The equation can be solved using the quadratic formula when the following expression is used: [tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]
What is quadratic formula?The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.
The following general quadratic equation is given:
ax² + bx + c = 0
As a result, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation. Quadratum is the Latin word for square, and since the area of a square with side length x is given by x2, this is the case.
A quadratic equation's solution(s) can be found using the quadratic formula in elementary algebra. Graphing, factoring (direct factoring, grouping, AC technique), completing the square, and other methods can be used to solve a quadratic equation in addition to the quadratic formula.
The given equation is x² - 4x + 3 = 0
When compared to the quadratic equation's general equation, we get a = 1, b = -4, c = 3.
When the coefficient values for the Sridhar Acharya formula are put in,[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex] which gives Option (A).
To learn more about quadratic formula, refer to:
https://brainly.com/question/1214333
#SPJ1
The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of p hat ?
Mu Subscript p hat = p = 0.12
Mu Subscript p hat = n p = 100 (0.12) = 12
Mu Subscript p hat = 1 minus p = 1 minus 0.12 = 0.88
Mu Subscript p hat = n (1 minus p) = 100 (1 minus 0.12) = 88
The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.
The sampling distribution of p hat follows a normal distribution thus,
Mu Subscript p hat = p
Here, the value of p = 0.12
Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
Learn more about normal distribution here:
https://brainly.com/question/29509087
#SPJ1
Answer:
A. Mu Subscript p hat = p = 0.12
Step-by-step explanation:
peter sets up a neurological study in which he wants to investigate three pre-defined groups of patients. each group of patients is already diagnosed with the same neurological syndrome. peter not only examines the average score for each group of patients, but also the scores for each individual patient. peter's study is an example of...
Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.
Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.
Learn more about Cross-sectional clinical study here brainly.com/question/15872876
#SPJ4
pls help due tomorrow!!!
Answer:
[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]
[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]
Solve for x ? Question in picture
Answer:
22
Step-by-step explanation:
x+35=56
56-35=22
x=22
Clinton borrows a certain amount of money and pays the principle amount and the interest back after 5 years. Calculate the simple interest rate if Clinton pays back double the amount he borrowed
Answer: The simple interest will be 20%.
Step-by-step explanation:
we know the simple interest of borrowed amount is:
S.I.= (P x R x T)/100 ..... (i)
where P⇒ Principal amount
R⇒ rate of interest
T⇒ time
and
total Pays Back amount = Principal amount + S.I.
Hence S.I. = Pays Back amount - Principal amount
Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means
if Principal amount = P
then Pays Back amount = 2P ⇒ S.I.= P
Rate of Interest = R
and Time = 5 years
P= (P x R x 5)/100
R= 100/5
R = 20%
Therefore, the simple interest is 20% annually.
Know more about Simple Interest.
brainly.com/question/13381098
Please help, I’ll give brainliest
Answer: Distributive property and Commutative property (of multiplication)
Step-by-step explanation:
From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.
From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.
HOPE THIS HELPS _- MM
Does the set of odd integers have the density property? Explain.
It should be noted that the set of odd integers has the density property. The density property states that for every subset of the real numbers that contains an infinite number of points, the interior of that subset contains a non-empty open interval. This is true
How to explain the informationThe set of odd integers is a countable subset of the real numbers, meaning that it can be put into a one-to-one correspondence with the natural numbers. However, even though it is countable, it still has an infinite number of points.
Since the set of odd integers contains an infinite number of points, it must contain a non-empty open interval in its interior. To see this, consider the interval (2n-1, 2n+1) for any positive integer n. This interval contains the odd integer 2n and its endpoints are both odd integers, so it is completely contained in the set of odd integers.
Therefore, the set of odd integers has the density property and is a dense subset of the real numbers.
Learn more about integer on:
https://brainly.com/question/17695139
#SPJ1
pls help me i need now and if the answer is correct i give free BRAINLIEST HERE!!!!
THANK YOU
The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;
m∠1 = 47.5°[tex]m\widehat{BD}[/tex] = 110°m∠COD = 55°[tex]m\widehat{CD}[/tex] = 20°m∠AOC = 100°m∠APB = 25°m∠ADB = 25°[tex]m\widehat{CD}[/tex] = 90°[tex]m\widehat{AB}[/tex] = 70°[tex]m\widehat{CD}[/tex] = 100°What is a secant of a circle?A secant is a line that has two points of intersection on a circle.
The specified parameters are;
1. The measure of arc [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°
Angle at the center of the circle = 2 × Angle at the circumference
Angle at the center of the circle = The arc angle of the circle
Therefore;
m∠DAC = 15°/2 = 7.5°
m∠ACO = 80°/2 = 40°
The external angle of a triangle theorem, indicates that we get;
m∠1 = 40° + 7.5° = 47.5°
m∠1 = 47.5°
2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°
The intersecting chords theorem indicates that we get;
m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])
[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°
[tex]m\widehat{BD}[/tex] = 110°
3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°
Therefore; m∠ACO = 90°/2 = 45°
m∠DAC = 20°/2 = 10°
The external angle theorem indicates that we get;
m∠COD = 45° + 10° = 55°
m∠COD = 55°
4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;
m∠ACO = 50°/2 = 25°
m∠CAO = 35° - 25° = 10°
[tex]m\widehat{CD}[/tex] = 2 × m∠CAO
Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°
[tex]m\widehat{CD}[/tex] = 20°
5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°
m∠AOC = 100°
6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°
The external secant, tangent theorem, indicates that we get;
m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])
m∠APB = (1/2) × (70° - 20°) = 25°
m∠APB = 25°
7. [tex]m\widehat{AB}[/tex] = 50°,
The angle at the center of a circle is twice the angle subtended at the circumference, therefore;
m∠ADB = 50°/2 = 25°
m∠ADB = 25°
8. m∠CAD = 45°
The angle formed by an arc at the center of a circle theorem, indicates that we get;
[tex]m\widehat{CD}[/tex] = 2 × m∠CAD
[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°
[tex]m\widehat{CD}[/tex] = 90°
9. m∠ACB = 70°
m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference
Therefore;
[tex]m\widehat{AB}[/tex] = 2 × m∠ACB
[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°
[tex]m\widehat{AB}[/tex] = 70°
10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°
m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])
Therefore; m∠(AOB) = 80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°
[tex]m\widehat{CD}[/tex] = 100°
Learn more on circle theorems related to the secants of a circle here: https://brainly.com/question/3003038
#SPJ1
a car dealership collected a sample of 1000 used cars for miles cars were driven. the sample included 20 different car models, across multiple years. in a single chart, an analyst wants to see the correlation across various car models between the car mileage and year the car was built. which chart is most appropriate? line chart none of the above heatmap chart scatterplot chart
The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.
In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.
A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.
To learn more about correlation here:
https://brainly.com/question/28898177
#SPJ4
SOLVING EQUATIONS Solve the equation. Check your solution.
49. b+7+12=30
Help Please im stuck
The exponential equation after solving gives -26.
What are Exponential Equations?Exponential equations are equations where the independent variable, x is in the exponent.
The given equation is,
[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]
We know that 125 = 5³
[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]
The base in the both sides of the equation is 5.
So,
7x + 5 = 3(2x - 7)
7x + 5 = 6x - 21
7x - 6x = -21 - 5
x = -26
Hence the value of x is -26.
Learn more about Exponential Equations here :
https://brainly.com/question/29506679
#SPJ1
A water tower is 16 meters tall. Close by, there is a crane that is 24 meters tall. If the water tower's shadow is 30 meters long, how long is the crane's shadow?
The crane's shadow is 45 meters long when the crane is 24 meters tall.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"
Let the shadow cast by the crane be x.
The triangle formed by the tower and by the crane are similar.
Using the rule of similar triangles we have:
16/24 = 30/x
16x = (30)(24)
x = 45
Hence, the crane's shadow is 45 meters long.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ1
1. an aerospace company has submitted bids on two separate federal government defense contracts. the company president believes that there is a 61% probability of winning the first contract. if they win the first contract, the probability of winning the second is 74%. however, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 20%. what is the probability that they lose both contracts?
The required probability of loosing both the contracts with 61% chances of winning first contract and 74% chances of second contract is equal to 0.1014.
Probability of winning the first contract 'P(A)' = 61%
= 0.61
Probability of winning the second contract 'P(B)' = 74%
= 0.74
Probability of loosing both the contracts is
= [ 1 - P(A) ] × [ 1 - P(B) ]
= [ 1 - 0.61 ] × [ 1 - 0.74 ]
= 0.39 × 0.26
= 0.1014
Therefore, the probability of loosing both the contracts as per given contracts winning possibility is equal to 0.1014.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
how many significant figures do each of the following measurements contain? type a number (i.e., 1, 2, 3, etc) for each of your responses, not the written word for the number.
Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2 significant figures.
Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.
Below are the key figures for each value reported.
(a) 2- 1significant digits
(b) 81.640 - 4 significant digits;
(c) 7.03 - 3 Significant Figures
(d) 0.003 - 1significant digits
(e) 0.0086 to 2 significant digits
(f) 3236 - 4 significant digits
(g) 8700 - 2 significant digits
know more about significant digits click here;
https://brainly.com/question/28338770
#SPJ4
Sarah charges $12 an hour when she
babysits. She also charges a non-refundabl
$5 fee just for showing up. What equation
could be used to represent the relationship
between x, the number of hours she
babysits, and y, the amount of money she
makes? jo
The equation which correctly shows the relationship between x, number of hours and y, the amount of money she makes is; y = 12x + 7.
What is the relationship between x and y as described?It follows from the task content that the relationship between y and x is to be.
By comparison with the slope-intercept equation; y = mx + c.
Since, slope, m is the rate of change; m = 12$ per hour.
Also, the nonrefundable one-time fee for showing up represents the y-intercept, c.
Therefore, the required equation is;
y = 12x + 5.
Read more on model equations;
https://brainly.com/question/28008720
#SPJ1
9 A square is graphed on the set of axes below, with vertices at
(-1,2), (-1,-2), (3,-2), and (3.2).
Which transformation would not carry the square onto itself
Answer:
With the information given, I would say a dialation.
Step-by-step explanation:
Rotation of 180 degree around point (1, 0). Therefore, option (3) is the correct answer.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Given that, the square with vertices (-1, 2), (-1, -2), (3, -2) and (3, 2).
(1) Reflection over the y-axis
Then the vertices become (1, 2), (1, -2), (-3, -2) and (-3, 2)
So, the transformation carries the square onto itself.
(2) Reflection over the x-axis
Then the vertices become (-1, -2), (-1, -2), (3, 2) and (3, -2)
So, the transformation carries the square onto itself.
(3) Rotation of 180 degree around point (1, 0)
(x, y) becomes (-y, x) 180° clockwise
So, the coordinate points are (-2, -1), (2, -1), (2, 3) and (-2, 3)
So, the transformation does not carries the square onto itself.
Therefore, option (3) is the correct answer.
Learn more about the transformation here:
https://brainly.com/question/11709244.
#SPJ2
"Your question is incomplete, probably the complete question/missing part is:"
A square is graphed on the set of axes below, with vertices at (-1,2), (-1,-2), (3,-2), and (3.2). Which transformation would not carry the square onto itself.
(1) Reflection over the y-axis
(2) Reflection over the x-axis
(3) Rotation of 180 degree around point (1, 0)
(4) Reflection over the line y=x-1
The price of a Loungy Chair was $400. The price of this chair has just gone up by 20%. Make a percent table to find the new price of the Loungy Chair
The percent table is:
100 % ⇒ $400
120 % ⇒ $480
The initial price of the Loungy chair was $400.
So, the initial price(P₀) = $400
The price of the chair has gone up by 20%
So, increase in price(r) = 20%
The final price will be calculated by using the formula:
P = P₀(1 + r/100) (where P is the final price)
P = 400(1 + 20/100)
P = 400(1 + 0.2)
P = 400 × 1.2
P = $480
Hence, the final price of the Loungy chair is $480
Percent table:
100 % ⇒ $400
120 % ⇒ $480
To learn more about percent table here:
brainly.com/question/12886995
#SPJ4
Pls show your work thank you will mark the Brainliest
Answer D
Step-by-step explanation:
Please help (will mark as brainlest)
Answer:
(9y + 4)(5x + 7)
Step-by-step explanation:
Barb is three times as old as her twin nieces Allie and Sam. The sum of their three ages is 55. How old is each person now?
Answers: Each twin is 11 years old. Barb is 33 years old
Work Shown:
x = age of each twin
3x = Barb's age
x+x+3x = 5x = total of their ages = 55
5x = 55
x = 55/5
x = 11
Each twin is 11 years old. Barb is 3x = 3*11 = 33 years old.
Check: twin1+twin2+barb = 11+11+33 = 55
The answers are confirmed.
A pole 6 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ian measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answer:
here you go
Step-by-step explanation:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.
What ordered pairs are the solutions of the system of equations shown in the graph
below?
The solutions of the system of equations are (-1, 2) and (3, -5)
What ordered pairs are solutions of the system of equations?Here we have a graph of a system of equations. The solutions are all the points where the graphs of the two equations intersect.
Here we can see two intersection points, thus, we have two solutions. We can see that the first intersection is at (-1, 2) and the second intersection is at (3, -5)
So these two are the solutions of the system of equations.
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
(b) a telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 6 to 13. what is the probability of a successful call? (round your answer to two decimal places.)
Probability of a successful call 0.3157 = 31.57%
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
A probability is the number of desired outcomes divided by the number of total outcomes.
The odds of making a sale on a single call are 6 to 13.
This means that in 6+13 = 19 calls, 6 are successful.
What is the probability of a successful call?
p = 6/19 =
0.3157 = 31.57% probability of a successful call.
know more about Probability click here;
https://brainly.com/question/24112280
#SPJ4
Help me with this question, I don't know how to solve
The simplified value is [tex]\frac{7a^{8}+12 }{21a^{5}}[/tex].
What is a mathematical expression?
A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is [tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}[/tex].
This can be simplified by cross-multiplying and adding.
[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{5}*a^{3}+4*3}{3*7a^{5}} \\=\frac{7a^{8}+12}{21a^{5}}[/tex].
Therefore the simplified value of the given expression is :
[tex]\frac{a^{3}}{3}+\frac{4}{7a^{5}}=\frac{7a^{8}+12 }{21a^{5}}[/tex]
To learn more about simplifying the expressions, refer to the link below:
https://brainly.com/question/723406
#SPJ1
12. Given the quadratic function f(x) = 4x² +7x+c, where c is some real number constant.
(a) If c = 3, are the zeroes of f(x) rational or irrational numbers? Explain how you arrived at your choice.
[3 points]
(b) Determine all values of c for which the graph of y=f(x) will have no x-intercepts. Show all work.
[3 points]
Step-by-step explanation:
A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.
For example:
[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]
Since root 1, is a perfect square, we will have rational roots.
B.
[tex] {b}^{2} - 4ac < 0[/tex]
[tex]49 - 16c < 0[/tex]
[tex] - 16c < - 49[/tex]
[tex]c > \frac{49}{16} [/tex]
If c is greater than 49/16, we will have no x intercepts.
Please, I need the answer to this question:
A goldsmith takes 2 hours to make a wedding ring and 3 hours to make a necklace. He can only work for a maximum of 12 hours a day. In a day, he has an order for at least 2 rings and 2 necklaces. On each wedding ring, he makes a profit of $50; on each necklace, he makes a profit of $60.
Assuming he makes x-rings and y-necklaces:
A) Write down all the inequalities correcting x and y
B) Show by shading the Region, R which satisfies all the inequalities in no.A above
C) How many rings and necklaces should the goldsmith make to maximize the profit?
a necklace is made from purple pyramids and yellow spheres in a 1 : 6 ratio
By simplifying the ratio and adding the fractions, we found that 1/7 of the beads are purple pyramids.
Ratios are used to compare two quantities or values. They are often expressed in the form of a fraction or as a percentage.
The given ratio of purple pyramids to yellow spheres is 1:6. This means that for every 1 purple pyramid, there are 6 yellow spheres. We can express this ratio as a fraction:
Purple pyramids : Yellow spheres = 1 : 6
This can be simplified by dividing both sides by 6:
1/6 Purple pyramids : 1 Yellow sphere = 1/6 : 1
Now, we can add the two fractions to get the total fraction of pyramids in the necklace:
1/6 + 1 = 7/6
This means that out of every 7 beads, 1 is a purple pyramid. We can express this as a fraction:
1/7 of the beads are purple pyramids.
So, the fraction of the beads that are pyramids is 1/7.
To know more about ratio here.
https://brainly.com/question/13419413
#SPJ4
Complete Question:
A necklace is made from purple pyramids and yellow spheres in a 1:6 ratio . What fraction of the beads are pyramids?
a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes. what is the water temperature in degrees fahrenheit , after 15 minutes
If the difference between the water temperature and the room temperature is halved every 5 minutes, then the water temperature in degrees fahrenheit, after 15 minutes 86 f
If a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes .
Temperature can be measured in degree celsius, degree fahrenheit and kelvin. so here the temperature measured in degree fahrenheit
Initially the difference between water and room temperature is,
212 - 68 = 144f
For every 5 minutes the difference of water and room temperature is halved,
After 5 minutes the difference is, 144/2 = 72 f
After 10 minutes the difference is, 72/2 = 36 f
After 15 minutes the difference is, 36/2 = 18 f
So the water temperature in degrees fahrenheit, after 15 minutes will be the sum of room temperature and difference between the temperatures of water and room after 15 minutes and it is given as, 18 f + 68 f = 86 f
Therefore, the water temperature in degrees fahrenheit, after 15 minutes is 86 f.
Learn more about temperature here:
https://brainly.com/question/11464844
#SPJ4
A family purchased tickets to a museum and spent a total of $38.00. The family purchased 4 tickets. There was a $1.50 processing fee for each ticket. Write and solve an equation that can be used to find x, the cost of one ticket to the museum. Show your work or explain your answer.
Answer:
Equation: 4(x + 1.5) = 38
Ticket Cost: $8, or x = 8
Step-by-step explanation:
The processing fee for each ticket is $1.50, or 1.5. This applies to each ticket, meaning that the price of one ticket (or x) should be added to 1.5. x + 1.5 represents the sum of a ticket and the processing fee. Since there were 4 tickets purchased, x + 1.5 is multiplied 4 times. That results in 4(x + 1.5). Finally, the total amount of money spent was $38, so 4(x + 1.5) = 38.
4(x + 1.5) = 38
4x + 6 = 38
4x = 32
x = 8
Check:
4 * 8 = 32 (cost of 4 tickets)
4 * 1.5 = 6 (cost of 4 processing fees)
32 + 6 = 38 (4 tickets + 4 processing fees = total)
Uriel collects aluminum cans, crushes them with a hand can-crushing machine, and turns the crushed cans in once a month for extra money. Uriel can crush 3 cans in 23 of a minute. What is the rate, in cans per minute, at which Uriel crushes aluminum cans?
If Uriel can crush 3 cans in 23 of a minute, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.
The problem gives us information about the number of cans Uriel can crush and the time it takes him to do so. We want to find the rate at which he crushes the cans, which is a measure of how many cans he can crush per minute.
To find this rate, we use a proportion. A proportion is a statement that two ratios are equal. In this case, we can set up a proportion that relates the number of cans Uriel crushes to the time it takes him to do so, and the rate at which he crushes the cans:
3 cans / (2/3 min) = x cans / 1 min
Here, the first ratio is the number of cans Uriel can crush in 2/3 of a minute (which is the same as saying that he can crush 3 cans in 2/3 of a minute). The second ratio is the unknown rate at which Uriel crushes cans per minute.
To solve for the unknown rate, we use cross-multiplication. This involves multiplying both sides of the proportion by the same value in order to isolate the unknown variable on one side of the equation.
In this case, we can cross-multiply by the denominators of each ratio:
3 cans × 1 min = (2/3 min) × x cans
Simplifying the left-hand side, we get:
3 cans × 1 min = 3 cans/min
Simplifying the right-hand side, we get:
(2/3 min) × x cans = 2x/3 cans/min
Putting these together, we get the equation:
3 cans/min = (2x/3) cans/min
We can now solve for x by isolating it on one side of the equation. To do this, we can multiply both sides by 3/2:
(3/2) × 3 cans/min = x cans/min
Simplifying, we get:
4.5 cans/min = x cans/min
Therefore, Uriel crushes aluminum cans at a rate of 4.5 cans per minute.
To learn more about proportion click on,
https://brainly.com/question/305941
#SPJ4
