The number of time it take Katherine to drive from home back to college is: 3 hrs 21 min.
How to find the time?Going home:
Rate = 65.1 mph , distance = x miles ; time = distance /rate = x/ 65.1 hrs
Going to college:
Rate = 70.7 mph ; distance = x miles ; time = x/70.7 hrs
Equation:
x/70.7+ x/ 65.1= 11
70.7x + 65.1x = 7 × 65.1 × 70.7
Combine like terms
135.8x = 32,217.99
Divide both side by 135.8x
x = 32,217.99/ 135.8
x = 237.25 miles
Home back to college
= 237.25 /70.7
=3.35 hrs
= 3 hrs 21 min
Therefore it take Katherine 3 hrs 21 min.
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Solve for x
X+59+80+50=180
Answer: x= -9
Step-by-step explanation:
Add like terms excluding x in: x+59+80+50=180
= x+189=180
[Transposing 189 to RHS] x=180-189
So x= -9
Here is a function, double numbers (int x), what data type will this function return?.
The function will return the data type double.
Simply put, a function is a "chunk" of code that you can reuse repeatedly rather than having to write it out several times. Programmers can divide a problem into smaller, more manageable chunks, each of which can carry out a specific task, using functions.
Function declaration type will be as follows in general,
return type function name(argument 1, argument 2,...)
In the given question the declaration is double numbers (int x).
The return type is double, the name of the function is numbers and it has one argument which in an integer.
Hence, the return type of the function is double.
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PLEASE HELP ME HERE ITS DUE TOMMOROW! I'LL GIVE U 30 POINTS FOR THIS!!!
Answer:
1.9
2.3
3.6
4.5
5.20
Step-by-step explanation:
hope it helps
isosceles triangle abc has a perimeter of 96 centimeters. the base of the triangle is line segment a c and measures 24 centimeters.
The measure of the line segment AB is 36cm .
In the question ,
it is given that ,
The triangle ABC is a isosceles triangle ,
that means side AB = side BC ,
and the length of base AC = 24 cm .
given the perimeter of the triangle is 96 cm .
So ,
AB + BC + AC = 96
AB + AB + AC = 96 .....because AB = BC
2AB + AC = 96
Substituting the value of AC = 24 cm
2AB + 24 = 96
Subtracting 24 from both the sides , we get
2AB = 96 - 24
2AB = 72
Dividing both sides by 2 ,
we get ,
AB = 72/2 = 36 .
Therefore , The measure of the line segment AB is 36cm .
The given question is incomplete , the complete question is
Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is Line segment A C and measures 24 centimeters.
What is the measure of Line segment AB ?
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Determine the equation of the polynomial, f(x), of minimum degree whose graph is shown above. Write your answer in factored form.
f(x)=____
Answer:
[tex]f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]
Step-by-step explanation:
The root -2 has a multiplicity of 2, and corresponds to a factor of [tex](x+2)^2[/tex].
The root 1 has a multiplicity of 1, and corresponds to a factor of [tex](x-1)[/tex].
The root 3 has a multiplicity of 1, and corresponds to a factor of [tex](x-3)[/tex].
So, [tex]f(x)=a(x+2)^2(x-1)(x-3)[/tex].
Since [tex]f(0)=10[/tex],
[tex]10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)[/tex]
Find the prime factorization of
the number 68.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [×]
Enter the number that belongs in the green box.
The prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the prime factorization of the number 68
Prime factorization is a process of writing all numbers as a product of primes.
The prime factorization of 68 is 2×2×17
The prime factors of 68 are 2 and 17.
The least prime number is 2 and greatest prime number is 17.
Hence the prime factorization of the number 68 is 2×2×17 and least prime number is 2 and greatest prime number is 17.
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Convert the following equations from standard form to slope intercept form. -2x+3y=-6
Converting the given equations from standard form to slope intercept form gives
standard form -2x + 3y = -6 slope intercept y = 2x/3 - 2How to Convert the equations from standard form to slope interceptInformation given in the question include
-2x+3y=-6
Standard form of linear equations is of the form Ax + By = C
The slope intercept form is y = mx + c
rearranging the equation
-2x + 3y = -6
3y = 2x - 6
y = 2x/3 - 2
The equation of the line in slope intercept form is y = 2x/3 - 2
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The perimeter of a rectangle is 68 cm. If the diagonal 26
is 26 cm, find the dimensions of the rectangle.
The dimensions of the rectangle are either 10cm x 24cm or
24cm x 10cm having perimeter 68 cm.
What is Pythagorean theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
A rectangle has 4 angles measure of each is 90°.
A diagonal of rectangle divides it into two right angled triangles.
Pythagorean theorem can be applied on these triangles to get the desired values.
According to the given question:
Let the length and breadth of rectangle be x and y .
Perimeter: 2x + 2y = 68 (Given)
Using Pythagorean theorem diagonal: [tex]x^2+y^2=26^2[/tex]
Using perimeter, x + y = 34
∴ x = 34 - y
Substituting this is the equation for diagonal
[tex](34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0[/tex]
Therefore dimensions of rectangle are either 10cm x 24cm or
24cm x 10cm.
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Find the measure of all three interior angles and exterior angles
Check the picture below.
Answer:
Exterior angle: 86°
Base angle: 43°
Base angle: 43°
Third angle: 94°
Step-by-step explanation:
First we'll find x, then calculate all the angles.
There is a mark on two of the sides of the triangle. Two sides are the same. This is an isosceles triangle. So that means the base angles are the same also. One is marked 5x - 12, so the other base angle is also 5x - 12.
The marked exterior angle has a special relationship with the two remote interior angles.
If you add the two remote interior angles it equals the exterior angle.
8x-2 = 5x-12 + 5x-12
Combine like terms.
8x - 2 = 10x - 24
Subtract 8x.
-2 = 2x - 24
Add 24.
22 = 2x
Divide by 2.
11 = x
Now we can find all the angles.
The exterior angle is 8x - 2
= 8(11) - 2
= 88 - 2
= 86°
Base angle is 5x - 12
= 5(11) - 12
= 55 - 12
= 43°
The last angle in the triangle is a linear pair with the exterior angle. Or (Also,) the three angles in the triangle add up to 180°.
Angle+43°+43°=180°
Angle + 86 = 180
Angle = 94°
what is the probability of rolling a yahtzee on the first round? round your answer to 4 decimal places. enter your answer into variable
The probability of rolling a yahtzee on the first round is calculated to be 6/46656 or 1/7776
Given that,
A dice is rolled for one time .
To find : The probability that a yahtzee will be rolled on the first round.
Your first die will be one of the 6 possible results 6/6 times
That will match on the second die 1/6th of the time.
The third, fourth, and fifth dice all share this characteristic.
Multiplying the all probabilities that the first die will be a yahtzee which is
P( yahtzee will be rolled on the first round) = Product of all possible outcomes of each time a dice is rolled.
6/6*1/6*1/6*1/6*1/6*1/6=6/46656 or 1/7776
Therefore, probability that a yahtzee will be rolled on the first round is 1/7776.
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PLEASE HELP!!!
for points
Complete each row of the table.
The Hiking club will be 0.6.
The completion for the row of the table will be:
Grade 7
Dance club: 0.25
Hiking club: 0.75
Total : 1
Grade 8:
Dance club: 0.40
Hiking club: 0.60
Total : 1
How to calculate the values?
The dance club for grade 7 will be calculated as:
= Number of dancers / Total number
= 5/20
= 0.25
The hiking club will be:
= 15/20
= 0.75
The dance club for grade 8 will be calculated as:
= Number of dancers / Total number
= 20/50
= 0.4
The hiking club will be:
= 30/50
= 0.6
Hence, The Hiking club will be 0.6.
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Please write a linear equation that has m=-4 and has an x-intercept of (5,0)!
Answer:
If you use y = mx + b, your equation would be y = -4x + 20
Step-by-step explanation:
M is always the slope, and to find the x-intercept, you just set y = 0 and in this case it would be 0 = -4x + 20. If you subtract 20 from both sides you get -20 = -4x and to find x, you just divide by -4 and get -20/-4, which equals 5. You're welcome :)
We need to determine the value of the y-intercept for this equation. Let's start by finding all other information about the x-intercept.
If the x-intercept is x = 5, f(5) = 0. So, now let's solve for b.
f(5) = -4(5) + b
0 = -4(5) + b
0 = -20 + b
0 + 20 = -20 + 20 + b
b = 20
We have m and b now, so:
y = -4x + 20
Graph the polynomial
1- g(x) = (x+5)^4
2- f(x) = 7- (x) ^4.
3- h(x) = 1/4 ( x-3 )^4
Don't forget to find x-int. and y-int.
Answer:
The x-intercept is the point where the graph crosses the x-axis; it can be found by setting y = 0 and solving for x.
The y-intercept is the point where the graph crosses the y-axis; it can be found by setting x = 0 and solving for y.
1) g(x) = (x + 5)⁴
y-intercept: g(x) = (0 + 5)⁴ → (0, 625)x-intercept: 0 = (x + 5)⁴ → (-5, 0)2) f(x) = 7 - x⁴
y-intercept: f(x) = 7 - 0⁴ → (0, 7)x-intercept: 0 = 7 - x⁴ → (±[tex]\sqrt[4]{7}[/tex], 0)3) h(x) = ¼(x - 3)⁴
y-intercept: h(x) = ¼(0 - 3)⁴ → (0, [tex]\frac{81}{4}[/tex])x-intercept: 0 = ¼(x - 3)⁴ → (3, 0)The graphs are labeled below.
A new pair of Jordans are going to drop in a couple weeks and you know you just have to have them. It looks like the/il
be expensive, so you decide to start babysitting your cousin to make the money. You already have $42 saved up and
you will make $6 for every hour of babysitting. The shoes will cost at least $90.
a) What’s the initial cost
Answer:
incomplete question..please complete the question to get the answer. there are some missing details
A spherical balloon has a 8-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere.
a. Find the volume of the fully-inflated balloon.
b. Find the volume of the half-inflated balloon.
c. What is the radius of the half-inflated balloon?
The volume of the fully inflated balloon is 267.95 cubic inches, the volume of half-inflated balloon is 133.97 cubic inches and it's radius is 3.17in
Volume of a SphereThe volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
The formula of a sphere is given as
v = 4/3πr³
But diameter = 2 * radius
radius = diameter / 2
radius = 8/2
radius = 4in
The volume of the fully inflated balloon will be
v = 4/3πr³
v = 4/3 * 3.14 * 4³
v = 267.95in³
The volume of the fully inflated balloon is 267.95in³
b) The volume of the half-inflated balloon will half the size of the current volume
v = 267.95in³ / 2 = 133.97in³
c) v = 4/3πr³
133.97 = 4/3 * 3.14 * r³
r = 3.17in
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Find the slope and the y-intercept of the line.
y=4x-7
Answer:
slope: 4
Y intercept: -7
Step-by-step explanation:
slope intercept form is y=Mx+b
m- slope
b- y intercept
Looking at this equation where m is 4 is so the slope is 4
And where b is -7 is so the y intercept is -7
Hopes this helps please mark brainliest
Rewrite each expression without using absolute value bars.
|3r-15| if r<5
Rewriting the expression |3r-15| without using absolute value bars gives
3r < 15 for r < 5
How to write the expression without using the absolute value barsAbsolute value do not give negative values it gives only the positive value
The given expression is |3r-15|
|3r - 15| < 0
|3r| < |-15|
3r < 15
If r < 5 then say 4
|3r - 15|
|3 * 4 - 15|
|12 - 15|
|-3| = 3
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Consider function f.
f(x) = 2² - 2 + 6
Which statement is true about the parabola modeled by function ?
O A.
OB.
O C.
O D.
The parabola has a minimum value of 5.75.
The parabola has a maximum value of 5.75.
The parabola has a maximum value of 0.5.
The parabola has a minimum value of 0.5.
The parabola has a minimum value of 5.75.
From the question, we have
f(x)=x^2-x+6
a=1, b=-1, c=6
Δ=b^2-4ac
=1-24
=-23<0
So f(x)=0 has no solution.
x=-b/2a=-(-1)/2=1/2
f(1/2)=1/4-1/2+6
=23/4 is the minimum
=5.75
The parabola has a minimum value of 5.75.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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2. Carmen, Memo, Poncho y Jocelyn están en
una carrera de bicicletas. Carmen lleva 3/5
del trayecto, Memo 4/7, Poncho 3/4 y
Jocelyn 1/2, ¿quién lleva más recorrido?
Poncho ha recorrido más trayecto de la carrera de bicicletas, con una fracción de 3/4 del recorrido.
Problema de comparación de fracciones:
Carmen lleva: 3/5 del trayecto
Memo: 4/7
Poncho: 3/4
Jocelyn: 1/2
Una forma de comparar las fracciones es usando un mismo denominador, esto es posible con el Mínimo Común Múltiplo (MCM):
MCM(2,4,5,7) = 2² · 5 · 7 = 140
Fracciones con mismo denominador:
3/5 = (3 · 7 · 4)/(5 · 7 · 4) = 84/140
4/7 = (4 · 5 · 4)/(7 · 5 · 4) = 80/140
3/4 = (3 · 5 · 7)/(4 · 5 · 7) = 105/140
1/2 = (1 · 2 · 5 · 7)/(2 · 2 · 5 · 7) = 70/140
Comparando:
70/140 < 80/140 < 84/140 < 105/140
1/2 < 4/7 < 3/5 < 3/4
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Given h(x)=-x+5h(x)=−x+5, find h(-3)h(−3).
The expression we get from the given functions h for all real numbers x.
h(-3)= 8
Given that,
All real numbers x are defined by the functions h.
h(x)= -x+5
We have to find the expression
h(-3)
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
Take the functions,
h(x)= -x+5
Now, Take
h(-3) =-(-3)+5 = 3+5= 8
Therefore, The expression we get from the given functions h defined for all real numbers x.
h(-3)=8
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Identify the variation as a direct, inverse, joint, or combined.
xy/z=c
The given equation is a combined variation.
We have been given an equation is
[tex]\frac{xy}{z}[/tex]
This is an equation in which we have three variables and one constant.
This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.
So, Direct and inverse options are discarded.
So, either It can be joint or combined
In joint variation both the variables are directly proportional
Hence, given equation is not joint because if we rewrite the equation we will get [tex]y = \frac{cz}{x}[/tex] both the variables are not directly proportional.
In combined, one variable is directly proportional and the other one is inversely proportional.
From [tex]y = \frac{cz}{x}[/tex] we can see that z is directly proportional and x is inversely proportional.
Hence the answer is, the given equation is combined variation.
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(w+1)°
91 ° algebraic
The value of w in Angle (w + 1)° is 88
Given,
Angle (w + 1)°
Angle 91°
We have to find the value of w.
Here,
Linear pair of angles;
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Then,
Here the given angles are linear pair.
So,
(w + 1)° + 91 = 180
w + 1 + 91 = 180
w + 92 = 180
w = 180 - 92
w = 88
Then,
Angle (w + 1)° = 88 + 1 = 89°
Therefore,
The value of w in Angle (w + 1)° is 88
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If h(x) = 3x² – 5x – 2, find h(2)
Answer:
h(2) = 0
Step-by-step explanation:
1) 2 * 2 = 4
2) 4 * 3 = 12
3) 5 * 2 = 10
4) 12 - 10 - 2 = 0
Fully factorise this expression
Answer:
3k(7k + 4)
Step-by-step explanation:
1. Find the GCF of all terms in the polynomial
2. Express each term as a product of the GCF and another factor.
3. Use distributive property to factor out GCF
4. The first three terms of an infinite geometric sequence are m- 1,6, m + 8.
(a)write down two expressions for r.
(b) the find two possible values of m.
(c) Hence, find two possible values of (r)
For the given infinite geometric sequence,
(a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
What are Geometric Series?
A geometric sequence's finite or infinite terms are added together to form a geometric series. The geometric series that corresponds to the geometric sequence a, [tex]a,ar, ar^{2} ,..., ar^{n-1} ,...[/tex] is [tex]a+ar+ar^{2}+...+ar^{n-1} +...[/tex] Clearly, "series" means "sum." The phrase "geometric series" refers specifically to the total of words with a common ratio between every adjacent pair of them. Finite and infinite geometric series are both possible.What is the Common Ratio of an Infinite Geometric Sequence?
The common ratio (r) of a geometric sequence or series is defined as the ratio between the two consecutive terms of it.The common ratio of an infinite geometric sequence, [tex]a_{0} , a_{1} ,a_{2} ,a_{3} ,...[/tex] is given as [tex]r=\frac{a_{1} }{a_{0} } =\frac{a_{2}}{1}[/tex]In the question, the first three terms of an infinite geometric sequence are given as, m-1, 6, m+8
[tex]\implies a_{0} =m-1, a_{1}=6,[/tex] and [tex]a_{2}=m+8[/tex]
So, the common ratio is calculated as,
[tex]r=\frac{6}{m-1}=\frac{m+8}{6}[/tex]
Here, there are two expressions,
[tex]r=\frac{6}{m-1}[/tex] ------(1), and [tex]r= \frac{m+8}{6}[/tex] ------(2)
Simplifying (1), we get
[tex]r(m-1)=6[/tex] -----(3)
Simplifying (2), we get
[tex]6r=m+8\\\implies r= \frac{m}{6}+\frac{8}{6}[/tex] ------(4)
Now, substituting the values of (4) in (3), we get
[tex](\frac{m}{6}+\frac{8}{6})(m-1)=6\\\implies \frac{m^{2} }{6}-\frac{m}{6} +\frac{2m}{3}-\frac{2}{3} =6\\\implies m^{2}+3m-4=36\\[/tex]
Solving further, we get
[tex]\implies m^{2}+3m-40=0\\\implies m=5, m=-8[/tex]
So, when [tex]m=5, r=\frac{6}{5-1}=\frac{3}{2}[/tex]
Also, when [tex]m=-8, r=\frac{6}{-8-1}=-\frac{2}{3}[/tex]
Therefore, (a) the two expressions for r are [tex]r=\frac{6}{m-1}[/tex] and [tex]r= \frac{m+8}{6}[/tex]
(b) The two possible values of m are -8 and 5.
(c) The two possible values of r are [tex]-\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex]
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yvaries directly as x
and y=30 when x=5,find
a) K b) equation
need help po i need it right now po complete answer po
help please and thankyou6
In triangle ABC, the value of angle A is 60°.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the triangle ABC,
b=5cm, c=10cm
And by using Pythagoreans theorem,
a²=c²-b²
a²=10²-5²
a²=75
Use cosine rule to determine the angle A,
cosA=b²+c²-a²/2bc
cosA=25+100-75/2×5×10
cosA=50/100
cosA=1/2
cosA=cos60
⇒A=60°
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an article summarizes a report of law enforcement agencies regarding the use of social media to screen applicants for employment. the report was based on a survey of 731 law enforcement agencies. one question on the survey asked if the agency routinely reviewed applicants' social media activity during background checks. for purposes of this exercise, suppose that the 731 agencies were selected at random, and that you want to use the survey data to decide if there is convincing evidence that more than 25% of law enforcement agencies review applicants' social media activity as part of routine background checks.
a) The sampling proportion's mean value is 0.25. 0.016 is the standard deviation. The form resembles a bell.
b) There is a 10% possibility of getting this number, p=0.27 or more, given a sample proportion, so I wouldn't be surprised.
c) Since there is no chance that the sample fraction of 0.31 will occur, I would be shocked if it did.
Given,
a) The null hypothesis proportion would be the middle of the sampling distribution (p-0.25). So, p=0.25 is the sampling proportion's mean value.
This would be the standard deviation:
σp = √(p (1 - p) / n) = √(0.25 × 0.75/731) = 0.016
The distribution would resemble a binomial distribution, hence the form would be bell-shaped.
b) By calculating the z-value and checking for its probability in the standard normal distribution, we may determine the likelihood of a value p=0.27 in this distribution.
z = (p - π) / σp = (0.27 - 0.25) / 0.016 = 0.02/0.016 = 1.25
p(z > 1.25) = 0.106
There is a 10% probability of achieving this value, p=0.27 or more, for a sample proportion, so I wouldn't be surprised.
c) We repeat the calculation for p=0.31
z = (p - π) / σp = (0.31 - 0.25) / 0.016 = 0.06/0.016 = 5
p(z > 5) = 0.000
I would be astonished to see that value because the probability of this sample fraction occurring at p=0.31 is zero.
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Two Tofurkys will serve six people. How many people will fourteen Tofurkys serve?
how to solve this and answer
After simplifying the equation, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.
From the given question,
Let that chemist used x, y, z liters of 20%, 35% and 80% solution respectively.
Then according to the given information,
x+y+z=54..........(1)
As we know that in x liters having 20% acid, in y liters having 35% acid, in z liters having 80% acid and in total mixture having 50% acid.
So the equation should be
x ×20%+y×35%+z×80%=54×50%
On simplifying we get
20x+35y+80z=2700
4x+7y+16z=540...............(2)
As given that the number of 80% solution used in 2 times the number of liters of 35% solution used.
So z=2y
Now putting the value of z in equation (1)
x+y+2y=54
x+3y=54
Subtract 3y on both side
x+3y−3y=54−3y
x=54−3y
Now putting the value of x and z in equation (2)
4(54−3y)+7y+16×2y=540
Simplifying
216−12y+7y+32y=540
216+27y=540
Subtract 216 on both side
216+27y−216=540−216
27y=324
Divide by 27 on both side
27/27 y=324/27
y=12
Now putting the value of y in x=54−3y to find the value of x
x=54−3×12
x=54−36
x=18
Now putting the value of y in z=2y to find the value of z
z=2×12
z=24
Hence, the chemist used 18 liters of 20% solution, 12 liters of 35% solution and 24 liters of 80% solution.
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