Answers
Answer:
C [tex]P(v)=2(v+7)[/tex]
Step-by-step explanation:
Lets say that [tex]P(v)=y[/tex] for simplicity.
In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.
As we are already given the inverse, doing the same process again will give us the original function.
First we can set up the equation
[tex]y=\frac{1}{2} v-7[/tex]
Next we can switch the location of the variables
[tex]v=\frac{1}{2} y-7[/tex]
Now we can solve for y
[tex]v=\frac{1}{2} y-7\\\\v+7=\frac{1}{2} y\\\\y=2(v+7)\\\\P(v)=2(v+7)[/tex]
This gives us the function
[tex]P(v)=2(v+7)[/tex]
Answer:
C P(v) = 2(v+7)
Step-by-step explanation:
To find P(v), we need to take the inverse of P^-1 (v)
y = 1/2 v-7
Exchange y and v
v = 1/2 y-7
Solve for y
Add 7 to each side
v+7 = 1/2 y -7+7
v+7 = 1/2y
Multiply each side by 2
2(v+7) = 1/2 y*2
2(v+7) = y
P(v) = 2(v+7)
Related Questions
myra's stamp collection consisted of 120 stamps in october. By the following march, her collection had grown to 138 stamps. By how much did her collection increase between october and march
Answers
Answer:
18 stamp increase
15 % increase
Step-by-step explanation:
To find the increase in number , we take the number of stamps in march and subtract the stamps in october
128-120 = 18
To find the percent increase, we take the number of stamps that we gained over the original amount of stamps * 100%
percent increase = 18/120 * 100%
.15 * 100%
15% increase
Myra's stamp collection increased by 18 stamps from October to the following March. This is calculated by subtracting the number of stamps she had in October (120 stamps) from the number she had in March (138 stamps).
To find out by how much Myra's stamp collection has increased between October and March, you simply need to subtract the number of stamps she had in October from the number she had in March. She had 120 stamps in October, and by March, she had 138 stamps.
To calculate the increase, we'll use the following steps:
Take the number of stamps in March: 138 stamps.Subtract the number of stamps she had in October: 120 stamps.The difference will give us the increased number of stamps.Doing the math:
138 stamps (in March) - 120 stamps (in October) = 18 stamps
So, Myra's collection increased by 18 stamps between October and March.
Determine the horizontal, vertical, and slant asymptotes: y=x2+2x-3/x-7
Answers
Answer:
vertical asymptote: x = 7slant asymptote: y = x+9Step-by-step explanation:
The vertical asymptotes are found where a denominator factor is zero (and there is no corresponding numerator factor to cancel it). Here, that is at x = 7.
There is no horizontal asymptote because the numerator is of higher degree than the denominator.
When you divide the numerator by the denominator, you get ...
y = (x +9) +60/(x -7)
Then when x gets large, the behavior is governed by the terms not having a denominator: y = x +9. This is the equation of the slant asymptote.
The function y = (x^2 + 2x - 3) / (x - 7) has a vertical asymptote at x = 7 and a slant asymptote at y = x. It does not have a horizontal asymptote.
Explanation:
The function given is y = (x^2 + 2x - 3) / (x - 7). When identifying the asymptotes, we need to consider three types: horizontal, vertical, and slant.
For vertical asymptotes, we look for values of x that make the denominator of the function zero. In this case, x = 7 is a vertical asymptote.
For horizontal or slant asymptotes, we compare the degree of the polynomial in the numerator with the degree of the polynomial in the denominator. Since the degree of the numerator (which is 2) is larger than the degree of the denominator (which is 1), there's no horizontal asymptote. However, we have a slant asymptote which is determined by long division of the polynomials or using synthetic division.
The slant asymptote is therefore y = x.
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Evaluate the expression
5⋅x3x2\dfrac{5\cdot x^3}{x^2}
x
2
5⋅x
3
start fraction, 5, dot, x, start superscript, 3, end superscript, divided by, x, start superscript, 2, end superscript, end fraction
for
x=2x=2
x=2
x, equals, 2
Answers
The simplified expression for [tex]\((5 \cdot x^3) / (x^2)\) is \(5 \cdot x\).[/tex]
When x = 2, the result is [tex]\(5 \times 2 = 10.[/tex]
The answer is 10.
To evaluate the expression[tex]\((5 \cdot x^3) / (x^2)\) for \(x = 2\),[/tex] we first need to simplify the given expression.
Given:
[tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]
Simplifying, we divide the powers of x :
[tex]\[ x^3 / x^2 = x^{3-2} = x^1 = x. \][/tex]
So the expression simplifies to:
[tex]\[ 5 \cdot x. \][/tex]
Now substitute x = 2 :
[tex]\[ 5 \cdot 2 = 10[/tex]
Thus, the value of [tex]\((5 \cdot x^3) / (x^2)\) when \(x = 2\)[/tex] is: 10.
Question : Evaluate the expression [tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]for x = 2. start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for x=2x=2x, equals, 2.
If f(x) = 2x - 3 and g(x) = Radical over x-8,
what is (fºg)(24)?
Answers
Answer:
5
Step-by-step explanation:
Plug in 24 for x in your g(x) equation.
[tex]g(24)=\sqrt{24-8} \\g(24)=\sqrt{16} \\g(24)=4[/tex]
Next, plug in your g(x) value, 4, to your f(x) equation for x.
[tex]f(4)=2(4)-3\\f(4)=8-3\\f(4)=5[/tex]
Which of the following points lies on the circle whose center is at the origin and whose radius is 10?
Answers
Answer:
C.(5 sqrt(2), 5 sqrt(2)
Step-by-step explanation:
The point which lie on the circle is :
[tex](5\sqrt{2},5\sqrt{2})[/tex]
Step-by-step explanation:It is given that the circle is centered at origin and has a radius of 10 units.
We know that if (h, k) represents the coordinate of the center of circle and r is the radius of the circle then the equation of circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here we have:
[tex]h=0\ ,\ k=0\ and\ r=10[/tex]
Hence, the equation of circle is given by:
[tex](x-0)^2+(y-0)^2=10^2\\\\i.e.\\\\x^2+y^2=100------------(1)[/tex]
If we substitute the given point into the equation of the circle and it makes the equation true then the point lie on the circle and if it doesn't make the equation true then the point do not lie on the circle.
a)
[tex](\sqrt{10},0)[/tex]
i.e.
[tex]x=\sqrt{10}\ and\ y=0[/tex]
i.e. we put these points in the equation(1)
[tex](\sqrt{10})^2+(0)^2=100\\\\i.e.\\\\10=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
b)
[tex](0,2\sqrt{5})[/tex]
i.e.
[tex]x=0\ and\ y=2\sqrt{5}[/tex]
i.e. we put these points in the equation(1)
[tex](0)^2+(2\sqrt{5})^2=100\\\\i.e.\\\\20=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
c)
[tex](5\sqrt{2},5\sqrt{2})[/tex]
i.e.
[tex]x=5\sqrt{2}\ and\ y=5\sqrt{2}[/tex]
i.e. we put these points in the equation(1)
[tex](5\sqrt{2})^2+(5\sqrt{2})^2=100\\\\i.e.\\\\50
+50=100\\\\i.e.\\\\100=100[/tex]
which is a true statement .
Hence, this point lie on the circle.
What ia the measure of x?
Answers
Answer:
58
Step-by-step explanation:
Rule: the exterior angle = the sum of the two angles that do not share a side with the exterior angle. Put in much simpler terms <DAB = <B + <C
Solution
<C + <B = <DAB
<C + 56 = 114 Subtract 56 from both sides
<C +56-56 = 114-56 Combine
<C = 58
x = 58
Find the value of x. Then find the measure of each labeled angle.
x = 110; the labeled angles are 110º and 70º.
x = 70; the labeled angles are 110º and 70º.
x = 20; the labeled angles are 160º and 20º.
x = 20; the labeled angles are 60º and 20º.
Answers
Answer:
x = 70; the labeled angles are 110º and 70º.
Step-by-step explanation:
The full degrees will add up to 180º. There are 2x and +40.
Equation: [tex]2x+40=180[/tex]
Solve: [tex]2x+40=180\\\\180-40=140\\\\2x=140\\\\x=70[/tex]
Since x=70, 70+40 will equal to 110.
Therefore, "x = 70; the labeled angles are 110º and 70º." is correct.
The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.
Answers
Answer:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
Step-by-step explanation:
If the regular octagon has a perimeter of 122.4cm, then each side is [tex]\frac{122.4}{8}=15.3cm[/tex]
The measure of each central angle is [tex]\frac{360\degree}{8}=45\degree[/tex]
The angle between the apothem and the radius is [tex]\frac{45}{2}=22.5\degree[/tex]
The segment XY=a is the height of the right isosceles triangle.
We can use the Pythagoras Theorem with right triangle XYZ to get:
[tex]a^2+7.65^2=20^2[/tex]
[tex]a^2=20^2-7.65^2[/tex]
Therefore, the correct options are:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
Answer:3rd and 4th anwser
HELPPPP!!!!!!!!!!!!!!!! (10 points) We want to know the probability that a student selected randomly from her class would have an “A” (90 or above) in her class. Find the probability. Explain HOW to find the probability
Answers
Answer:
23 out of 91
around 1/3 of the class
Step-by-step explanation:
the total number of students so around the third part of the class
i rlly hate math, pweaseeee help me asap!!!
Answers
Answer:
See explanation.
Step-by-step explanation:
Part C)
[tex]5+(-10)[/tex]
When adding a positive to a negative, the result will be the sign of the larger absolute value. In this case, 10 is greater than 5, so the result will be negative.
Adding a negative is also the same thing as subtracting a positive.
[tex]5+(-10)\\5-10\\-5[/tex]
For your second problem, 5 is larger than 3, so the result will be positive.
[tex]5+(-3)\\5-3\\2[/tex]
-----
When adding a positive to another positive, the result will be positive.
[tex]5+3\\8[/tex]
When adding a number to zero, the answer will always be the number.
[tex]5+0\\5[/tex]
Part D)
When multiplying a positive times a negative, the result will always be negative.
[tex]5*(-10)\\-50[/tex]
[tex]5*(-3)\\-15[/tex]
-----
When multiplying a positive times a positive, the result will always be positive.
[tex]5*10\\50[/tex]
When multiplying a positive or a negative times zero, the result will always be zero.
[tex]5*0\\0[/tex]
Can someone help me with this math question
Answers
Answer:
The coordinates of D' are (1,-1)
Step-by-step explanation:
The point D in the figure has co-ordinates (2,-2) as shown in the figure.
The figure is dilated by a factor of 1/2
So, multiply the coordinates of D (2,-2) by 1/2
D' = (1/2*2, 1/2*-2)
D' = (1,-1)
So, the coordinates of D' are (1,-1)
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 45% of his final grade. His midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answers
Answer:
76.5CStep-by-step explanation:
Apply the weights to the scores and add them up:
5% × midterm + 15% × project + 35% × homework + 45% × final
= 0.05(75) +0.15(93) +0.35(78) +0.45(70)
= 76.5
The student has a solid letter grade of C.
The student's overall final score is 76.5 which is between 70 and 79, the students earned a C.
To calculate the student's overall final score, we can use the following formula:
Final grade = (midterm score * midterm weight) + (project score * project weight) + (homework score * homework weight) + (final exam score * final exam weight)
where midterm weight is the percentage of the final grade that the midterm counts for, project weight is the percentage of the final grade that the project counts for, homework weight is the percentage of the final grade that the homework assignments count for, and final exam weight is the percentage of the final grade that the final exam counts for.
In this case, the midterm weight is 5%, the project weight is 15%, the homework weight is 35%, and the final exam weight is 45%. The student's midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70.
Therefore, the student's overall final score is calculated as follows:
Final grade = (75 * 0.05) + (93 * 0.15) + (78 * 0.35) + (70 * 0.45)
Final grade = 3.75 + 13.95 + 27.3 + 31.5
Final grade = 76.5
Therefore, the student's overall final score is 76.5.
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Safari Adventure Theme Park is a selfguided theme park in which people drive through a park filled with African wildlife. They are given a map and a written guide to the wildlife of the park. They charge $20.00 per car plus $2.00 per person in the car. The number of people per car can be represented by the random variable X which has a mean value μX = 3.2, and a variance σ2x = 1.4. What is the mean of the total amount of money per car that is collected entering the park?
Answers
Answer:
$26.40
Step-by-step explanation:
For a linear function, the mean of the function is the function of the mean:
20 + 2.00·μX = 20 + 2.00·3.2 = 20 + 6.40 = 26.40 . . . . dollars
The mean total amount collected per car entering the Safari Adventure Theme Park is $26.40.
The mean of the total amount of money collected per car entering the park can be calculated by finding the expected value of the total amount, considering the price per car and per person. In this case, the mean total amount collected per car = price per car + (mean number of people per car) * price per person. Substituting the given values: 20 + 3.2 * 2 = $26.40.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. in an earlier study, the population proportion was estimated to be 0.23. how large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.03? round your answer up to the next integer.
Answers
Answer:
The sample size must be greater than or equal to 756
Step-by-step explanation:
The formula to calculate the error of the proportion is the following
[tex]E=z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}[/tex]
where p is the proportion, n the sample size, E is the error and z is the z-score for a confidence level of 95%
For a confidence level of 95% [tex]z_{\alpha/2}=1.96[/tex]
We know that for this case [tex]p=0.23[/tex]
We require that the error be 0.03 as maximum
Therefore we solve for the variable n
[tex]z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}\leq0.03\\\\1.96*\sqrt{\frac{0.23(1-0.23)}{n}}\leq0.03\\\\\sqrt{\frac{0.23(1-0.23)}{n}}\leq \frac{0.03}{1.96}\\\\(\sqrt{\frac{0.23(1-0.23)}{n}})^2\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{n}\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\leq n\\\\n\geq\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\\\\n\geq756[/tex]
Answer:
1305
Step-by-step explanation:
Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. Round to three decimal places as needed.
A. 0.241
B. 0.29
C. 0.373
D. 0.322
Answers
Answer: D. 0.322
Step-by-step explanation:
Given : Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure.
Then, the probability that the next person who comes in to give blood will have high blood pressure will be :_
[tex]\dfrac{\text{People had high blood pressure}}{\text{Total people}}\\\\=\dfrac{397}{1232}\\\\=0.32224025974\approx0.322[/tex]
Hence, the estimated probability that the next person who comes in to give blood will have high blood pressure = 0.322
The probability that the next person who comes in to give blood will also have high blood pressure is 0.322, calculated by dividing the number of people with high blood pressure (397) by the total number of people (1232).
Explanation:The question is asking for the probability that the next person to come in and give blood will have high blood pressure based on previous data. We calculate probabilities by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is a person having high blood pressure, and the total number of outcomes is the total number of people.
Simply divide the number of people with high blood pressure (397) by the total number of people (1232). Doing this gives: 397 / 1232 = approximately 0.322.
Therefore, the estimate of the probability that the next person who comes in to give blood will also have high blood pressure is 0.322.
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A recent study claimed that half of all college students "drink to get drunk" at least once in a while. Believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk". What type of statistical inference is this?
Answers
Answer: Hypothesis testing
Step-by-step explanation:
In statistics , Hypothesis testing is a general procedure to check the results of a experiment or a survey to confirm that they have actual and valid results.
Given claim : A recent study claimed that half of all college students "drink to get drunk" at least once in a while. By believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk".
Here the College Alcohol Study is just testing the results of the survey .
Hence, this is is s a type of Hypothesis testing.
What is this (pic provided) written as a single log?
Answers
Answer:
Step-by-step explanation:
when logs are added, they can be multiplied to produce a simplified log.
log_5(4*7) + log_5(2)
log_5(4*7*2)
log_5(56)
Apple trees cost $ 30 each, and cherry trees cost $ 40 each. Rohan has $ 600 to spend on fruit trees.
a) Let x represent the number of apple trees purchased, and let y represent the number of cherry trees purchased.
b) Write an equation that illustrates the different ways Rohan can purchase apple trees and cherry trees and spend exactly $ 600 .
Equation:
Answers
Answer:
A) Apples: $30x
Cherry: $40y
B) ($30x)+($40y)=600
Which expression is a sum of cubes?
Answers
Answer:
-27a³b⁶+ 8a⁹b¹²
Step-by-step explanation:
In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.
The exponents of a and b in both terms in the expression are divisible by 3.
The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.
ANSWER
[tex]- 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
EXPLANATION
When we can write an expression in the form
[tex] {(x)}^{3} + {(y)}^{3} [/tex]
then it is a sum of cubes.
To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.
This tells us that the first option will be the best choice.
[tex] - 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
We can rewrite this as:
[tex] { (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3} [/tex]
We apply this property of exponents:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
This gives us
[tex] {( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3} [/tex]
Therefore the correct option is A
What’s the length of BD ?
Answers
Answer:
BD = 4.99
Step-by-step explanation:
You can simply use the trigonometric identity tangent to solve for length BD.
Tan = opposite/adjacent
In this case we have,
Tan 31 = 3/BD
BD = 3/Tan 31
BD = 4.99
Since tan = oposite/adjacent we can plug in the values we know.
Find the product. 8y 3(-3y 2)
Answers
For this case we must find the product of the following expression:
[tex]8y ^ 3 (-3y ^ 2) =[/tex]
We have to by law of signs of multiplication:
[tex]+ * - = -[/tex]
Also, by definition of multiplication of powers of the same base, we put the same base and add the exponents, then the expression is rewritten as:
[tex]-24y ^ {3 + 2} =\\-24y ^ 5[/tex]
Answer:
[tex]-24y ^ 5[/tex]
Answer:
The Answer is -24y^5
Step-by-step explanation:
We know this because multiplying 8 by -3 = -24
Then we have to combine the exponents and we get 5.
Hope I helped. I used a website called mathwa3 to help, the 3 stands for a y.
Have a great day!!!
When solving the proportion x−26=1x+3, Santos first starts by using the Cross Product Property, multiplying the extremes and the means, to get 6=x2+x−6. Then, he subtracts 6 from both sides of the equation 6=x2+x−6 and finds the equation 0=x2+x−12. Part A: What should Santos do next to solve the equation? Part B: What is/are the solution(s) to the proportion? Select one answer for Part A, and select all answers that apply for Part B.
Answers
Answer:
A: factor the equation to (x -3)(x +4) = 0
B: solutions are x=-4, x=3
Step-by-step explanation:
A: Santos has the equation in standard form. Several options for solution are available: graphing (see attached), completing the square, factoring, using the quadratic formula. I find factoring to get to the solution most directly. The other methods work just as well.
To factor the equation, Santos needs to find two factors of -12 that have a sum of +1. Those would be +4 and -3. Putting these numbers into the binomial factors, Santos would have ...
(x +4)(x -3) = 0
__
B: The values of x that make the factors zero are ...
x = -4, x = 3
To solve the equation, Santos should first factor the quadratic equation, then use the Zero Product Property to find the solutions, which are x = 3 and x = -4.
Explanation:For Part A, Santos should factor the quadratic equation x2 + x - 12 = 0. This can be done by finding two numbers that add to 1 (the coefficient of x) and multiply to -12 (the constant term). These numbers are 4 and -3. So the factored form of the equation is (x - 3)(x + 4) = 0.
For Part B, to find the solutions to the proportion, he should use the Zero Product Property which states that if the product of two factors is zero, then at least one of the factors must equal zero. This gives us the solutions x - 3 = 0 and x + 4 = 0. Solving for x in each case provides the solutions: x = 3 and x = -4.
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If f(x) = 2x + 2 and g(x) = x3, what is (gºf)(2)?
Answers
Answer:
216
Step-by-step explanation:
(g∘f)(x) = g(f(x))
f(2) = 2·2 +2 = 6
g(f(2)) = g(6) = 6³ = 216
Answer:
216
Step-by-step explanation:
Correct Plato
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answers
For this case, we have by definition that:
[tex]C = (F-32) * \frac {5} {9}[/tex]
If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:
[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]
Finally, the temperature equals 10 degrees Celsius.
Answer:
10 degrees Celsius
The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.
Explanation:To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.
Step-by-step conversion:Start with the Fahrenheit temperature: 50°F.Subtract 32 from the Fahrenheit temperature: 50 - 32 = 18.Multiply by 5/9 to convert to Celsius: 18 × 5/9 = 10°C.Thus, when the temperature is 50°F, it is equivalent to 10°C.
What is the slope of the line x = 3?
Answers
Answer:
1/3 = .33
THE UNIT RATE IS 1 TO 3
Answer:
infinite slope
Step-by-step explanation:
Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y
Also recall that the slope of a vertical straight line is undefined (or infinite slope)
hence the slope of x=3 is infinite.
Determine the measure of arc CED.
A. 180°
B. 99°
C. 198°
D. 81°
Answers
Answer:
C
Step-by-step explanation:
An angle whose vertex lies on a circle and whose sides are 2 chords of the circle is one half the measure of the intercepted arc.
arc CED is the intercepted arc, hence
arc CED = 2 × 99° = 198°
Answer:
C) 198
Step-by-step explanation:I took the test
Which of the following is the correct notation for -48-89
Answers
Answer:
Step-by-step explanation:
Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:
-48
-89
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-137
Bubble wrap sells in sheets, and each sheet has 1 million individual spherical bubbles, each with a diameter of 0.01 m. What is the total volume of air contained in the bubbles of one sheet of bubble wrap? Round to the nearest tenth.
Answers
Answer: The total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Step-by-step explanation:
Volume of sphere :-
[tex]V=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of the sphere.
Given : Diameter of the bubble = 0.01 m
Then Radius of the bubble = [tex]\dfrac{0.01}{2}=0.005\ m[/tex]
Volume of each bubble:-
[tex]V=\dfrac{4}{3}(3.14) (0.005)^3[/tex]
Also, Number of bubbles in each sheet = 1,000,000
Then , the total volume of air contained in the bubbles of one sheet of bubble wrap will be :-
[tex]\dfrac{4}{3}(3.14) (0.005)^3\times1,000,000=0.52333333\approx0.5\ \text{cubic meters} [/tex]
Hence, the total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Drag the tiles to the boxes to form correct pairs.
Multiply the sets of numbers and match them with their products.
Answers
Answer:
[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]
[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]
Step-by-step explanation:
The first expression is
[tex](-\frac{3}{4})(\frac{7}{8})[/tex]
On simplification we get
[tex]-\frac{3\times 7}{4\times 8}[/tex]
[tex]-\frac{21}{32}[/tex]
Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].
The second expression is
[tex](\frac{2}{3})(-4)(9)[/tex]
On simplification we get
[tex](\frac{2}{3})(-36)[/tex]
[tex]-\frac{72}{3}[/tex]
[tex]-24[/tex]
Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].
Similarly,
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]
The sets of numbers are:
(-7)(-1.2) <-> 8.4
(-2 1/2)(-2) <-> 5
(2.5)(-2)<->-5
(7) (-1.2) <-> -8.4
The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.
(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.
(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.
(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.
(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.
To know more about sets:
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Does the point “is on the circle shown? Explain.
Answers
Answer:
Option 2: Yes, the distance from (-2,0) to (1,√7) is 4 units
Step-by-step explanation:
The point is:
(1,√7)
If the point lies on the circle, then the distance of point and the center of circle should be equal to the radius of the circle.
The radius can be viewed from the diagram that it is 4 units.
The center is: (-2,0)
Now, distance:
[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}}\\ d = \sqrt{(-2-1)^{2}+ (0-\sqrt{7} )^{2}}\\ d = \sqrt{(-3)^{2}+ (-\sqrt{7} )^{2}}\\=\sqrt{9+7}\\ =\sqrt{16}\\ =4[/tex]
Hence, option 2 is correct ..