Given that Angelo's kayak travels 10km/h in still water, and the river's current flows at a rate of 4km/h.
Travelling downstream means Angelo is travelling with the current, that is the current of the water will add to Angelo's speed.
Their combined speed will be;
[tex]\begin{gathered} v=10\text{ km/h + 4 km/h} \\ v=\text{ 14 km/h} \end{gathered}[/tex]To travel 35 km downstream;
[tex]\text{distance = 35km}[/tex]Recall that;
[tex]\begin{gathered} \text{speed = }\frac{\text{ distance}}{\text{time}} \\ \text{time = }\frac{\text{ distance}}{\text{ speed}} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} \text{time = }\frac{35\operatorname{km}}{14\text{ km/h}} \\ \text{time =2.5 hours} \end{gathered}[/tex]Therefore, it'll take 2.5 hours
[tex]undefined[/tex]I need whit math thats all(x-2) +(x+6)
To simplify the expression (x-2) +(x+6), you have to follow these steps:
1.Get rid of the parentheses:
(x-2) +(x+6)
x -2 + x + 6
2. Combine like terms:
x + x - 2 + 6
2x + 4
So the answer is 2x + 4
Solve this system of equations usingthe substitution method.y = x + 9y = -4x – 612] [UN
The given system of equations is
[tex]\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}[/tex]We will substitute y in equation (2) by equation (1)
[tex]x+9=-4x-6[/tex]Now, add 4x to both sides
[tex]\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}[/tex]Subtract 9 from both sides
[tex]\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{-15}{5} \\ x=-3 \end{gathered}[/tex]Substitute x by -3 in equation (1) to find y
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]The solution of the system is (-3, 6)
I need help on this question please?
parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
What is a parabola in math?
Drawing a parabola for the quadratic function f(x) = ax2 + bx + c results in a U-shaped curve.When an is smaller than zero, the parabola's graph is downward (or opens downward).When the value of an is greater than 0, the parabola's graph ascends (or opens up). The locus of points in that plane that are equally spaced apart from the direct x and the focus is known as the parabola.A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.A parabola's general equation is written as y = a(x - h)2 + k or x = a(y - k)2 + h.Vertex here is indicated by (h, k).The typical form is y = a(x - h)2 + k.-9(x_6)²_1
= -9(x-6)1
=-9x+54
Differentiate x
-9
-9(x-6)²
Subtract
d/dx(-9(x-6)
Calculate x-6
d/dx (-9x+54)
-9x1-1
-9x
=-9
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Identify the vertex: y = (x+10)2+ 2 a. (10,2) b. (-10, -2) c. (-10,2) ) d. (10, -2)
Given a quadratic equation in vertex form
[tex]y=a(x-h)^2+k[/tex][tex]\begin{gathered} \text{ wh}ere\text{ a, h, and k are constants, } \\ \text{then the point (h, k) is the vertex of the function} \end{gathered}[/tex]In our case,
[tex]y=(x+10)^2+2[/tex]h = -10, and k= 2
Therefore the vertex is (-10, 2)
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
we know that
The total numbers in the spinner are 10
The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers
so
To find out the probability, divide the total numbers that are greater than 6 by the total number
therefore
P=4/10
Percent
P=4/10(100)
the answer is
P=40% o P=4/10 or P=0.4What is the sum of the first five terms in this series? 6 - 6/3+6/9-6/27+•••
A 61/81
B 16
C 122/27
D 20/3
The sum of the first five terms in this series is 4 14/27.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The first five terms
6
-6/3
6/9
-6/27
+6/81
The first thing to do is change all the fractions denominators to 81.
Sum = 6*81/81 - 6(27)/81 + 6 × 9/81 - 6 × 3/81 + 6/81
Now add
Sum = 366/81
Sum = 4 14/27
Sum = 4.5185
Recall the first term. It was increased by 6 × 81/81. Nothing is affected by the 81 over 81 in terms of value. 6 × 81/81 remains 6. It merely makes combining it with the other members of the series simpler.
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Rewrite the polynomial .22 – 52 + 6 as 2? + m2 + n2 +6, where m. n = 6 and m +n=-5. What are the values of m and n?
Answer:
m = -2 and n = -3
Explanation
Given the polynomial
x^2 - 5x + 6
Rewrite as x^2 +mx + nx + 6
x^2 - 2x - 3x + 6
Compare
mx = -2x
m = -2
Similarly;
nx = -3x
n = -3
Hence m = -2 and n = -3
5/8p−3/4=4
A) p=95/32
B) p=26/5
C) p=38/5
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]
Add 3/4 to both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]
Convert 4 to the fraction 16/4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]
Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]
Multiply both sides by 8/5, the reciprocal of 5/8.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]
Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]
We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]
Therefore, the answer is option C.Could you please set it up in the form of "systems of equations" meaning, set to different equations with "x" and "y" ??
That is what they want me to do in class.
There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.
Explain the System of equations?A set of two linear equations with two variables is a system of linear equations.
ax + by = C
A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.
Ex: ax+b = 0
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i need helpppp plsssssss
Rewrite the expression (17x3 – 12x2 + 6x - 4)/(x – 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the synthetic division method.
Given that
The equation is
[tex]\frac{17x^3-12x^2+6x-4}{x-1}[/tex]and we have to convert it into the form of
[tex]\begin{gathered} q(x)+\frac{r(x)}{b(x)} \\ where\text{ q\lparen x\rparen is quotient, r\lparen x\rparen is remainder, and b\lparen x\rparen is divisor.} \end{gathered}[/tex]What is the distance from Point B (-1, 11) to line y = -1/3x - 6?
Answer in simplest radical form
The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.
The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).
Comparing the equation y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.
It is clear that the coefficient of x, A = -1 ÷ 3.
The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.
Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,
d = 15.811.
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Solve for r.
r - 15 / -1 = -4
Answer:
r=19
Step-by-step explanation:
15-r=-4
r=19
:]
At the local food stand, the vendor sells small drinks for $1.25 each and large drinks for $2.50 each. They sold 155 drinks today and made $265. How many small drinks and how many large drinks did they sell?
Answer:
98 small drinks and 57 large drinks.
Explanation:
Let's call x the number of small drinks and y the number of large drinks.
If they sold 155 drinks, we can write the following equation:
x + y = 155
In the same way, they made $265, so
1.25x + 2.50y = 265
Because each small drink cost $1.25 and each large drink cost $2.50.
Now, we can have the following system of equations
x + y = 155
1.25x + 2.50y = 265
Solving the firs equation for y, we get:
x + y - x = 155 - x
y = 155 - x
Replacing this on the second equation:
1.25x + 2.50y = 265
1.25x + 2.50(155 - x) = 265
Then, solving for x, we ge:
1.25x + 2.50(155) - 2.50(x) = 265
1.25x + 387.5 - 2.50x = 265
-1.25x + 387.5 = 265
-1.25x + 387.5 - 387.5 = 265 - 387.5
-1.25x = -122.5
-1.25x/(-1.25) = -122.5/(-1.25)
x = 98
Finally, we can find the value of y replacing x = 98
y = 155 - x
y = 155 - 98
y = 57
Therefore, they sell 98 small drinks and 57 large drinks.
mario's school is also planning a smaller rectangular are as a sitting spot. A scale drawing of the sitting sot is shown. redraw the sitting spot on the grid at a scale of i grid unit/4 feet.
write and simplify the ratio of the new scale
The ratio of the new scale that we are to be having is going to be 1/2
How to simplify the new scale of the gridwe have the ratio to be 1 grid unit / 2 ft
the new scale ratio is given as 1 grid unit / 4 ft
We have to divide the ratio of the original scale to the new scale that we have here
This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)
This can be written as
1/4 * 2/1
when we rewrite it we would have 2/4
= 1/2
This is 1 unit 2 feet
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Suppose that IQ scores have a bell-shaped distribution with a mean of 101 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are at least 73? Please do not round your answer.
Answer:
Explanation:
From the information given,
mean = 101
standard deviations = 14
We need to find the number of standard deviations between 73 and the mean.
Number of standard deviations = (73 - 101)/14 = - 28/14 = - 2
It is 2 standard deviations from the mean. According to the empirical rule, 95% of the population lies between 2 standard deviations of the mean. The required area is to the right of 2 standard deviations since we want to find the least score. Thus, the probability of having IQ scores are at least 73 is
We would convert to percentage by multiplying by 100
7=1/4ax, solve for a
The given expression is
[tex]7=\frac{1}{4}ax[/tex]Solving for a means that we need to isolate that variable.
First, we need to multiply the equation by 4
[tex]7\cdot4=4\cdot\frac{1}{4}ax\rightarrow28=ax[/tex]Second, we divide the equation by x
[tex]\frac{28}{x}=\frac{ax}{x}[/tex]Therefore, the answer is
[tex]a=\frac{28}{x}[/tex]Harriet sells prints of her photographs, and is deciding what her minimum order should be during a sale. The equation that relates to her profit, y, from a minimum order of size x is 12x - 4y = 48.
Part A
What are the x-intercept and the y-intercept of the graph of her profit?
A. X-intercept: 3; y-intercept: -12
B. X-intercept: 4; y-intercept: 12
C. X-intercept: 4; y-intercept: -12
D. X-intercept: 3; y-intercept: 12
Part B
What should her minimum order size be, to make a profit?
Consider the given linear equation,
[tex]12x-4y=48[/tex]PART A
Substitute y=0 to obtain the x-intercept,
[tex]\begin{gathered} 12x-4(0)=48 \\ 12x=48 \\ x=4 \end{gathered}[/tex]Thus, the x-intercept is 4 .
Substitute x=0 to obtain the y-intercept,
[tex]\begin{gathered} 12\mleft(0\mright)-4y=48 \\ -4y=48 \\ y=-12 \end{gathered}[/tex]Thus, the y-intercept is -12 .
Therefore, option C is the correct choice
PART B
The linear equation can also be written as,
[tex]\begin{gathered} 4y=12x-48 \\ y=\frac{12}{4}x-\frac{48}{4} \\ y=3x-12 \end{gathered}[/tex]The minimum limit to make a profit can be calculated as,
[tex]\begin{gathered} y>0 \\ 3x-12>0 \\ 3x>12 \\ x>\frac{12}{3} \\ x>4 \end{gathered}[/tex]Note that the order of photograph must be an integer. The next integer after 4 is 5.
So the minimum order size to make a profit should be 5.
Write the following expression in its simplest form-2/3(9/2x + 15/2)
Given the expression
-2/3(9/2x + 15/2)
Open the parenthesis;
= -2/3(9/2 x) - 2/3(15/2)
= -18x/6 - 30/6
= -3x - 5
Hence the expression in its simplest form is -3x - 5
a. Find the value of x given that r ll s.The measure of angle 1 = (63-x)The measure of angle 2 = (72-2x)b. Find the measure of angle 1 and the measure of angle 2.
In the given illustration, angle 1 and angle 2 are corresponding angles.
Note that corresponding angles in parallel lines are congruent.
angle 1 measures (63 - x)
angle 2 measures (72 - 2x)
Since both angles are congruent with each other, equate the angles :
[tex]\begin{gathered} 63-x=72-2x \\ \text{Solve for x, put the variables to the left side and the constant to the right side :} \\ -x+2x=72-63 \\ x=9 \end{gathered}[/tex]The measure of angle 1 will be :
[tex]63-9=54[/tex]The measure of angle 2 will be :
[tex]72-2(9)=54[/tex]ANSWERS :
a. x = 9
b. angle 1 = 54 degrees
angle 2 = 54 degrees
which of the following is a function. then graph the function.
A relationship is a function if and only if for each input, there exists only one output i.e an input cannot have two or more outputs.
We can determine which of the relationship is a function by plotting a graph of the relationship.
The only correct option is the relationship:
[tex]y=x^2[/tex]The graph of the function is shown below:
4. Describe the transformation from the parent graph of y - 4 = – 2(x – 3)?. Graphboth the parent graph and the transformed graph on the grid provided. Plot at leastthree distinct points for each.
Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph
both the parent graph and the transformed graph on the grid provided. Plot at least
three distinct points for each.
we have that
the parent function is
y=x^2
Is a vertical parabola open upward with the vertex at (0,0)
the transformed function
is
y-4=-2(x-3)^2
y=-2(x-3)^2+4
Is a vertical parabola open downward with vertex at (3,4)
so
The transformations are
1) Reflection over x-axis
Rule is
(x,y) ------> (x,-y)
y=x^2 ------------------> y=-x^2
2) Vertical Dilation with a scale factor of 2
Rule
(x,y) --------> (x,2y)
y=-x^2 ----------> y=-2x^2
3) Translation 3 units at right and 4 units up
Rule is
(x,y) --------> (x+3,y+4)
y=-2x^2 --------> y=-2(x-3)^2+4
see the graph to better understand the problem
a box is filled with 3 red cards, 6 Blue cards, and 6 green cards. A card is chosen at random from the box. what is the probability that it is a red or a green card? write your answer as a fraction in simplest form
Probability of red or green card = 3/5
Explanation:Number of red cards = 3
Number of blue cards = 6
Number of green cards = 6
Total number of cards = 6 + 6 + 3 = 15
Probability of red or green card = Probability of red card + Probability of green card
Probability of red card = number of red cards/total number of cards
Probability of red card = 3/15
Probability of green card = number of green cards/total number of cards
Probability of green card = 6/15
Probability of red or green card = 3/15 + 6/15
Probability of red or green card = 9/15
In simplest term:
Probability of red or green card = 3/5
Answer:
85% but in a fraction 17/20
Step-by-step explanation:
Of the 120 families, approximately___pay more than $5710 annually for day car per child.
1) Considering a Normal Distribution, then we can write out the following:
[tex]P(X>5710)=P(X-\mu>5710-6000)=P(\frac{X-\mu}{\sigma}>\frac{5710-6000}{1000})[/tex]Note that we're dealing with probabilities.
2) Let's find out the Z-score resorting to a table, we get:
[tex]Z=\frac{x-\mu}{\sigma}=\frac{5710-6000}{1000}=-0.29[/tex]2.2) So we can infer from 1 and 2:
[tex]P(X>5710)=P(Z>-0.29)=0.6141[/tex]Notice that this distribution refers to 120 families
I need help with this question I not sure but my answer was number 3 i for sure
To solve this problem, we have to compute the circumference of a circle of diameter:
[tex]d=840ft.[/tex]Recall that the circumference of a circle is given by the following formula:
[tex]C=d\pi,[/tex]where d is the diameter.
Therefore, the circumference of the reservoir is:
[tex]C=\frac{22}{7}*840ft=2640ft.[/tex]Answer:[tex]2640ft.[/tex]the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the domain of the function.
The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.
What is domain of a function?The domain of a function is the complete set of possible values of the independent variable.
Also a domain of a function refers to "all the values" that go into a function.
From the graph the domain of the function of the volume of the of liquid in the bucket is calculated as follows;
The minimum value of the volume of liquid in the bucket = 0
The maximum value of the volume of liquid in the bucket = 7.5 liters
The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}
0 ≤ V ≤ 7.5 liters
Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.
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You are told that a 95% confidence interval for the population mean of a normally distributed variable is 17.3 to 24.5. if the population was 76, what was the sample standard deviation?
The sample standard deviation of the population with confidence interval of 95% is 13.57
What is standard deviation?Standard deviation gives a value that measures how much the given value differ from the mean.
How to find the sample standard deviationGiven data form the question
95% confidence interval
population mean of a normally distributed variable is 17.3 to 24.5
population was 76
Definition of variables
confidence interval = CI = 95%
mean = X = 17.3 to 24.5
taking the average, X = 21.45
standard deviation = SD = ?
Z score = z = 1.96
from z table z score of 95%confidence interval = 1.96
sample size = n = 76
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]
[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]
SD = √76 * 1.5561
SD = 13.56577
SD ≈ 13.57
The standard deviation is solved to be 13.57
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The function P(m) below relates the amount of time (measured in minutes)
Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the
number of problems completed.
P(m) = 12 +9
Which equation below represents the inverse function M(p), which takes the
number of problems completed as input and returns the number of minutes
worked?
OA. M(p) = 6p + 54
OB. M(p) = 6p - 54
OC. M(p) = 54p - 6
OD. M(p) = 54p + 6
The inverse function of a function f in mathematics exists a function that reverses the operation of f. The number of problems completed as input and returns the number of minutes worked exists m(p) = 6p - 54.
What is meant by inverse function?An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.
Given: P(m) = (m/6) + 9
Determine the inverse function
P(m) = (m/6) + 9
Represent P(m) as P
P = (m/6) + 9
Swap the positions of P and m
m = (p/6) + 9
We are to make p the subject.
Subtract 9 from both sides, then we get
m - 9 = (p/6) + 9 - 9
m - 9 = (p/6)
Multiply through by 6
6(m - 9) = (p/6) × 6
simplifying the above equation, we get
6(m-9) = p
6 m-54 = p
Rearranging the above equation, we get
p = 6m - 54
Swap the positions of P and m
m = 6p - 54
m(p) = 6p - 54
Therefore, the correct answer is option C. M(p)=6p - 54
The complete question is:
The function below relates the amount of time (measured in minutes) Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the number of problems completed.
P(m) = (m/6)+9
Which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked?
A. M(p)=54p + 6
B. M(p)=54p - 6
C. M(p)=6p - 54
D. M(p)=6p + 54
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Answer:6p-54
Step-by-step explanation:
14. PR is the diameter of the circle with centre O. If mZPRQ = 65°. What will be the measure of
mZPOQ?
A. 65⁰
B. 90⁰
C. 130⁰
D. 150⁰
calculate the area of this trapiziuem
Answer:
............where is it?