Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.
How to work out Ashley's and Saskia's numbers?In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent Ashley's number.Let the variable y represent Saskia's number.Translating the word problem into an algebraic equation, we have the following:
x - 1 = 3y .....equation 1.
4x + y = 95 .......equation 2.
Making x the subject of formula in equation 1, we have:
x = 3y + 1 .......equation 3.
Substituting equation 3 into equation 2, we have:
4(3y + 1) + y = 95
12y + 4 + y = 95
13y = 95 - 4
13y = 91
y = 91/13
y = 7.
For the value of x, we have:
x = 3y + 1
x = 3(7) + 1
x = 21 + 1
x =22.
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The volume of
a refrigerator, in cubic centimeters, is given
by the function V(x) = (x)(x + 1)(x – 2). Write a
new function for the volume of the refrigerator
in cubic millimeters if x is in centimeters.
The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000
How to rewrite the function expression?From the question, we have the following parameters that can be used in our computation:
A function expression
The function expression is given as
V(x) = (x)(x + 1)(x – 2)
Where if x is in centimeters and V(x) is in cubic centimeters
The new function for the volume of the refrigerator is stated to be in cubic millimeters
Using the above as a guide, we have the following:
1 cubic centimeters = 1000 cubic millimeters
So, we have
V(x) = (x)(x + 1)(x – 2)
1 cubic centimeters = 1000 cubic millimeters
Cross multiply
V(x) * 1000 = 1* (x)(x + 1)(x – 2)
Divide both sides by 1000
V(x) = (x)(x + 1)(x – 2)/1000
Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000
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On a hot day, a fan has a mark on the tip of one blade. The equation y
=20cos(x) + 25 represents the height of the mark, y centimeters, above the
table x seconds after the fan is turned on. What is the height of the mark
above the table when it is closest to the table?
===================================================
Explanation:
Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).
Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:
20*cos(x)+25
20*(-1) + 25
-20 + 25
5
The height of the fan tip is 5 cm when it is the closest to the table.
Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is [tex]5 \le y \le 45[/tex]
Find the missing length indicated. Leave your answer in simplest radical form.
Please help due today!!
Answer:
C) 25
Step-by-step explanation:
First, solve for the height (red dotted line) using the Pythagorean theorem 9²+b²=15²
81+b²=225
b²=225-81
b²=12
Then set up a ratio.
x/12=9/15
simplify
x/12=3/5
cross-multiply
3x=60
x=20
This gives us the base. Now we can solve for x using the Pythagorean theorem again.
20²+15²=x²
400+225=x²
625=x²
√x²=√625
x=25
7 x (n + 3) = (7 x 2) + (7 x 3)
Answer:
N = 2
Step-by-step explanation:
We must solve for N.
Solve inside the parenthesis if needed, otherwise open them
7n + 21 = (14) + (21)
Now solve, then simplify
7n + 21 = 35
7n = 35 - 21
7n = 14
N = 2
Anybody who knows Pre Calc?? My last offer here
Solution PLS!
Answers:
true speed = 26.935546 knotstrue bearing = 102.265139 degreesThe values are approximate. Round them however you need to.
====================================================
Explanation:
The diagram you have drawn is correct if you're only considering one current. Specifically current #1 which has the bearing of 290 degrees moving at 25 knots.
The red angle is 290 degrees. The remaining portion that is needed to get a full 360 degrees is 360-290 = 70. This adds to the blue portion in quadrant 1, which is 90, and we get 70+90 = 160. So the blue angle is 160 degrees.
The vector for current #1 is <25*cos(160), 25*sin(160)>
This approximates to <-23.4923155, 8.5505036>
All of this is for current #1.
------------
Vector #2 is much more simple in terms that there aren't messy decimal approximations here. The direction is due north, which means that the vector is pointing straight up toward 90 degrees.
We can then say: <12*cos(90), 12*sin(90)> = <12*0, 12*1> = <0, 12>
Vector #2 is <0,12>
When you wrote <12,0>, you were on the right track, but you had the coordinates swapped in the wrong order.
----------
Then we have to account for a wind going 4 knots in the southwest direction. This is at the angle 225 degrees (we rotate 180 degrees plus another 45 to get 225). So,
vector #3 = <4*cos(225), 4*sin(225)> = <-2.8284271, -2.8284271>
This vector's coordinates are approximate
---------
To recap everything so far, vectors 1 through 3 are the following
p = <-23.4923155, 8.5505036>q = <0, 12>r = <-2.8284271, -2.8284271>I'm using variables to represent the vectors at this point, so we can then add them up to get...
s = p+q+r
s = <-23.4923155, 8.5505036> + <0,12> + <-2.8284271, -2.8284271>
s = <-23.4923155+0+(-2.8284271), 8.5505036+0+(-2.8284271)>
s = <-26.3207426, 5.7220765>
Vector s represents the sum of the three vectors p, q, and r. The two currents and the wind ultimately combine together to push the boat in the direction and along the length of vector s.
----------------------
Now that we know the coordinates of vector s, we use them to find the true speed and true bearing of the boat.
speed = sqrt(a^2 + b^2)
speed = sqrt( (-26.3207426)^2 + (5.7220765)^2 )
speed = 26.935546 knots, which is approximate
angle = arctan(b/a)
angle = arctan(5.7220765/(-26.3207426))
angle = -12.265139
Add 360 to this angle to find that we get to the coterminal angle of -12.265139+360 = 347.734861 degrees
This angle is in quadrant 4, which is the southeast quadrant. If we rotate another 360-347.734861 = 12.265139 degrees, going counterclockwise, then we'll face directly east. Then another 90 degree counterclockwise rotation has us face directly north.
In total, the true bearing is approximately 90+12.265139 = 102.265139 degrees
So we'll start aiming north, and then rotate roughly 102.265139 degrees toward the east to get to the true bearing.
What's 6+89 .help me pls I'm going to kermit sewer side
Answer:
95
Step-by-step explanation:
Answer:
95
please don't
Which graph represents the compound inequality?
-3
-5 -4 -3 -2 -1 0 1
2
3 4
5
-5 4 -3 -2 -1 0 1
2 3 4 5
-5 4 -3 -2 -1 0 1
2
3
4
5
OG
-5 4 -3 -2 -1 0 1 2 3 4 5
Answer:
4th option
Step-by-step explanation:
open circle means more than or less than
n is more than -3 but less than 1
The radius of a cylinder is 7 in and the height is 24 in.
Find the Volume.
O 117611
O 126011
O 36011
148011
Answer:
A. 1,176π
Step-by-step explanation:
Volume of a cylinder = πr²h
Radius (r) = 7 in. (given)
Height (h) = 24 in. (given)
Plug in the values into the formula for volume
V = π*7²*24
V = π*49*24
V = 1,176π
what is the coefficient of Q in the sum of
(2/3q - 3/4) and (-1/6q - 2)
please help me out
Find the solution for x if |5x – 2| = 13.
Answer:
x=1 if that's 15 x
Step-by-step explanation:
An item on sale costs 80% of the original price. The original price was 33%
The sale price of the item is given by the equation A = $ 26.40
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the sale price of the item be represented as A
Now , the equation will be
The original price of the item = $ 33
An item on sale costs 80% of the original price
So , the sale price of the item A = 80 % x original price of the item
Substituting the values in the equation , we get
The sale price of the item A = ( 80 / 100 ) x 33
The sale price of the item A = 0.80 x 33
The sale price of the item A = $ 26.40
Therefore , the value of A is $ 26.40
Hence , the sale price is $ 26.40
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Solve -3x + 2y = 5 for y
Answer:
y=4
Step-by-step explanation:
Answer:
y=2.5
Step-by-step explanation:
first you add -3x to both sides so you get 5-3x and then divide that by 2 to get Y by itself so now you have 5/2 - 3/2x and when you put in the equation y=5/2 - 3/2x in DESMOS, the answer is 2.5
Maria flips a coin 20 times. The coin only lands on tails 9 times. According to theoretical
probability how many more times would Maria have expected the coin to land on tails?
Answer:
1
Step-by-step explanation:
A coin only has two outcomes. Meaning that she has a 50/50 chance of landing on each side. So, 50% of 20 is 10. According to the theoretical probabilty, the coin would have landed on heads 10 times and tails 10 times. So, for that to be true Maria would have had to land on tails one more time.
How do logarithmic functions model real-world problems and their solutions? Give a specific example and explain.
The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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If k × k × k = 1; then k =
Answer: k^3=1
Step-by-step explanation:
Answer:k^3=1
Step-by-step explanation:
Given m=35000kg g= 9.81N Find W (in kN)
Step-by-step explanation:
check the pic for workings
ans is 343.35KN
FOR BRAINIEST PLEASE ANSWER ASAP
Match each equation with the type of conic section it
represents.
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
Define equation.
Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.
Here,
are the definitions of each equation:
1. x^2 + y^2 - 4x + 6y - 5 = 0
The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.
2. x^2 - 6y = 0
The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.
3. 4x^2 + 9y^2 = 1
This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.
4. 7x^2 - 9y^2 = 343
A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.
Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.
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The California Department of State Police keeps track of the number of points received for various traffic violations by drivers. The department is interested in examining the relationship between the number of points received and the insurance premium. Some information on the point category and the insurance premium category is given below:
Point category
Insurance premium category Low Medium High
Cheap 12% 38% 50%
Medium 29% 33% 27%
Expensive 29% 23% 27%
Which distribution is displayed in the above table?
a. The joint distribution of premium category and point category.
b. The marginal distribution of point category
c.The conditional distribution of premium category given point category
d. The conditional distribution of point category given premium category
Answer:
nice
Step-by-step explanation:
e
On a piece of paper graph f(x) = 3x if x<3 2x if x>3 then determine which answer choice matches the graph you drew
The graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.
What is a piecewise function?
The graph of a piecewise function contains numerous curve components. It signifies that it has a plethora of definitions based on the value of the input. In other words, a piecewise function behaves differently depending on the input.
We have:
f(x) = 3x if x ≤ 3
f(x) = 2x if x > 3
We can draw the piecewise function as shown in the attached picture.
At x = 3
f(3) = 3(3) = 9 because f(x) = 3x if x ≤ 3
Thus, the graph of a piecewise function f(x) = 3x if x ≤ 3 and f(x) = 2x if x > 3 is shown in the picture.
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Change this radical to an algebraic expression with fractional exponents.
3√a
The fractional form of the expression [tex]\sqrt[3]a[/tex] is [tex]a^{\frac{1}{3}[/tex]
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical expression [tex]\sqrt[3]a[/tex].
We know this describes the cube root of a or one-third root of a.
This can be written as a fractional exponent as [tex]a^{\frac{1}{3}[/tex].
Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
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Three views of a solid are shown. What is this three-dimensional solid?
Answer:
pyramid
Step-by-step explanation:
Help me plz I will give brainiest
Answer:
Side A = 11
Side B = 16
Side C = 25
I added an image that shows what I did in case you need it.
There are 24 students in a class, and three of them are named Madison. There are no other students in the class with the same name.
If the teacher calls on students randomly, which of the following BEST describes the probability of a Madison being chosen?
If you cannot see, zoom in on the photo.
Do not answer if you don’t know the answer.
Whoever answers correctly will get Brainliest!
Answer:
Mizuki is here to help! The answer is D!
Step-by-step explanation:
Ok... So there are 24 students in the class and no other students in the class has the same name right? So the fraction should be [tex]\frac{3}{24}[/tex] since there are three madisons, which will be 0.125!
Since three people have the same name, everyone else gets less probability of getting called so the answer would be D.
Answer:
Option D
Step-by-step explanation:
Total Students in a class: 24
Total Madisons in the class: 3
Denominator is always the total number of something so; [tex]\frac{3}{24}[/tex]
3/24 = 0.125
Any other student would have a probability of [tex]\frac{1}{24}[/tex] of being chosen which is less than [tex]\frac{3}{24}[/tex], therefore, Option D is the most sensible one.
Hope this helps!
I need some help please.
Step-by-step explanation:
Answer: 2/4, 4,8, etc.
Step-by-step explanation:
Hello!
So basically, what I think this question is asking is for an equivalent fraction to 1/2. There are countless fractions that are the same as this and I listed a couple above!
Hope this helps! :D
Jane had 4 1/2 apples. she divided them so that she had just enough fourths of an apple for each friend and herself. how many of them were there?
Answer:
18 fourths
Step-by-step explanation:
4.5 x 4=18
or
each apple would produce 4 fourths so 4 apples would produce 16. Then 1/2 apple would produce 2 fourths so 16 + 2 = 18
Which box plot represents the data above?
W.
X.
Y.
Z.
A.
Z
B.
W
C.
X
D.
Y
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
8. The volume of a box is 7923 cubic meters. If its base has an area of 57 square meters, what is its height?
Answer:
if the stone makes 150 revolution per minute, the tension force of the string on the stone is
2. In right triangle RST, altitude SV is drawn to its hypotenuse. We also know RT = 20 and VT = 4. Find the value of h. Show your reasoning.
Answer:
This PDF should help :) https://www.hauppauge.k12.ny.us/cms/lib/NY01913704/Centricity/Domain/371/RR%202.pdf
Step-by-step explanation:
PLS HELP ME ILL GIVE BRAINLY
Answer:
i would but i doint see no image maybe repost it
Step-by-step explanation:
Answer:
1000m
3 minutes
1000/3
Answer is approx 333km per minute
600km
12hr
600/12
answer is 50km/hr
Step-by-step explanation: