The table shows a different number of rides along with the cost.
Each number of rides has a different cost. Therefore, it is a linear function that can be written as y = mx + b
Here, b is the y-intercept or the point at which the line crosses the y-axis. It lies on x = 0. For 0 rides, the cost would also be zero. Therefore, b = 0.
Also, m is the slope that is the difference of y values over the x values. Therefore, it is calculated using
m = (y2 - y1) / (x2 - 1)
To find that, we need to take two points from the graph. Let's pick the first two points:
(2, 3)
(5, 7.5)
Just put the values in the slope equation
m = (7.5 - 3) / (5 - 2)
m = 4.5/ 3
m = 1.5
Now, put the values of m and b in the standard equation.
y = mx + b
y = 1.5x + 0
y = 1.5x
Therefore, y = 1.5x calculates the cost to go on x number of rides.
Item 3595
To decorate a cake, you make a shade of orange icing using 24 drops of red food
coloring for every 8 drops of yellow.
How many drops of yellow food coloring would you need if you use 9 drops of red food
coloring?
CLEAR
CHECK
2
3
8
12
Answer:
3
Step-by-step explanation:
if u use 24 drops of red food/c and 8 drops of of yellow to make orange , then you have to divide 24 by 8 = 3 and so 9÷3 =3 yellow drops to make orange
logx+5 64 = 2
Please help!!
Solve and round to the nearest 100th
Explain how
WILL GIVE BRAINIEST FIRST ANSWER
The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.
solve the equation logₓ(64) + 5 = 2, we can follow these steps:
Step 1: Move the constant term to the other side of the equation:
logₓ(64) = 2 - 5
logₓ(64) = -3
Step 2: Rewrite the equation in exponential form:
x^(-3) = 64
Step 3: Rewrite 64 as a power of x:
x^(-3) = x^6
Step 4: Set the exponents equal to each other:
-3 = 6
The equation -3 = 6 is not true, which means there is no real solution to the given equation.
Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.
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How do you find the angle for 2?
Answer:
m<2 = 130°
Step-by-step explanation:
m<1 + m<2 = 180° (angles on a straight line/linear pair theorem)
First, we need to find m<2.
m<1 + 90° + 40° = 180° (sum of triangle)
Add like terms
m<1 + 130 = 180
Subtract 130 from each side
m<1 = 180 - 130
m<1 = 50°
Thus:
50° + m<2 = 180°
Subtract 50° from each side
m<2 = 180 - 50
m<2 = 130°
Solve the system of inequalities by graphing.
y ≥ 2
y < 4
Select a line to change it between solid and dotted. Select a region to shade it.
The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.
Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.
x ≥ –3; y ≥ x – 2
x > –3; 5y ≥ –4x – 10
x > –3; y ≥ –x + 1
x > –2; y ≥ –x – 1
The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).
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Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answer:
25 + 9^3
Step-by-step explanation:
how tall is the house? please do not round for your answer can someone please help me?
height of the house is 28.4 ft
Explanation:shadow of the house = 57 feet
height of the house = ?
Height of the girl = 4.7 feet
shadow of the girl = 9.4m
The formula:
height of the house/shadow of the house = height of the girl/shadow of the girl
\(\begin{gathered} \frac{height\text{ of the house}}{57}=\frac{4.7}{9.4} \\ \text{cross multiply:} \\ 9.4(\text{height of the house) = 4.7(57)} \\ \end{gathered}\)\(\begin{gathered} \text{height of the house = }\frac{4.7(57)}{9.4} \\ \text{height of the house = }28.4\text{ f}eet \end{gathered}\)it is 325 meters around a track. Jada ran around the track 12 times. how many kilometers did jada run?
The total distance Jada ran around the track is 3.9 kilometers.
Explain about distance ?
Distance is a measure of how far apart two points or objects are. It is typically measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, which means it only has magnitude and no direction.
There are different ways to measure distance depending on the situation. For example, in one dimension, the distance between two points can be measured as the absolute value of the difference between their coordinates. In two or three dimensions, distance can be calculated using the Pythagorean theorem.
Given by the question:
The total distance Jada ran can be calculated by multiplying the distance around the track by the number of times she ran around it:
Total distance = 325 meters × 12 = 3900 meters
To convert meters to kilometers, we need to divide by 1000 since there are 1000 meters in a kilometer:
Total distance = 3900 meters ÷ 1000 = 3.9 kilometers
Therefore, Jada ran 3.9 kilometers.
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The half-life of phosphorus-32 is approximately 24.3 days.
Determine a so that A(t)=A0at describes the amount of phosphorus-32 left after t days, where A0 is the amount at time t=0. ROUND TO SIX DECIMAL PLACES.
Please help every answer has been incorrect so far.
Answer:
\(A=A_0(0.971878)^t\)
Step-by-step explanation:
The half-life of Phosphorus-32 is approximately 24.3 days.
We have the equation:
\(\displaystyle A = A_0 (a)^t\)
And we would like to determine a.
First, since it is half-life, a=1/2.
Second, since the half-life for our element is 24.3 days, we need to substitute t for t/24.3. This yields:
\(\displaystyle A = A_0 (\frac{1}{2})^\frac{t}{24.3}\)
In this way, if t=24.3, then we would have one half-life.
We can rewrite our equation as:
\(\displaystyle A = A_0 (\frac{1}{2}^\frac{1}{24.3})^t\)
Approximate, rouding to six decimal places. So, our function is:
\(A=A_0(0.971878)^t\)
Therefore, our new a is:
\(a\approx0.971878\)
This will give the amount of Phosphorus-32 left after t days, giving the initial amount of A₀.
27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 35 college students are randomly selected, find the probability that
a. Exactly 9 of them major in STEM.
b. At most 11 of them major in STEM.
c. At least 11 of them major in STEM
The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.
The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.
The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.
a. Exactly 9 of them major in STEM.
In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:
P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶
where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.
b. At most 11 of them major in STEM.
To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.
The probability of at most 11 students majoring in STEM can be calculated as follows:
P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.
c. At least 11 of them major in STEM.
The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)
Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:
P(X >= 11) = 1 - P(X < 11) = 31.8%
Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.
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A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.
What is the approximate area of the triangle? Round to the nearest tenth.
Area of a triangle = One-1/2bh
Answer:
161.8cm²
Step-by-step explanation:
solve for height which is the opposite
opp=x
sin(theata)= opp./hyp.
sin23=x/30
x=30×sin23
x=11.72cm
height=opposite
height=11.72cm
base=adjacent
base=27.6cm
½of 27.6cm=13.8
13.8cm×11.72cm=161.74 (2d.p)
161.74 rounded to the nearest tenths= 161.7
I'm not sure if it's the answer but it's the closest thing to the options
Which triangle is similar to △JKH?
1. △MKN
2. △JOG
3. △MQL
4. All triangles are similar to △JKH
Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN
What are similar triangles in geometry?Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.
The given parameter is Line a is parallel to Line b, which gives: a║b
Two triangles are similar if they satisfy the following conditions:
Two angles in one triangle are equal to two angles in the other triangle.Each of the three corresponding sides of the two triangles are proportional.Two sides of one triangle are proportional to the corresponding two sides on the other triangle, and the included angle between the specified two sides in both triangles are congruent.According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN
Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN
Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.
The correct option for the triangle similar to ΔJKH is option 1. ΔMKN
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Daniel and Paul went exploring in the woods. On the first day Daniel saw 3 rabbits and Paul saw 8 deer. On the second day Daniel saw 4 rabbits and Paul saw 7 deer. On which day of hunting did Daniel and Paul catch a higher ratio of rabbits to deer?
Answer:
first day when they say 3 rabbits and 8 deers 3:8
what is the sum of the geometric series 4∑ t=1 6t-1
Answer:
Hello friend kya in snap and p to Trisha
Which of the following functions is quadratic?
A.f(x) = 2/x^2
B. f(x) = 3(3-x)
c. f(x) = 7^2
D. f(x) = 2x^2 +3x - 5
Answer:
D
Step-by-step explanation:
the 'x' term is squared but not in the denominator
Find a number that
has exactly 7 different prime factors.
Explain how you found it.
Answer:
957,697,598
Step-by-step explanation:
You want a number that has 7 different prime factors.
PrimesIf we choose 7 primes at random from the first 20, we might have the list ...
{2, 11, 13, 23, 41, 53, 67}
The product of these primes will have 7 different prime factors.
2 × 11 × 13 × 23 × 41 × 53 × 67 = 957,697,598
The number 957,697,598 has exactly 7 different prime factors.
__
Additional comment
Any of these factors might have a power greater than 1 without changing the number of different primes. We chose to keep it simple.
The second attachment shows the first 20 prime numbers.
Miss Rose went shopping with 120 she spent 78. What percentage of her money did she spend
Miss Rose spent 65 percentage of her money.
Define percentagePercentage is a way of expressing a fraction or a proportion as a fraction of 100. It is a number or ratio expressed as a fraction of 100, denoted by the symbol "%".
To find the percentage of Miss Rose's money that she spent, we can use the formula:
percentage = (part/whole) x 100
where "part" is the amount she spent, and "whole" is the initial amount of money she had.
In this case, Miss Rose had 120 and spent 78, so the percentage of her money that she spent is:
percentage = (78/120) x 100 = 65
Therefore, Miss Rose spent 65% of her money.
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Bottles of sparkling water usually cost $1.69 each. This week they are on sale for 4 for $5. What is the unit price of the bottles now that they are on sale?
Answer:
1.25$
Step-by-step explanation:
Answer:
$1.25?
Step-by-step explanation:
1.25 × 4 = 5
I hope this is right :)
to 2 Decimal Places
2) 0.11 0.88
4) 0.06) 0.54
Answer:
2)
Step-by-step explanation:
Answer:
1)11.0, 2)88.0, 3)6.0, 4)54.0
Please kindly help
According to a newspaper article 15% more home remodeling was done in 1985 than in 1984. Professionals performed 75% of all remodeling. If $80.4 billion was spent on residential remodeling in 1985 what was the value of the work done by professionals in 1985?
(1) $ 8.4 billion
(2) $12.06 billion
(3) $20.1 billion
(4) $60 billion
(5) $60.3 billion
Answer:
(3) $20.1 billion
Step-by-step explanation:
hope it help
Answer:
(5) $60.3 billion
Step-by-step explanation:
Since the mode is the most frequently occurring data value, it
Select one:
a. is always larger than the mean
b. can never be larger than the mean
c. must have a value of at least two
d. is always larger than the median
e. None of these answers is correct.
Any answer without justification will be rejected automatically.
The correct answer is option (e): None of these answers is correct.
The statement "the mode is the most frequently occurring data value" is true. However, none of the options provided accurately describes the relationship between the mode and the mean.
The mode and the mean are different measures of central tendency and can have different values. There is no general rule or guarantee that the mode will always be larger or smaller than the mean. The relationship between the mode and the mean depends on the specific dataset and its distribution. Therefore, none of the provided options correctly describes the relationship between the mode and the mean.
someone please help
Answer:
<D=<N
Step-by-step explanation:
Corresponding angle, both in third digit, others are in different digits.
PLS GIVE BRAINLIEST
Answer:
Step-by-step explanation:
∠D≅∠N
because if you write them in the same order they will be coresponding parts
Multiply: 3,217 × 5,716
Answer:
Step-by-step explanation:
183,883,72
Answer:
18388372
Step-by-step explanation:
1 )Use the algorithm method.
3 2 1 7
× 5 7 1 6
1 1 1 4
1 9 3 0 2
3 2 1 7 0
2 1 1 4
2 2 5 1 9 0 0
1 1 3
1 6 0 8 5 0 0 0
1 1 1
1 8 3 8 8 3 7 2
==================step 2==================2 )Therefore, 3217 × 5716 = 18388372.
18388372
Prove that
(secx+tanx)² =CSCx+1/CSC x-1
To prove that (secx+tanx)² = (cscx+1)/(cscx-1), we will start with the left-hand side (LHS) of the equation and simplify it step by step until it matches the right-hand side (RHS) of the equation.
LHS: (secx+tanx)²
Using the trigonometric identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the LHS as:
LHS: (1/cosx + sinx/cosx)²
Now, let's find a common denominator and simplify:
LHS: [(1+sinx)/cosx]²
Expanding the squared term, we get:
LHS: (1+sinx)² / cos²x
Next, we will simplify the denominator:
LHS: (1+sinx)² / (1 - sin²x)
Using the Pythagorean identity sin²x + cos²x = 1, we can replace 1 - sin²x with cos²x:
LHS: (1+sinx)² / cos²x
Now, let's simplify the numerator by expanding it:
LHS: (1+2sinx+sin²x) / cos²x
Next, we will simplify the denominator by using the reciprocal identity cos²x = 1/sin²x:
LHS: (1+2sinx+sin²x) / (1/sin²x)
Now, let's simplify further by multiplying the numerator and denominator by sin²x:
LHS: sin²x(1+2sinx+sin²x) / 1
Expanding the numerator, we get:
LHS: (sin²x + 2sin³x + sin⁴x) / 1
Now, let's simplify the numerator by factoring out sin²x:
LHS: sin²x(1 + 2sinx + sin²x) / 1
Using the fact that sin²x = 1 - cos²x, we can rewrite the numerator:
LHS: sin²x(1 + 2sinx + (1-cos²x)) / 1
Simplifying further, we get:
LHS: sin²x(2sinx + 2 - cos²x) / 1
Using the fact that cos²x = 1 - sin²x, we can rewrite the numerator again:
LHS: sin²x(2sinx + 2 - (1-sin²x)) / 1
Simplifying the numerator, we have:
LHS: sin²x(2sinx + 1 + sin²x) / 1
Now, let's simplify the numerator by expanding it:
LHS: (2sin³x + sin²x + sin²x) / 1
LHS: 2sin³x + 2sin²x / 1
Finally, combining like terms, we get:
LHS: 2sin²x(sin x + 1) / 1
Now, let's simplify the RHS of the equation and see if it matches the LHS:
RHS: (cscx+1) / (cscx-1)
Using the reciprocal identity cscx = 1/sinx, we can rewrite the RHS:
RHS: (1/sinx + 1) / (1/sinx - 1)
Multiplying the numerator and denominator by sinx to simplify, we get:
RHS: (1 + sinx) / (1 - sinx)
Now, we can see that the LHS and RHS are equal:
LHS: 2sin²x(sin x + 1) / 1
RHS: (1 + sinx) / (1 - sinx)
Therefore, we have proven that (secx+tanx)² = (cscx+1)/(cscx-1).
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Please help!!
If you could explain how you solved this in detail it would be much appreciated.
When x^3+kx^2+2kx+6 is divided by (x-2), the remainder is 30. Find k.
Simplifying this equation, we get:
8 + 4k + 4k + 6 = 30
8k + 14 = 30
8k = 16
k = 2
Therefore, the value of k is 1.
What is polynomial?In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,
\(3x^2 + 2x - 1\)
is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.
The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.
Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.
We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:
\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)
where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.
Now, let's substitute x = 2 into the equation above:
\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)
Simplifying the left-hand side, we get:
\(8 + 4k + 4k + 6 = 30\)
\(16k = 16\)
\(k = 1\)
OR
8 + 4k + 4k + 6 = 30
8k + 14 = 30
8k = 16
k = 2
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Let f (x) = x - 4 . Graph g(x) = f (5x)
Choose the description of the transformation from the graph of f to the graph of g.
A.) The graph of g is a horizontal stretch of the graph of f by a factor of 5.
B) The graph of g is a horizontal shrink of the graph of f by a factor of 1/5
C) The graph of g is a vertical stretch of the graph of f by a factor of 5
D) The graph of g is a vertical shrink of the graph of f by a factor of 1/5
And what points would be plotted on a graph?
The graph of g(x) is on the image at the end, and the correct option for the transformation is B.
Which is the transformation applied?We define a horizontal dilation of scale factor k as:
g(x) = f(k*x)
if k > 1, we have a stretch.
if 0 < k < 1, we have a shink of scale factor 1/k
Here we have:
g(x) = f (5x) = 5x - 4
We can notice that k = 5, then we have a stretch, thus, the correct option is B.
The graph of function g(x) can be seen in the image at the end.,
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Maggie rewrote the expression 36 + 27 as two factors using the greatest common factor and the distributive property. Write the expression Maggie created.
Answer:
9(4+3)
Step-by-step explanation:
The GCF of 36 and 27 is 9. Dividing 36 and 27 by 9, I used the distributive property and got the equation 9(4+3)
PLEASE HELP ME ASAPPPP
Answer: 3 good luck
Step-by-step explanation:
The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price? Store A: Sale of 30% off and a successive discount of 10% off. Store B: Sale of 20% off and a successive discount of 20% off. Store C: Sale of 40% off. a. All of the stores have the same discounted price. b. You can get the lowest price at Store A. c. You can get the lowest price at StoreB. d. You can get the lowest price at Store C.
Answer: D.
You can get the lowest price at Store C
The lowest price is at Store C, where the price is $113.75 after the discount.
You can get the lowest price at Store C.
Option D is the correct answer.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Let's first calculate the price of the snowboard after the discounts at each store:
Store A:
The first discount is 30% off, so the price becomes 0.7 times the original price.
0.7 x $189.59
= $132.71
The successive discount is 10% off, so the price becomes 0.9 times the discounted price.
0.9 x $132.71
= $119.44
Store B:
The first discount is 20% off, so the price becomes 0.8 times the original price:
= 0.8 x $189.59
= $151.67
The successive discount is 20% off, so the price becomes 0.8 times the discounted price.
= 0.8 x $151.67
= $121.34
Store C:
The discount is a straight 40% off, so the price becomes 0.6 times the original price.
= 0.6 x $189.59
= $113.75
Therefore,
The lowest price is at Store C, where the price is $113.75 after the discount.
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Helppppppppppppppp ASAP
Patrick is in a grocery store parking lot, 90meters away from his car. If he pushes his shopping cart at a constant velocity of 2meterspersecond toward his car, how much time will it take him to get one-third of the way to his car?
Write your answer as a whole number.
15 seconds of time will it take him to get one-third of the way to his car
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given,
Patrick is in a grocery store parking lot, 90meters away from his car
Patrick pushes his shopping cart at a constant velocity of 2meterspersecond toward his car.
We need to find time will it take him to get one-third of the way to his car
one-third of the way to his car means 1/3 of 90 which is 30 meters.
Speed =Distance/ Time
Time=Distance/speed
=30/2
=15 units.
Hence, 15 seconds of time will it take him to get one-third of the way to his car
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