the sunglasses will never hit the ground.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The height of the sunglasses at time t is given by the function h(t) = 16t^2 + 5776.
When the sunglasses hit the ground, their height will be 0. So we need to find the value of t that makes h(t) = 0.
16t^2 + 5776 = 0
Dividing both sides by 16, we get:
t^2 + 361 = 0.
This equation has no real solutions since t^2 is always non-negative and can never be equal to a negative number.
Therefore, the sunglasses will never hit the ground.
Learn more about function, by the following link.
https://brainly.com/question/25638609
#SPJ1
A total of 100 people went to the
movies. A ticket cost $4 for adults and
$2 for children. The total sales
amounted to $276. How many children
and adults attended the movies?
Using a system of equations, the number of children and adults who attended the movies is as follows:
Children = 62Adults = 38.What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also known as simultaneous equations.
The total number of people who went to the movies = 100
The unit cost of adult tickets = $4
The unit cost of children tickets = $2
The total sales = $276
Let the number of children who attended the movies = x
Let the number of adults who attended the movies = y
Equations:x + y = 100 ... Equation 1
2x + 4y = 276 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 200 ... Equation 3
Subtraction Equation 3 from Equation 2:
2x + 4y = 276
-
2x + 2y = 200
2y = 76
y = 38
Substitute y = 19 in equation 1:
x + y = 100
x + 38 = 100
x = 62
Check in Equation 2:
2x + 4y = 276
2(62) + 4(38) = 276
124 + 152 = 276
Learn more about a system of equations at https://brainly.com/question/13729904.
#SPJ1
Given the parent function f(x)=√x and a new function g(x)=√x+6+3.
Select from the drop-down menus to correctly describe the changes on the graph from f(x) to g(x)
1. The graph will shift 6 units ___
UP , DOWN , LEFT , RIGHT
2. and 3 units ____
UP , DOWN , LEFT , RIGHT
Answer:
up down
Step-by-step explanation:
Calculate the cross product (+)×(5+4)
assuming that
×=⟨1,1,0⟩,×=⟨0,3,1⟩,×=⟨2,−1,1⟩
The cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.
To calculate the cross product (+)×(5+4)We need to use the vector cross product formula:
a × b = |a| |b| sin(θ) n
Where
a and b are the two vectors being multiplied, |a| and |b| are their magnitudesθ is the angle between themn is a unit vector perpendicular to both a and b (in the direction determined by the right-hand rule)Using the given values of ×, we have:
(+) × (5+4) = ⟨1, 1, 0⟩ × ⟨5, 4, 0⟩
= |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(θ) n
Where θ is the angle between ⟨1, 1, 0⟩ and ⟨5, 4, 0⟩. To find θ, we can use the dot product formula:
a · b = |a| |b| cos(θ)
⟨1, 1, 0⟩ · ⟨5, 4, 0⟩ = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| cos(θ)
1(5) + 1(4) + 0(0) = √2 √41 cos(θ)
9 = 2√41 cos(θ)
cos(θ) = 9/(2√41)
θ ≈ 20.11 degrees
Now we can plug in the values to find the cross product:
(+) × (5+4) = |⟨1, 1, 0⟩| |⟨5, 4, 0⟩| sin(20.11) n
= √2 √41 sin(20.11) n
= (2/√41) ⟨-2sin(20.11), 3sin(20.11), 2√2cos(20.11)⟩
= ⟨-0.362, 0.536, 0.489⟩
Therefore, the cross product of (+) and (5+4) is approximately ⟨-0.362, 0.536, 0.489⟩.
Learn more about cross product here : brainly.com/question/31056901
#SPJ1
Mary is planning to buy a mobile phone that costs $500. She can choose any of five different payment plans with varying simple interest rates and periods:
plan 1: 6% for 10 months
plan 2: 8% for 12 months
plan 3: 10% for 14 months
plan 4: 12% for 18 months
plan 5: 14% for 12 months
Which plan offers the lowest monthly payments?
As a result, Plan 4's $38.89 monthly premium is the lowest.
How to find the lowest monthly payments ?The monthly premium you pay for health insurance. You typically have to pay additional fees for your health care in addition to your premium, such as a deductible, copayments, and coinsurance.
(P + Simple Interest) / (500 + 58.33) / 14 = $42.02 is the formula for the monthly payment.
Plan 4: P = $500
t = 18/12 years, and r = 0.12
Simple interest equals $500 * 0.12/* (18/12) = $90.
(P + Simple Interest) / t = ($500 + $90) / 18 = $38.89 is the monthly payment.
Plan 5: P = $500
t = 12/12 years, and r = 0.14.
Simple interest is equal to $500 * 0.14 * (12/12) = $70.
(P + Simple Interest) / t = ($500 + $70) / 12 = $47.50 is the amount due each month.
As a result, Plan 4's $38.89 monthly premium is the lowest.
To know more about premium visit:-
https://brainly.com/question/7511249
#SPJ1
Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, she will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result?
a. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05.
b. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05.
c. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
d. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05
Compute the estimated Cohen’s d to measure the size of the treatment effect.
Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment.
Estimated Cohen’s d =
Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.
The correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
What is standard deviation?A statistical measure known as the standard deviation depicts how variable or dispersed a set of data is. It is determined by taking the square root of the variance, which is the sum of the squared deviations from the data set mean. While a large standard deviation suggests that the data points are more dispersed, a small standard deviation suggests that the data points tend to be close to the mean. It can be used to assess the variability between different data sets and is frequently used as a gauge of a data set's consistency or reliability.
Given, level of significance = 0.05.
n = 49 and sample > 30
Thus, using z-score we have:
z = 4.04 - 3.68 / (0.70/7) = 3.60
Now, p-value = 0.000318
Now, for P < 0.05 we have:
cohens D = 4.04 - 3.67 / 0.70 = 0.51
This shows a medium increase.
Hence, the correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
The estimated Cohen’s d is given as:
Cohen’s d = (M - μ) / σ
The sample standard deviation is not given, so we cannot calculate the exact value of Cohen's d.
The sample standard deviation will determine the estimated Cohen's d in this situation, although if it is greater than 0.2, it might be regarded as having a small effect size.
Learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ1
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]
Hurit Imala works 40 hours a week as a clerk in a local store. She earns $8.50 an hour. Assuming she is paid for 52 weeks annually, what is her gross annual pay?
Answer:
Hurit Imala's gross annual pay is $17,680
Step-by-step explanation:
Hurit Imala works 40 hours a week, so her weekly pay would be:
40 hours/week x $8.50/hour = $340/week
To find her annual pay, we need to multiply her weekly pay by the number of weeks in a year:
$340/week x 52 weeks/year = $17,680/year
Therefore, Hurit Imala's gross annual pay is $17,680.
Help me with this question
Answer:27.5 i hope you really like this answer i hope its right too
Answer:
46
Step-by-step explanation:
You want to know the number of regular pentagonal prism marshmallows that can be covered with 1.5 L of chocolate if each cm² takes 0.5 mL. The base area is 7 cm², and each rectangular face is 2 cm by 5 cm.
AreaThe area of each marshmallow is the sum of the areas of the 2 bases and 5 faces. Each face is a 2 cm by 5 cm rectangle, so has an area of ...
A = LW
A = (5 cm)(2 cm) = 10 cm²
The bases each have an area of 7 cm², so the total area is ...
total area = base area + face area
total area = 2 × 7 cm² + 5 × 10 cm² = 64 cm²
ChocolateEach cm² takes 0.5 mL of chocolate to cover it, so the chocolate required for one marshmallow is ...
(0.5 mL/cm²)(64 cm²) = 32 mL
1.5 L of chocolate is 1500 mL, so the number that can be covered is ...
(1500 mL)/(32 mL/marshmallow) = 46 7/8
Kaitlyn can completely cover 46 marshmallows with the chocolate she has.
the lenghth of a picture frame is 7 inches more than th width. For what values of x is the perimeter of the picture frame greater than 154 inches
Answer:
x > 35
Step-by-step explanation:
Let's denote the width of the picture frame as "x" inches.
According to the problem, the length of the picture frame is 7 inches more than the width, so it can be expressed as "x + 7" inches.
The perimeter of the picture frame can be found by adding up the lengths of all four sides, which is given by:
Perimeter = 2*(length + width)
Substituting the values of length and width in terms of x, we get:
Perimeter = 2*(x + 7 + x)
Perimeter = 4x + 14
Now we can set up an inequality to find the values of x for which the perimeter is greater than 154 inches:
4x + 14 > 154
Subtracting 14 from both sides, we get:
4x > 140
Dividing both sides by 4, we get:
x > 35
Therefore, the values of x for which the perimeter of the picture frame is greater than 154 inches are x > 35.
A line has a slope of -2 and passes through the point (-2, -3). Write its equation in slope-
intercept form.
The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.
Given: Slope (m) = -2 and point (-2, -3)
Step 1: Use the point-slope form of a line's equation to find the equation of the line in point-slope form:y - y1 = m(x - x1) (where x1,y1 are the coordinates of the given point)y - (-3) = -2(x - (-2))y + 3 = -2(x + 2)Step 2: Simplify the equation by distributing the -2:y + 3 = -2x - 4Step 3: Solve for y by subtracting 3 from both sides of the equation:y = -2x - 7Therefore, the equation of the line in slope-intercept form is y = -2x - 7.A boat is heading towards a lighthouse, where Lamonte is watching from a vertical distance of 141 feet above the water. Lamonte measures an angle of depression to the boat at point � A to be 21 ∘ ∘ . At some later time, Lamonte takes another measurement and finds the angle of depression to the boat (now at point � B) to be 57 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 812 feet.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Here lines AC and ED are parallel. So alternate angles are equal. Now the corresponding angles in triangle ADC and BDC.
In Δ ADC ,
=> tan 9 = opposite / adjacent = 141/AC
=> AC = 141/ tan9= 890.2389.
Now In ΔBDC,
=> tan 61 = 141/BC
=> BC = 141/tan 61 = 78.1575
Now distance AB = AC - BC = 890.2389 - 78.1575 = 812 feet.
Hence the distance from point A to point B is 812 feet.
To learn more about triangle refer the below link
https://brainly.com/question/17335144
#SPJ1
NEED HELP!! 9.1 Puzzle Time
What Do You Get When You Cross a Computer With a Lifeguard?
6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.
What is Pythagoras Theorem?The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.
6. For a = 20, b = 99 using the Pythagoras Theorem we have:
x² = a² + b²
x² = 20² + 99²
x² = 9801
x = 99
7. For a = 60, b = 91 we have:
x² = 60² + 91²
x² = 10521
x ≈ 102.56
8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.
a = 20, b = 21, and c = 29
Here,
20² + 21² = 841
29² = 841
Hence, the triangle is right.
9. For a = 15, b = 19, and c = 24. We have:
15² + 19² = 556
24² = 576
The triangle is acute.
10. For a = 11, b = 23, and c = 26. We have:
11² + 23² = 650
26² = 676
The triangle is acute.
11. Using the Pythagoras Theorem we have:
x² = 53² - 45²
x² = 1044
x ≈ 32.28
The value of x is 32.28
12. x² = 41² - 9²
x² = 1600
x = 40
The value of x is 40.
Learn more about Pythagoras Theorem here:
https://brainly.com/question/343682
#SPJ1
Answer:
Step-by-step explanation:
At West Point School District, enrollment increased from 320 students in 2019 to 225 students in 2020. What is the percent of change in enrollment? Round to the nearest percent.
Answer:95
Step-by-step explanation: cause 320 - 225 = 95
The following are equivalent radicals
3√3 = √27
-
3√6 = √54
3√7 = √63
What would be an equivalent form of 3√11 ? Explain
how you know.
You made $75 an hour with your commission pay. This month I want to increase that by 20% so that I make
The vertices of a rectangle are plotted.
A graph with both the x and y axes starting at negative 8, with tick marks every one unit up to 8. The points negative 5 comma 2, 4 comma 2, negative 5 comma negative 4, and 4 comma negative 4 are each labeled.
What is the area of the rectangle?
15 square units
30 square units
45 square units
54 square units
The area of the rectangle is d. 54 square units.
What is rectangle?A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.
The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.
From the given points, we can see that the length of one pair of parallel sides of the rectangle is:
4 - (-5) = 9 units
And the length of the other pair of parallel sides of the rectangle is:
2 - (-4) = 6 units
Therefore, the area of the rectangle is:
9 units × 6 units = 54 square units.
So the area of the rectangle is d. 54 square units.
Learn more about area of rectangle on:
https://brainly.com/question/2607596
#SPJ1
Please help !!!!!!!!!
The expression can be said to be equivalent because they could be simplified to give the same result.
What are equivalent expressions?Equivalent expressions are two or more mathematical expressions that have the same value for all values of the variables involved. In other words, if you substitute the same values for the variables in two different expressions that are equivalent, you will get the same result.
Thus we can see that; 1/2x^3(8x + 10x^6) is equivalent to x^4(5x^4 + 4) as shown
Learn more about equivalent expressions:https://brainly.com/question/28170201
#SPJ1
Solve the equation
x^2 + 11x - 26 = 0
The two solutions of the quadratic equation x² + 11x - 26 = 0 are x = 2 and x = -13
How to solve the quadratic equation?Here we have the quadratic equation:
x² + 11x - 26 = 0
A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.
To solve it we need to use the quadratic formula, it will give:
[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}[/tex]
Now we can simplify that and we will get two solutions, these are:
[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}\\\\x = \frac{-11 \pm15}{2}[/tex]
Then the two solutions of the quadratic equation are:
x+ = (-11 + 15)/2 = 4/2 = 2
x- = (-11 - 15)/2 = -26/2 = -13
Learn moer about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
Task 1abcd: Suppose we have n = 60 puppies (across several litters from these two dogs). For the sample, we have the (previously observed) sample proportion
= 0.3833.
Suppose we wanted to use this sample to determine if there is evidence that p = the population proportion of puppies who are spotted is greater than 0.25.
a. State the hypotheses about the population proportion p.
H0:
H1:
H0 is the null hypothesis stating with that the population proportion of
puppies who are spotted is less than or equal to 0.25,
H0: p <= 0.25
H1: p > 0.25
Why do you use the term "hypothesis"?In a scientific setting, a hypothesis (plural: hypotheses) is a tested
claim regarding the causal connection between two or more variables
or a suggested explanation for a phenomenon that has been
observed.
where H0 is the null hypothesis stating that the population proportion
of puppies who are spotted is less than or equal to 0.25, and H1 is the
alternative hypothesis stating that the population proportion of puppies
who are spotted is greater than 0.25.
To know more about hypotheses Visit:
https://brainly.com/question/18064632
#SPJ1
A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at α = .05. (a) State the null and alternative hypothesis in symbolic form. (b) Find the test statistic (preferably obtained using technology). Sketch a graph of the normal distribution clearly showing the test statistic (rounded to two decimal places) and the critical region, α=.05. (c) Decide and explain your choice to reject the null or fail to reject the null. (d) Write a summary statement addressing the original claim
Answer:
A watch manufacturer believes that 60% of men over the age of 50 wear watches. So, the manufacturer took a simple random sample of 275 men over the age of 50, and 170 of those men wore watches. Test the watch manufacturer's claim at α = 0.5 using PHANTOMS.
sinusodial math equations
f. The height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm. g. when θ = 160 is -4.33 cm. h. g(θ) is 10. i. k = 150.
Describe Function?A function is a mathematical concept that describes the relationship between two sets of numbers or values, called the domain and the range. It assigns to each value in the domain a unique value in the range. The domain is the set of all possible input values, while the range is the set of all possible output values.
A function can be represented by an equation, a graph, or a table of values. The equation of a function typically has a variable, often denoted as x, that represents the input or independent variable, and a formula that expresses how the input is transformed to obtain the output or dependent variable, often denoted as y.
f. At 6:00 am, the minute hand is pointing directly up, so the angle rotated by the minute hand from 6:00 am is θ = 0. Plugging this into the function h(θ) = 10 cosθ + 13, we get:
h(0) = 10 cos(0) + 13 = 23
So, the height of the endpoint of the minute hand above the bookshelf at 6:00 am is 23 cm.
g. To find the height of the endpoint of the hour hand above the bookshelf when θ = 160, we need to convert θ to the angle rotated by the hour hand from 6:00 am. Since the hour hand rotates 30 degrees for every hour, or 0.5 degrees per minute, the angle rotated by the hour hand from 6:00 am is 30(5) + 0.5(0) = 150 degrees.
So, we need to find g(150), which is:
g(150) = -10 cos(150/12) + 13 = -4.33
Therefore, the height of the endpoint of the hour hand above the bookshelf when θ = 160 is -4.33 cm.
h. The amplitude of g(θ) is the absolute value of the coefficient of the cosine function, which is 10. So, the amplitude of g(θ) is 10.
i. The endpoints of the minute hand and hour hand meet when they are pointing in the same direction, so the angle rotated by the minute hand from 6:00 am must be a multiple of 30 degrees. To find the smallest possible value of k, we need to find the smallest multiple of 30 that is greater than or equal to 150 (the angle rotated by the hour hand from 6:00 am). This is 30(5) = 150.
So, the smallest possible value of k is when the minute hand has rotated 150 degrees from 6:00 am, which is at 5:00 am and 30 seconds. Therefore, k = 150.
To know more about angle visit:
https://brainly.com/question/12193412
#SPJ1
The question is In the image
the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
how to solve probability?
There are 38 possible outcomes for a single spin of the American roulette wheel. Out of these 38 slots, two are labeled 0 and 00, and half of the remaining 36 slots are red and half are black.
Therefore, the probability of the marble landing on a black slot is 18/38 or 9/19. This is because there are 18 black slots out of a total of 38 slots.
Similarly, the probability of the marble landing on a 00 slot is 1/38.
To find the probability of the marble landing on either a 00 or black slot, we can add the probabilities of these two events. That is,
P(00 or black) = P(00) + P(black)
= 1/38 + 9/19
= (1 + 18)/38
= 19/38
Therefore, the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
It is important to note that while the probability of winning on a single bet in roulette may seem attractive, the game has a high house edge, meaning that the odds are in favor of the casino. Therefore, it is important to gamble responsibly and within one's means.
To know more about probability visit :-
https://brainly.com/question/13604758
#SPJ1
find the values of X and Y
The values of x and y for the right triangle are 4 and 7.21
How to evaluate for the values of x and y for the triangleThe perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.
by Pythagoras, the hypotenuse for the bigger of the two triangles is calculated as;
√(6² + 9²) = 10.82
the angle opposite the side length 6 for triangle with hypotenuse 10.82 and the angle opposite the side length x for triangle with hypotenuse y are the same by proportion, so:
x/6 = 6/9 {opposite/adjacent}
x = 36/9 {cross multiplication}
x = 4
also;
4/y = 6/10.52 {opposite/hypotenuse}
y = 42.08/6
y = 7.21
Therefore, the values of x and y for the right triangle are 4 and 7.21
Read more about right triangle here:https://brainly.com/question/2920412
#SPJ1
Write three dollars and 65 cents
as an improper fraction (and then reduce).
Answer:
300/65
Step-by-step explanation:
Answer:
3 65/100 then the simplified version is 13/20
Step-by-step explanation:
Find the value of x:
With regards to the above geometry problems the value of x are given below.
a) Here x = 15
b) here x = 28
These are solved using proportions.
How does proportion help to solve the above problems?Proportion helps to solve the above problems by setting two ratios equal to each other and cross-multiplying to solve for the unknown variable, which satisfies the ratio relationship between the two quantities.
a)
To solve for x, we can cross-multiply the fractions and simplify:
x/20 = 9/12
Cross-multiply:
12x = 9 * 20
Simplify:
12x = 180
x = 15
Therefore, the solution to the equation x/20 = 9/12 is x = 15.
b)
To solve for x, we can cross-multiply the fractions and simplify:
15/(x-3) = 18/(x+2)
Cross-multiply:
15(x+2) = 18(x-3)
Simplify:
15x + 30 = 18x - 54
Subtract 15x from both sides:
30 = 3x - 54
Add 54 to both sides:
84 = 3x
Divide both sides by 3:
x = 28
Therefore, the solution to the equation 15/(x-3) = 18/(x+2) is
x = 28.
Learn more about proportions:
https://brainly.com/question/29474065
#SPJ1
Geometry task!!!
Please help for all three , a) , b) , and c)
The power emitted by the star's surface is much greater than the power generated by its interior.
How to explain the informationa) The power generated by the star's interior can be calculated using the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(7x10^8)³ ≈ 1.41x10^27 cm³
Multiplying this volume by the power generated per cubic centimeter, we get:
P(interior) = 3x10^-7 watts/cm^3 x 1.41x10^27 cm^3 = 4.23x10^20 watts
The power emitted by the star's surface can be calculated using the formula for the surface area of a sphere:
A = 4πr²
Substituting r = 7x10^8 cm, we get:
A = 4π(7x10^8)^2 ≈ 6.16x10^18 cm^2
Multiplying this area by the power emitted per square centimeter, we get:
P(surface) = 6,000 watts/cm² x 6.16x10^18 cm^2 = 3.70x10^22 watts
We can see that the power emitted by the star's surface is much greater than the power generated by its interior.
b) Following the same process as in part (a), we get:
V = (4/3)π(5x10^12)³ = 5.24x10^38 cm³
P(interior) = 3x10^-7 watts/cm^3 x 5.24x10^38 cm^3 = 1.57x10^32 watts
A = 4π(5x10^12)^2 ≈ 3.14x10^26 cm²
P(surface) = 6,000 watts/cm^2 x 3.14x10^26 cm^2 = 1.88x10^30 watts
Again, we see that the power emitted by the star's surface is much greater than the power generated by its interior. However, the difference between the two quantities is much smaller in this case compared to the previous case.
Learn more about power on
https://brainly.com/question/1634438
#SPJ1
A desk is on sale for $119, which is 65% less than the regular price.
Answer:
320 would be the regular price
Step-by-step explanation:
Read the following text from a student essay. How can the writer best improve his or
her organization?
Ponies are a type of horse, but there are significant differences between ponies and
horses. Ponies are generally shorter than horses. Ponies also tend to live longer than
horses. Horses are considered to be over fifty-eight inches tall, and ponies are less
than that. Horses usually live to be twenty-five to thirty years old. Most ponies live
to be thirty-five or even forty.
by adding missing commas
moving the first sentence to the end of the paragraph
by moving the first sentence to the second paragraph
by reordering sentences to keep the related ideas together
The writer can best improve their organization by reordering sentences to keep related ideas together.
Who is called writer?
Writers are individuals who use written words to communicate ideas, stories, or information to a particular audience. They may work in various fields such as journalism, creative writing, copywriting, technical writing, or academic writing. Writers can be novelists, poets, essayists, screenwriters, playwrights, and more, and their work can take many forms, such as books, articles, blogs, scripts, and speeches. Writing is a skill that can be developed and honed through practice, and good writers are able to engage and captivate their readers with their words.
Here,
The writer can best improve their organization by reordering sentences to keep related ideas together. Here's a possible reorganization of the text:
Ponies and horses have significant differences. Horses are considered to be over fifty-eight inches tall and usually live to be twenty-five to thirty years old. In contrast, ponies are generally shorter than horses, with a height of less than fifty-eight inches, and they tend to live longer, often up to thirty-five or even forty years.
This revision keeps the sentences that relate to each other together, creating a clear and logical progression of ideas. Additionally, it removes the redundant statement of defining ponies as a type of horse, which is already well-known information.
Learn more about essay here,
https://brainly.com/question/30849680
#SPJ1
11. A local grocery store has 7 different kinds of hot sauce that you would love try.
However, you only have enough money to purchase 5 of the different flavors. How
many of the flavors of hot sauce are possible for you to purchase?
we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by: C(7,5) = 21
what is combinations ?
Combinations, on the other hand, refer to the selection of objects from a set without considering their order. For example, the combinations of 2 letters from the set "ABC" are "AB", "AC", and "BC". The order of the letters in each combination does not matter, so "AB" and "BA" are considered the same combination.
In the given question,
This is a combination problem, since we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by:
C(7,5) = 7! / (5! * 2!) = (76543) / (54321) = 21
Therefore, you can purchase 21 different combinations of 5 flavors of hot sauce
To know more about combinations , visit:
https://brainly.com/question/10525991
#SPJ1
Knowing that the given sides are congruent, find the perimeter of the
triangle. *Congruent is EQUAL
9x-3
4x+7
Answer:
Step-by-step explanation:
9x-3=4x+7
+3
9x=4x+10
-4x=-4x
5x=10
divide the 5 by 10 which equals 2.
x=2
