1)-y\text{ =(-1)(5-3x)}[/tex][tex]y\text{ = -5+3x}[/tex]Where the y-intercept is -5 and the slope is 3x.
To find the line parallel we need to know that the parallel lines have the same slope.
The parallel line also intercepts y at point (0,-7).
[tex]y=mx+b[/tex]Replace the slope=m = 3
and the y-intercept is -7.
So the parallel line is:
[tex]y=3x-7[/tex]Plot the Trapezoid ABCD with vertices A(-8,-4),B(-5, -1), C(0, -2), and D(-4,-8) in the x-axis.
Let's begin by listing out the information given to us:
ABCD is a trapezoid
A (-8, -4); B (-5, -1); C (0, -2); D (-4, -8)
We will proceed to plotting this points on a Cartesian plane, we have:
Let f(x) = 2x-1 and g(x) = x2 - 1. Find (f o g)(-7).
Answer: (f o g)(-7) = 95
Step by step solution:
We have the two functions:
[tex]\begin{gathered} f(x)=2x-1 \\ g(x)=x^2-1 \end{gathered}[/tex]We need to find (f o g)(-7) or f(g(-7)), first we evaluate g(-7):
[tex](f\circ g)(-7)=f(g(-7))[/tex][tex]g(-7)=-7^2-1=49-1=48[/tex]Now we evaluate f(48):
[tex]f(48)=2\cdot48-1=96-1=95[/tex]Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]The statement listed below is false. Let p represent the statement.
We will have that the negation of the statement would be:
*That product did not emerge as a toy in 1949. [Option B]
Given that events A and B are independent with P(A) = 0.08 and P(B) = 0.25,determine the value of P(A and B), rounding to the nearest thousandth, ifnecessary.
To find: P(AandB)
P(AandB)=P(A)*P(B)
P(AandB)=0.08*0.25
P(AandB)=0.02
Thus the required answer is 0.02
The one-to-one function f is defined below.
The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively
How to determine the inverse function?The definition of the function is given as
f(x) = 6x/7x - 5
Rewrite the function as
y = 6x/7x - 5
Next, we swap or switch the variables x and y
So, we have the following equation
x = 6y/7y - 5
Cross multiply in the above equation
This gives
x(7y - 5) = 6y
Open the brackets
7xy - 5x = 6y
Collect the like terms
7xy -6y = 5x
Factor out y
y(7x -6) = 5x
So, we have
y = 5x/(7x -6)
Express as inverse function
f-1(x) = 5x/(7x -6)
Using a graphing calculator, we have
Domain: x < 6/7 or x > 6/7
Range: f(x) < 5/7 or f(x) > 5/7
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