Conducting a hypothesis test at the 5% significance level we can conclude that the girls' mean is higher than the boys' mean.
To conduct a hypothesis test to determine if the girls' mean is higher than the boys' mean, you will need to use a two-tailed hypothesis test with a significance level of 5%. The null hypothesis is that the girls' mean is not higher than the boys' mean, and the alternative hypothesis is that the girls' mean is higher than the boys' mean. The test statistic is calculated using the formula:
Test statistic = (Girls' mean - Boys' mean) / (Standard deviation of the difference / √(sample size))
The test statistic for this study is calculated as: (3.3 - 1.6) / (1.6/√40) = 4.375.
Using a 5% significance level and two-tailed hypothesis test, the critical value for this test is 1.96. Since the test statistic (4.375) is greater than the critical value (1.96), the null hypothesis can be rejected.
Therefore, we can conclude that the girls' mean is higher than the boys' mean.
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Find the area of the complex figure. 31 m 69 m, 31 m, 23 m, 23 m, 12 m
The area of the complex figure is 1863 m².
What is area?
Area is a measure of the size or extent of a two-dimensional surface or shape, such as a square, circle, or rectangle. It is the amount of space inside the boundaries of a shape, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).
The area of give figure :
= area of two rectangles + area of middle rectangle
we know that area of rectangle is length* breadth
so, area of give two rectangles = 2 × length × breadth
= 2 × 31 × 23
= 1426m²
similarly, area of the middle rectangle = length × breadth
= (69-23-23) × (31-12)
= 23 × 19
= 437 m²
∴ The area of give figure= 1426m²+437 m²
= 1863 m²
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A carnival charges a $10 entrance fee and $2 per ride. Write an equation to represent this situation.
y = mx + b
Answer:
y = 2x + 10
Step-by-step explanation:
What we know:
10 dollar entrance fee
2 dollars PER ride
"per" is an important word since it tells us that the x will be there.
That means that, if its a 10 dollar entrance fee and 2 dollars per ride, it will be 2x + 10.
[tex]y=2x+10[/tex]
Scary drew a rectangle with a perimeter of 20 inches then he tried to draw a square with a perimeter of 20 inches draw three different rectangles that Gary could have drawn, then draw the square if possible
Scary drew a rectangle with a perimeter of 20 inches and its dimensions are 6 by 4 and the square is a 5 in × 5 in square.
We know that a square has 4 identical sides.
The square's perimeter is equivalent to the product of its four sides. The square's side length continues to be the same as the circumference measurement unit.
Perimeter = Side + Side + Side + Side = 4 Side
Perimeter = 4 × side of the square
If ‘a’ is the length of side of square, then perimeter is:
Perimeter = 4a unit
therefore,
20 = 4 × side length
side length = 20/4 = 5 in
it is a 5 in × 5 in square.
We know that a rectangle has 2 pairs of sides that are equally long inside their pair.
The entire distance that the rectangle's outer boundary covers is referred to as its perimeter. Its length is expressed in units. The perimeter calculation is provided by:
Perimeter, P = 2 (Length + Width)
and so, you have in this case a perimeter of
= 2 × 6 + 2 × 4
= 12 + 8
= 20 in
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20 cookies if 3/4 are given away how many are left
Answer:5
Step-by-step explanation:
the set of all positive integers that are divisible by both 15 and 35 is infinite. what is the least positive integer in this set?550105210525
The least positive integer that will be divisible by both 15 and 35 will be 105.
The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.
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Is it possible to dilate the satellite in the activity so that the number of square feet of surface area is equal to the number of cubic feet of volume? Explain or show your
reasoning.
No, it is not possible to dilate a satellite in such a way that the number of square feet of surface area is equal to the number of cubic feet of volume.
What is volume?In mathematics, the volume of an object is a measure of the amount of three-dimensional space that the object occupies. Volume is typically expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the context. Volumes are used in a wide variety of fields, including physics, engineering, and architecture, among others. For example, the volume of a container can be used to determine how much liquid it can hold, or the volume of a room can be used to calculate how much air conditioning is needed to cool the space.
Here,
This is because the units of measurement for surface area and volume are fundamentally different, and therefore cannot be equated without introducing additional variables. For example, consider a cube with a side length of 1 foot. Its surface area would be 6 square feet (since there are 6 sides to the cube, each with an area of 1 square foot), while its volume would be 1 cubic foot (since it occupies a space with a volume of 1 cubic foot). These two measurements cannot be equated without introducing additional variables. Therefore, it is not possible to dilate a satellite in a way that would make the number of square feet of surface area equal to the number of cubic feet of volume.
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True or False: Simple random sample gets us independence, and the success-failure conditions is satisfied since 289 and 400−289 = 111 are both at least 10
the statement is true.the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.
Simple random sampling is a type of probability sampling technique wherein every member of the population has an equal and independent chance of being selected. Independence means that the selection of one unit does not affect the selection of any other unit. The success-failure condition is an important condition of simple random sampling, which states that the size of each of the two groups (i.e., success and failure) should be at least 10. In this case, the two groups are 289 and 111, which are both greater than 10. Therefore, the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.
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Which equation is inverse to the equation
The expression which represents this condition is x=-15z/y
Define Inverse variation meansA link between two variables known as inverse variation occurs when one variable's value rises while the other one's value falls, and vice versa. Inverse variation can be represented mathematically as y = k/x, where y and x are the variables, k is the constant of proportionality, and the product of y and x is constant.
When the value of x increases the value of y decreases.
When the value of x decreases the value of y increases.
So for an inverse variation we have the expression
y=k/x or
x=k/y
The expression which represents this condition is
x=-15z/y
Hence option b) or the second option is the right answer.
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The complete question is attached below.
How does the volume of a cone relate to the volume of a cylinder with
a congruent base and the same height?
1 The volume of the two figures are the same
2 The volume of the cone is 3 times as large
3 The volume of a cylinder is twice as large
4 The volume of the cone is 1/3 as large
The comparison of the volume of a cone relative to the volume of a cylinder with the same dimensions is given as follows:
4 The volume of the cone is 1/3 as large.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
For the volume of the cylinder, the equation is given as follows:
V = πr²h.
The volume of the cylinder is triple the volume of the cone, hence the volume of the cone is one third of the volume of the cylinder.
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Find the coordinate of the terminal point for each angle.
Help with 8, 10, and 12 please.
Therefore, the coordinates of the terminal points are: (0, 1),(-√2/2, -√2/2) ,(-1/2, -√3/2)
What is coordinate?A coordinate is a set of numerical values that uniquely determines the position of a point in space. In two-dimensional space, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal distance from a reference point, and y represents the vertical distance from the same reference point. In three-dimensional space, a coordinate is represented by a triplet of numbers (x, y, z), where x, y, and z represent the horizontal, vertical, and depth distances from the reference point, respectively.
by the question.
Pi/2 is an angle in radians, and it corresponds to an angle of 90 degrees in degrees. The terminal point for this angle lies on the positive y-axis and has coordinates (0, 1).
315 degrees is an angle in degrees, and it corresponds to an angle of 7π/4 radians in radians. To find the terminal point for this angle, we can use the unit circle. Starting from the positive x-axis (the initial side), we rotate 315 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 5π/4 radians. The terminal point lies in the third quadrant and has coordinates (-√2/2, -√2/2).
240 degrees is an angle in degrees, and it corresponds to an angle of 4π/3 radians in radians. To find the terminal point for this angle, we can again use the unit circle. Starting from the positive x-axis (the initial side), we rotate 240 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 4π/3 radians. The terminal point lies in the third quadrant and has coordinates (-1/2, -√3/2).
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hi!!
pls answer this
worth 93 points!!!
screenshot and circle plsss
Answer:
a. already done
b. x=3, x=4, and x=5
c. x=2, x=3, x=4, and x=6
Step-by-step explanation:
The < symbol means less than, so all values of x less than what is stated are correct
The ≤ symbol means less than or equal to, so all values of x less than, and what is stated are correct
The answer is in the screenshot.
Let me know if it helps
write an expression that is equivelent to 1/4x +1 3/4x- 2/3-1/2x
The expression equivalent is 9+2x/6x
What is a fraction?A fraction is a part of a whole. It is the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator
1/4x +1 3/4x - 2/3-1/2x
1/4x + (4x + 3/4x) - 2/3 - 1/2x
(1 + 4x + 3)/4x - (4x - 3)/6x
4 + 4x/4x - 4x - 3/6x
(3(4 + 4x) - 2(4x - 3))/12x
(12 + 12x - 8x + 6)/12x
(18 + 4x)/12x
(9 + 2x)/6x
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John claims that more than 25% of Wenatchee population prefer TACO BELL. To support his claim, he selected a sample of 200 people in Wenatchee and observed that 63 prefer Taco Bell. At a= 0.05, is
there enough evidence to support his claim? Justify your answer by stating what is (a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed) you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value
Hint: You can use the formula for z-Test for proportion
The test value is 0.636, and the critical z-value is 1.645. Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence.
What is test value?It is usually represented by the number of errors or defects found in a system or component during a test phase.
For this test, we use the formula for a z-test for proportions.
Let p be the proportion of Wenatchee population that prefers Taco Bell.
Null hypothesis: p = 0.25
Alternative hypothesis: p > 0.25
The critical z-value for this test is 1.645, which is the z-value corresponding to a=0.05.
The test value is calculated by taking the sample proportion of people preferring Taco Bell
(63/200 = 0.315)
and subtracting the null hypothesis proportion of people preferring Taco Bell (0.25).This gives us 0.065.
This value is then divided by the standard error of the proportion, which is calculated as the square root of
(p*(1-p)/n), where p is the null hypothesis proportion (0.25) and n is the sample size (200). This gives us a value of 0.636.
Therefore, the test value is 0.636, and the critical z-value is 1.645.
Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence to support John's claim that more than 25% of Wenatchee population prefer TACO BELL.
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Graph the quadric functions y=-2x^2 and y=-2x^2+ 4 on a separate piece of paper. Using those graphs, compare and contrast the shape and position of the graphs.
Can someone help with this, I have no idea what this means
*will give brainliest as well*
Step-by-step explanation:
Here are the graphs of the two functions:
y
|
|
|
| (1) (2)
| | |
------x------x-------
| | |
| (3) (4)
|
|
Function 1: y = -2x^2
The graph is a downward-facing parabola.
The vertex is located at (0, 0).
The y-intercept is 0.
The function is symmetric about the y-axis.
Function 2: y = -2x^2 + 4
The graph is also a downward-facing parabola.
The vertex is located at (0, 4).
The y-intercept is 4.
The function is symmetric about the y-axis.
Comparing and contrasting the two graphs:
Both functions are downward-facing parabolas.
Function 2 is a vertical shift of Function 1, as it has been shifted 4 units upwards.
The vertex of Function 2 is higher than the vertex of Function 1.
The y-intercept of Function 2 is higher than the y-intercept of Function 1.
The shape and symmetry of the two graphs are the same.
HEEELLLPPP I WILL GIVE YOU A BRAINILIST, find the Regression Equation and the final answer
Equation for the regression line is given as y = -0.95X + 8.99.
When the wind is blowing at a speed of 27 mph, the chill factor is -16.66.
What does a regression line mean?Regression coefficients are estimates of specific unknown properties that explain the relationship between a predictor variable and the related response.
In order to extrapolate the value of an unknown variable from a known variable, regression coefficients are used. The effect of a one-unit change in an independent variable on the dependent variable can be measured via linear regression by determining the equation of the best-fitted straight line. The procedure in question is regression analysis.
Calculation Overview
X's total is 45.
Total Y = 20
Mean X = 6.4286
Mean Y = 2.8571
Square sum (SSX) equals 113.7143.
Product total (SP) = -108.5714
Regression Equation = ŷ = bX + a
b = SP/SSX = -108.57/113.71 = -0.95477
a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497
y = -0.95477X + 8.99497
y = -0.95X + 8.99
The wind speed chill factor when it is 27 mph.
Using the output of the regression line shown above, we would solve for this.
y=-0.95X+8.99
y=-0.95X+8.99
y = -0.95 * 27 + 8.99
y = -25.65 + 8.99
y = -0.95 * 27 + 8.99
Conclusion: y = -16.66
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Find an equation of a circle centred
Center - radius equation for circle of radius r ,centered at (h,k) is :
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
you have r = √21
[tex]r^{2} =[/tex] (√21)^2 = 21
centre (h,k) = (0,0) so h =0 and k =0
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-0)^{2} + (y -0)^2 = 21[/tex]
[tex]x^{2} + y^{2} = 21[/tex]
Match each sentence with the inequality that could represent the situation
A. Han got $2 from Clare, but he has less than $20 1. x - 2 < 20
B. Mai spent $2 and has less than $20 2. 2x < 20
C. If Tyler had twice the amount of money he has, he
would have less than $20 3. x + 2 < 20
D. If Priya had half the money she has, he would
have less than $20 4. 1/2x < 20
Therefore, the area of the trapezoid is 60 cm².
What is trapezoid?A trapezoid is a four-sided polygon with two parallel sides (called bases) of different lengths, and two non-parallel sides (called legs). The legs of a trapezoid are usually not congruent and can be of different lengths. Trapezoids can have different shapes and sizes, but they always have at least one pair of parallel sides. The area of a trapezoid can be calculated using the formula:
[tex]Area = ((b_1 + b_2) * h) / 2,[/tex]
where b1 and b2 are the lengths of the parallel bases, h is the height or perpendicular distance between the two bases.
To calculate the area of a trapezoid, we use the formula:
[tex]Area = (b_1 + b_2) * h / 2[/tex]
where b1 and b2 are the lengths of the parallel sides of the trapezoid and h is the height (perpendicular distance) between the parallel sides.
In this case, we are not given which sides are the parallel sides and which one is the height, so we cannot directly apply the formula. However, we can make an educated guess based on the dimensions given.
Assuming that the two 8 cm sides are parallel, we can use the formula as follows:
[tex]Area = (b_1 + b_2) * h / 2[/tex]
[tex]Area = (8 cm + 16 cm) * 10 cm / 2[/tex]
[tex]Area = 120 cm^{2} / 2[/tex]
[tex]Area = 60 cm^{2}[/tex]
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PLEASE HELP NEOWWWW
Select the best interpretation of the following inequality. ∣−2.2−x∣>3
A) The distance between -2.2 and -x is greater than 3.
B) The distance between -2.2 and x is greater than 3.
C) The distance between 3 and -2.2 is greater than x.
Answer:
B) The distance between -2.2 and x is greater than 3.
Step-by-step explanation:
Factorise p²-10p+25
Answer:
Step-by-step explanation:
The expression p² - 10p + 25 can be factored as follows:
p² - 10p + 25 = (p - 5)²
This is an example of perfect square trinomial. It can be recognized as such because the first and last terms are perfect squares (p² and 25), and the middle term (-10p) is twice the product of the square roots of the first and last terms (2√(p²×25) = 2p×5 = 10p).
So, the factored form of the expression is (p - 5)².
Step-by-step explanation:
The answer to this question is (p-5)^2
the mean cost of a box of cheerios oat crunch is $4.00 and the variance is .35. if the price increases by 25 cents a box, what is the new variance?
The new variance is 0.41.
Given that the mean cost of a box of Cheerios oat crunch is $4.00 and the variance is 0.35.
The variance represents the average of the squared deviations from the mean, so we can write:
variance = (standard deviation)^2
The standard deviation is the square root of the variance, so we have:
standard deviation = sqrt(variance) = sqrt(0.35) = 0.59
Now, if the price of a box of Cheerios oat crunch increases by 25 cents, the new mean cost will be:
new mean = $4.00 + $0.25 = $4.25
To find the new variance, we need to calculate the new squared deviations from the mean and take their average. The squared deviation of each observation is given by:
(new cost - new mean)^2
We can simplify this expression by substituting the new mean and the original standard deviation:
(new cost - $4.25)^2 = (old cost - $4.00 + $0.25)^2 = (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2
The first term on the right-hand side is the squared deviation of the original cost, the second term represents the change in the squared deviation due to the increase in price, and the third term is a constant that does not affect the variance.
To find the new variance, we need to take the average of these squared deviations. Since the original variance was 0.35, we have:
new variance = (1/n) * [sum of (new cost - new mean)^2]
where n is the number of observations (we assume it is large enough to use the normal distribution approximation). Using the expression above for the squared deviation, we can write:
new variance = (1/n) * [sum of (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2]
We can simplify this expression by using the properties of summation:
new variance = (1/n) * [sum of (old cost - $4.00)^2] + (2/$n) * ($0.25) * [sum of (old cost - $4.00)] + ($0.25^2)
The first term is the original variance, the second term is zero (since the sum of deviations from the mean is always zero), and the third term is a constant that does not affect the variance. Therefore, the new variance is:
new variance = 0.35 + ($0.25)^2 = 0.41
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multiply 6 by f, then subtract 4 from the result
Swapping the contents of two variables requires a third variable that can serve as a temporary storage location. True False.
Answer:
True.
Step-by-step explanation:
True.
Let's say A = 5, and B = 10.
We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.
A = 5
B = 10
Introduce variable C.
C = A (now C contains 5)
A = B (now A contains 10)
B = C (now B contains 5)
In the last two steps above, you see that the values of A and B were swapped.
if drawing a red marble is 20% and a green marble is 28.57% and a blue marble 22.8% and a yellow marble is 22.85%, what is the probabilty of picking a red one then a green one then a blue one?
The probability of picking a red marble, then a green marble, and finally a blue marble is 0.091424%, or approximately 0.09%.
To find the probability of picking a blue marble, given that we have already picked a red and a green marble, we use the same method:
P(B|R and G) = P(R and G and B) / P(R and G)
where P(B|R and G) is the probability of picking a blue marble, given that a red marble and a green marble have been selected, and P(R and G and B) is the probability of picking a red marble, then a green marble, and finally a blue marble.
Using the given probabilities, we can plug in the values and simplify:
P(B|R and G) = (0.2 x 0.2857 x 0.228) / (0.2 x 0.2857) = 0.016
This means that if we have already picked a red marble, then a green marble, there is a 1.6% chance of picking a blue marble next.
Finally, to find the probability of picking a red marble, then a green marble, and finally a blue marble, we multiply the probabilities of each event together:
P(R and G and B) = P(R) x P(G|R) x P(B|R and G)
=> 0.2 x 0.2857 x 0.016 = 0.00091424 or 0.09%
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Unit 2: Logic & Proof
Homework 2: Compound Statements
A combination of two or more simple statements is a compound statement. The connectives generally used in mathematics are ‘and’, ‘or’, ‘if ’, ‘if and only if’.
In mathematics, like in any language, compound statements are created by combining simpler ones using connectives. The truth value of a compound statement is determined by the truth value of its smaller components.
There are four compound statements:
1. ¬p , Not p (i.e. the negation of p) : Negation
2. p ∧ q, p and q : Conjunction
3. p ∨ q, p or q : Disjunction
4. p → q, If p then q : Conditional
Beginning with the premise that P (the hypothesis) is true, we create a chain of implications, each of which has previously been proven to be true, ultimately leading to Q. (the conclusion). Imagine the chain has six consequences. As a result, the direct proof technique may be expressed combination as follows:
P, P ⇒ P1, P1 ⇒ P2, P2 ⇒ P3, P3 ⇒ Q1, Q1 ⇒ Q2, Q2 ⇒ Q.
If P and the implications in the previous chain are all true, we must derive that Q is likewise true logically. But, according to the truth table for P ⇒ Q, knowing that P ⇒ Q is a true statement does not indicate that P or Q are true, just that the inference is true. Recall that P can be false, Q can be true or false, and the inference might be true or false.
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Question: What are Compound Statements? Write proof and logic for the statements.
Find the distance between the two points in simplest radical form.
(-4, -6) and (2, -1)
The distance between the two points is [tex]\sqrt{61}[/tex]
Explanation:
Given that the two points are [tex](-4,-6)[/tex] and [tex](2,-1)[/tex]
We need to determine the distance between the two points in simplest radical form.
The distance between the two points can be determined using the
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let us substitute the coordinates [tex](-4,-6)[/tex] and [tex](2,-1)[/tex] in the above formula, we get,
[tex]d=\sqrt{(2+4)^2+(6+1)^2}[/tex]
Simplifying the terms, we get,
[tex]d=\sqrt{(6)^2+(7)^2}[/tex]
Squaring the terms, we get,
[tex]d=\sqrt{36+49}[/tex]
Adding, we get,
[tex]d=\sqrt{85}[/tex]
Simplifying, we have,
[tex]\sqrt{61}[/tex]
Thus, the distance between the two points in simplest radical form is [tex]\sqrt{61}[/tex]
Can someone solve this and thoroughly explain it to me, !!I will give brainliest!!
Answer:
11.9m
Step-by-step explanation:
explanation in picture :)
please mark brainliest
Answer:
11.81 is the height
what number is 120% more than 180?
how do you solve this step by step
txs for the help
two cyclists leave towns miles apart at the same time and travel toward each other. one cyclist travels faster than the other. if they meet in hours, what is the rate of each cyclist?
As per the travelling distance, if they meet in hours, then the rate of each cyclist is r₂ miles per hour.
Let's assume that the two towns are A and B, and the distance between them is d miles. Let the first cyclist start from town A and travel towards town B, and the second cyclist start from town B and travel towards town A. Let's also assume that the first cyclist travels at a rate of r₁ miles per hour, and the second cyclist travels at a rate of r₂ miles per hour.
Now, let's consider the time it takes for the two cyclists to meet. Since they are traveling towards each other, their combined speed is (r₁ + r₂) miles per hour. We can use the formula:
distance = speed × time
to find the time it takes for them to meet. Let t be the time taken for them to meet, then we can write:
d = (r₁ + r₂) × t
where d is the distance between the two towns.
Now, we need to solve for r₁ and r₂. We can use the fact that the two cyclists meet in hours to write:
t = d / (r₁ + r₂)
Substituting this expression for t in the equation we got earlier, we get:
d = (r₁ + r₂) × (d / (r₁ + r₂))
Simplifying this equation, we get:
r₁ + r₂ = d / t
Substituting the value of t, we get:
r₁ + r₂ = d / (d / (r₁ + r₂))
r₁ + r₂ = (r₁ + r₂)
This equation tells us that the sum of the rates of the two cyclists is equal to the distance between the two towns divided by the time it takes for them to meet.
We can now use algebra to solve for r₁ and r₂. Let's assume that r₁ is the faster cyclist, then we have:
r₁ = (d / t) - r₂
Substituting the value of t, we get:
r₁ = (d / (d / (r₁ + r₂))) - r₂
Simplifying this equation, we get:
r₁ = (r₁ + r₂) - r₂
r₁ = r₁
This equation tells us that the rate of the faster cyclist is equal to itself, which is obvious.
Now, we can find the rate of the slower cyclist by using the fact that:
r₂ = (d / t) - r₁
Substituting the value of t, we get:
r₂ = (d / (d / (r₁ + r₂))) - r₁
Simplifying this equation, we get:
r₂ = (r₁ + r₂) - r₁
r₂ = r₂
This equation tells us that the rate of the slower cyclist is also equal to itself, which is obvious.
Therefore, we can conclude that the rate of the faster cyclist is r₁ miles per hour, and the rate of the slower cyclist is r₂ miles per hour, where:
r₁ = (d / t) - r₂
r₂ = (d / t) - r₁
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if the given triangles are similar find the missing length
Answer 24 do you enderstand?
The length of a picture frame is 6 inches more than the width. For what values of x is the perimeter of the picture frame greater than 152 inches?
If the width of the picture frame is greater than 35 inches, then the perimeter of the frame will be greater than 152 inches.
Let's first set up an equation for the perimeter of the picture frame. The perimeter is the sum of the lengths of all four sides, and we know that the length is 6 inches more than the width. Let's use x to represent the width:
Perimeter = 2(length + width)
Perimeter = 2(x + (x+6))
Perimeter = 4x + 12
Now, we want to find the values of x for which the perimeter is greater than 152 inches. We can set up an inequality:
4x + 12 > 152
Subtracting 12 from both sides:
4x > 140
Dividing both sides by 4:
x > 35
So the width must be greater than 35 inches in order for the perimeter to be greater than 152 inches.
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