Answer:
The correct answer is - 625.36.
Step-by-step explanation:
Given:
Fixed mothly plan - 616
free minutes - 150
Used minutes - 170
Free text - 150
Used text - 182
Charging amount over free limit - 18p
Solution:
Number of minutes over the limit - 170 - 150 = 20
Number of text over the limit - 182 - 150 = 32
So the extra amount that will be add to the monthly charge would be -
(20*0.18) +(32*0.18)
and the total charge of the month would be -
= 616+(20*0.18) +(32*0.18)
= 616+3.60+5.76
= 625.36
Thus, the correct answer would be - 625.36
What is the area of the triangle? Make me brainlest pleas
Answer:
i looked it up
Step-by-step explanation:
Susan and Jim each own a lawn-care business. The amount Susan charges for lawn care by the hour is shown in the table. The amount Jim charges for lawn care by the hour is shown in the graph.
Answer:
Can you please provide the table so I can know the numbers.
Step-by-step explanation:
Thank you
Answer:
plss stop english plss lang po
he
The area of a rectangle is 216 inches squared. The ratio of the length to width is 3:2. Find the length and the width
Answer:
Length = 18 inches
Width = 12 inches
Step-by-step explanation:
Let the Length be 3x and width be 2x
Area= Length*Width=216 inches squared
216=3x*2x
216=6x²
x²=216/6
x²=36
x=√36
x=6 inches
Therefore
Length = 3x = 3*6 = 18 inches
Width = 2x = 2*6 = 12 inches
The average size of single-family homes in the U.S. is 2,390 square feet. A random sample of 100 homes in California yielded the mean of 2,507 square feet and the standard deviation of 257 square feet. Do the sample data provide sufficient evidence to conclude that the mean size of California homes exceeds the national average? Test using significance level of 0.01. (7 Points)
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2390 \ ft^2[/tex]
The sample size is n = 100
The sample mean is [tex]\= x = 2 507 \ ft^2[/tex]
The standard deviation is [tex]s = 257 \ ft^2[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 2390[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2390[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{s}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{2507 - 2390 }{ \frac{ 257 }{ \sqrt{100 } } }[/tex]
=> [tex]z = 4.55[/tex]
From the z table the area under the normal curve to the left corresponding to 4.55 is
[tex]p-value = P( X > 4.55 ) = 0.00[/tex]
From the value obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average
If the perimeter of this triangle is 15 centimeters, what is the value of n
Answer:
n = 5/2
Step-by-step explanation:
Add all of the sides up to make an equation
(5n - 6) + n + (2n + 1) = 15
8n -5 = 15
8n = 20
n = 5/2
Answer:
[tex]0.4cm[/tex]
Step-by-step explanation:
[tex]n + 2n+1 + 5n-6 = 15\\[/tex]
[tex]8n -5 = 15[/tex]
[tex]8n = 20[/tex]
[tex]n = \frac{8}{20}[/tex]
[tex]n = 0.4[/tex]
[tex]\therefore[/tex] the value of [tex]n[/tex] is [tex]0.4cm[/tex]
Hope this helps :)
In the diagram ce=12 units and be=5 units based on the given information what is ae?
Answer:
AE = 12 units
Step-by-step explanation:
ce is the same unit as AE
Answer:
C: 12 units
Step-by-step explanation:
Given the problem below what mistake did Bob make in solving the equation? Bob and his friends paid $30 for 3 sandwiches and and 3 bottles of water.
-Each sandwich cost the same amount.
-The bottles of water cost $1.50 each.
The equation 3(x + 1.50) = 30 can be used to determine x, the cost of each sandwich. Bob solved the equation using these steps: 3(x + 1.50) =30
3x + 1.50 = 30
3x = 28.50
x = 9.50
Answer:
Bob forgot to distribute 3 to 1.50 in the parentheses
Step-by-step explanation:
Bob made the mistake in his first step.
In the equation 3(x + 1.50) = 30, the 3 has to be distributed to both x and 1.50.
But, Bob only distributed it to x, which led him to get the wrong answer.
So, Bob's mistake when solving was that he forgot to distribute the 3 to 1.50
What is the nature of roots of x- 9x = 20 ?
a. nonreal
b. real, rational, and equal
c. real, rational, and unequal
d. real, irrational, and unequal
Answer:
Option C
Step-by-step explanation:
To find the nature of the roots we use the Discriminant formula which is:
[tex]D=b^2-4ac[/tex]
and given the equation and compare with the standard quadratic equation
[tex]x^2-9x=20\\x^2-9x-20=0\\ax^2+bx+c=0[/tex]
Here our a is 1 , b is -9 and c is -20 so we plug a, b, c into the Discriminant formula
[tex]D=b^2-4ac\\D=(-9)^2-4(1)(-20)\\D=81+80\\D=161[/tex]
Since D > 0 (greater than zero) our roots are real and unequal for the rational and irrational part we got know the the Discriminant's square root value if it is in decimals the nature of the roots are irrational if the Discriminant's value is a whole number then it is rational and so 161 has a square roots in points which is
[tex]D=\sqrt{161} \\D=12.6885[/tex]
So our answer is real , irrational and unequal which is Option C
(v^3-2v^2-78v+16) / (v+8)
Answer:
v^2-10v+2
Step-by-step explanation:
(v^3-2v^2-78v+16) /(v+8)
Factor
(v+8)(v^2-10v+2)/(v+8)=v^2-10v+2
1. A company that produces bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice. Assume that the population standard deviation is 10 milligrams. a) Construct a 95% confidence interval estimate for the mean sodium level. b) Construct a 99% confidence interval estimate for the mean sodium level.
Answer:
The 95% confidence interval is [tex] 101.13 < \mu < 104.87 [/tex]
The 99% confidence interval is [tex] 100.54 < \mu < 105.46 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 103 \ mg[/tex]
The population standard deviation is [tex]\sigma = 10 \ mg[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =1.8688 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 1.8688 < \mu < 103 + 1.8688 [/tex]
=> [tex] 101.13 < \mu < 104.87 [/tex]
Considering question b
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =2.4599 [/tex]
Generally 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 2.4599 < \mu <103 + 2.4599 [/tex]
=> [tex] 100.54 < \mu < 105.46 [/tex]
Here are the numbers of children in 15 elementary school classes. 17, 17, 18, 16, 16, 17, 17, 16, 19, 17, 20, 16, 18, 18, 18 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode.' JI
Answer:
mode = 17
Step-by-step explanation:
mode is the most common appearance of numbers in a dataset.
17 has 5 appearances
please click the heart button to give thanks :)
4x – 4y = -16
please help find the y value
Answer: y=x+4
Step-by-step explanation:
if you need to find the y
we divide the equation by 4
x-y=-4
add y on both sides
y=x+4
PLEASE HELP I NEED TO KNOW THE (RIGHT) ANSWER ASAP!
Answer:
Its an acute so 80 also because if you measure it it shows the same as C
Step-by-step explanation:
Sorry if its wrong tho hope that helped
-34 > -10 + 4x
Help ASAP
Step-by-step explanation:
-34 > -10 + 4x
-24 > 4x
x < -6.
Answer:
Hope it will help u plz brain-list the answer
Step-by-step explanation:
-34 > -10 + 4x
by transitive property of in-equality we get,
-10+4x<-34
4x<-34+10 ( adding 10 to both sides
4x<-24
x<-24/4 ( dividing 4 to both sides
x<-6 AnsThe cashier counts 80 bills, all with the same value. She gets a total of $800. What is the value of each bill?
help, help
Answer:
10 dollars
Step-by-step explanation:
Answer:
10!
Step-by-step explanation:
So the cashier counts 80 bills and if each bill was 10 dollars, then that would equal the total. ($800) Because 80 x 10 equals 800.
Hope this helps!. :)
help me on this question please
Answer:
7 6/18
Step-by-step explanation:
Answer:
3.71851851852
Step-by-step explanation:
What is the relationship between the ratios?
8/11 and 24/33
Drag and drop to correctly complete the statement.
The ratios are ________.
Enter your answer in the box.
Answer:The ratios are _Equivalent_______.
Step-by-step explanation:
Step 1
Equivalent ratios are ratios that have the same value even though they look different. When we divide or multiply a given ratio by the same number ( in the numerator and denominator )we get anther equivalent ratio.
Step 2
In the given ratios
8/11 and 24/ 33
8/ 11 x 3/ 3 = 24/ 33
also
24/33 ÷ 3/3 = 8/11
This shows that the relationship between the ratios are equivalent.
The number of adult Americans from a random sample of n adults who support a bill proposing to extend daylight savings time is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that more than 368 Americans support the bill.
Answer:
Right of X = 368.5
Step-by-step explanation:
By using the normal approximation to the Binomial random variable, we normally make use of continuity correction.
Using the rule of continuity;
P(X > K) turn out to be P(X > K + 0.5)
To determine the required probability:
∴
P(X > K) turn out to be P(X > K + 0.5)
P(X > 635) turn out to be P(X > 368 + 0.5)
⇒ P(X > 368.5) to the right.
Right of X = 368.5
Integrate the following problem:
[tex]\int {e^{-x} \cdot cos(2x)} \, dx[/tex]
P.S:
Have fun Lauren (and possibly Kelvy)!
Answer:
[tex]\displaystyle \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex]
Step-by-step explanation:
The integration by parts formula is: [tex]\displaystyle \int udv = uv - \int vdu[/tex]
Let's find u, du, dv, and v for [tex]\displaystyle \int e^-^x \cdot cos2x \ dx[/tex] .
[tex]u=e^-^x[/tex][tex]du=-e^-^x dx[/tex] [tex]dv=cos2x \ dx[/tex] [tex]v= \frac{sin2x}{2}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = e^-^x \cdot \frac{sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex] [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex]Now let's evaluate the integral [tex]\displaystyle \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex].
Let's find u, du, dv, and v for this integral:
[tex]u=-e^-^x[/tex] [tex]du=e^-^x dx[/tex] [tex]dv=\frac{sin2x}{2} dx[/tex] [tex]v=\frac{-cos2x}{4}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} - \int \frac{-cos2x}{4}\cdot e^-^x dx[/tex]Factor 1/4 out of the integral and we are left with the exact same integral from the question.
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Let's substitute this back into the first IBP equation.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Simplify inside the brackets.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ \frac{e^-^x \cdot cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Distribute the negative sign into the parentheses.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4} - \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Add the like term to the left side.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx + \frac{1}{4} \int cos2x \cdot e^-^x dx= \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex] [tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex]Make the fractions have common denominators.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x}{4} - \frac{e^-^x \cdot cos2x}{4}[/tex]Simplify this equation.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4}[/tex]Multiply the right side by the reciprocal of 5/4.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4} \cdot \frac{4}{5}[/tex]The 4's cancel out and we are left with:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{5}[/tex]Factor [tex]e^-^x[/tex] out of the numerator.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x(2 \cdot sin2x-cos2x)}{5}[/tex]Simplify this by using exponential properties.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x}[/tex]The final answer is [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex].
Answer:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Step-by-step explanation:
We would like to integrate the following integral:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx[/tex]
Since this is a product of two functions, we can consider using Integration by Parts given by:
[tex]\displaystyle \int u\, dv =uv-\int v\, du[/tex]
So, let’s choose our u and dv. We can choose u base on the following guidelines: LIATE; or, logarithmic, inverse trig., algebraic, trigonometric, and exponential.
Since trigonometric comes before exponential, we will let:
[tex]u=\cos(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=-2\sin(2x)\text{ and } v=-e^{-x}[/tex]
So, our integral becomes:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=(\cos(2x))(-e^{-x})-\int (-e^{-x})(-2\sin(2x))\, dx[/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\int e^{-x}\sin(2x)\, dx[/tex]
Since we ended up with another integral of a product of two functions, we can apply integration by parts again. Using the above guidelines, we get that:
[tex]u=\sin(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=2\cos(2x)\, dx\text{ and } v=-e^{-x}[/tex]
This yields:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[(\sin(2x))(-e^{-x})-\int (-e^{-x})(2\sin(2x))\, dx\Big][/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[-e^{-x}\sin(2x)+2\int e^{-x}\cos(2x)\, dx\Big][/tex]
We can distribute:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)-4\int e^{-x}\cos(2x)\, dx[/tex]
The integral on the right is the same as our original integral. So, we can isolate it:
[tex]\displaystyle \Big(\int e^{-x}\cos(2x)\, dx\Big)+4\Big(\int e^{-x}\cos(2x)\, dx)\Big)=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
Combine like integrals:
[tex]\displaystyle 5 \int e^{-x}\cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
We can factor out an e⁻ˣ from the right:
[tex]\displaystyle 5\int e^{-x}\cos(2x)\, dx=e^{-x}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Dividing both sides by 5 yields:
[tex]\displaystyle \int e^{-x}\cos(2x)\, dx=\frac{e^{-x}}{5}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Rewrite. We of course also need the constant of integration. Therefore, our final answer is:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Ronnie records the number of chirps per minute (x) that crickets make at different temperatures(Y ) in degree Fahrenheit. he determines that the association is linear and that the line of best fit is Y=1/6x+60.what is the interpretation of the slope and y intercept of this question?
Answer:
Step-by-step explanation:
Given
[tex]y = \frac{1}{6}x + 60[/tex]
Required
Interpret the slope and y intercept
The general form of an equation is:
[tex]y = mx + b[/tex]
Where
[tex]m=slope[/tex]
[tex]b = y\ intercept[/tex]
By comparison
[tex]m = \frac{1}{6}[/tex]
[tex]b = 60[/tex]
Interpretation:
Slope represents rate and y intercept represents the number of chirps at time 0.
So, the interpretations are:
Slope: The cricket chirps at a rate of [tex]\frac{1}{6}[/tex] chirps per minute
y intercept: The initial number of chirps is 60
6/8 = x/12. Pls help I’m failing math
Answer:
x=9
Step-by-step explanation:
Answer:
x = 9
Step-by-step explanation:
you want to get x alone and so you need to do the opposite of dividing which is multiplying, so you multiply each side by 12.
6/ 8 = x / 12
* 12 *12
6*12/ 8 = x [tex]\frac{6*12}{8}[/tex]
72/8=x [tex]\frac{72}{8}[/tex]
9=x
Hope this helped!
The difference in the price of 2 video games is $8.25. If one video game costs $19.50, which of the answer choices could represent the price of the other video game?
Answer:
the correct answer would be 11.25 or 27.75 unless the answer choices were some type of ratio
Step-by-step explanation:
If integral subscript C subscript 1 end subscript F with rightwards arrow on top times d r with rightwards arrow on top equals 6 and integral subscript C subscript 2 end subscript F with rightwards arrow on top times d r with rightwards arrow on top equals 13, find A. the line integral where C is the path from P to Q over C subscript 1 and then back to P over C subscript 2. integral subscript C F with rightwards arrow on top times d r with rightwards arrow on top equals _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
To my best understanding, you're given that
[tex]\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec r=6\text{ and }\int_{C_2}\vec F\cdot\mathrm d\vec r=13[/tex]
where C₁ and C₂ are some arbitrary paths, evidently starting at the point P and ending at the point Q, and you have to find the value of
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r[/tex]
where C is the path consisting of C₁ (from P to Q) and the reverse of C₂ (from Q back to P). So we have
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{C_1}\vec F\cdot\mathrm d\vec r - \int_{C_2}\vec F\cdot\mathrm d\vec r = 6-13 = \boxed{-7}[/tex]
Which equation has the solutions x=1+/- 5?
Ox^2+2x + 4 =0
Ox^2-2x + 4 =0
Ox^2+ 2x-4 = 0
Ox^2-2x – 4 =0
Answer:
[tex]x^{2} -2x-4=0[/tex]
Solving Steps
Use the quadratic formula
[tex]x=\frac{-(-2)(+/-)\sqrt{(-2)^2-4*1*(-4)} }{2*1}[/tex]
Multiply / Remove the parentheses / Evaluate
[tex]x=\frac{2(+/-)\sqrt{4+16} }{2}[/tex]
Calculate
[tex]x=\frac{2(+/-)\sqrt{20} }{2}[/tex]
Separate the solutions
[tex]x=\frac{2(+/-)2\sqrt{5} }{2} \\x=\frac{2-2\sqrt{5} }2}[/tex]
Simplify
[tex]x=1+\sqrt{5} \\x=1-\sqrt{5}[/tex]
A fair coin is tossed 20 times. The probability of getting the three or more heads in a row is 0.7870 and the probability of getting three or more heads in a row or three or more tails in a row is 0.9791.2
What is the probability of getting three or more heads in a row and three or more tails in a row?
Answer:
The value is [tex]P( H \ n \ T ) = 0.6049[/tex]
Step-by-step explanation:
From the question we are told that
The number of times is n = 20
The probability of getting three or more heads in a row is [tex]P(H) = 0.7870[/tex]
The probability of getting three or more heads in a row or three or more tails in a row is [tex]P(H \ u \ T ) = 0.9791[/tex]
Generally given that it is a fair coin , then [tex]P(H) = P(T) = 0.7870[/tex]
Here P(T) is probability of getting three or more tails in a row
Generally the probability of getting three or more heads in a row and three or more tails in a row is mathematically represented as
[tex]P( H \ n \ T ) = P(H) + P(T) - P( H \ u \ T )[/tex]
=> [tex]P( H \ n \ T ) = 0.7870 + 0.7870 - 0.9791[/tex]
=> [tex]P( H \ n \ T ) = 0.6049[/tex]
State which of the following sets of ordered pairs represent a function.
Set A: (5,2), (4, 3), (3, 4), (2,5)
Set B: (-1,-6), (0, 2), (1, 2), (3, 6)
Set C: (2, 1), (4, 2), (2, 3), (8,4)
Please select the best answer from the choices provided
A: Set C
B: Set B
C: Set A
D: Set A and Set B
Answer:
Option (D) is correct.
Step-by-step explanation:
A function can be termed as a process from a set of x values to a set of possible y-values where each x-value relates to exactly one y-value.
In other words, a relation can only be a function there is no repetition of x-values. It means a relation can not have duplicated inputs.
Given the sets
Set A: (5,2), (4, 3), (3, 4), (2,5)
Set B: (-1,-6), (0, 2), (1, 2), (3, 6)
Set C: (2, 1), (4, 2), (2, 3), (8,4)
It is clear that sets A and B represent the function because, in these sets, each x-value relates to exactly one y-value. In other words, there are no duplicated inputs.
But, set C has duplicated inputs i.e. x = 2 is repeated twice, and a function can not have a repeated input.
Therefore, we conclude that set A and set B represent a function.
Thus, option (D) is correct.
Kevin walked a total of 14.98 miles last week. He walked the same distance each of the 7 days. How many miles did Kevin walk each day?
Answer:
2.14?
Step-by-step explanation:
(I'm not good at explaining, but I THINK its 2.14)
the graph of a quadratic function is shown on the grid. which function is the best represented by this graph?
Answer:
Step-by-step explanation:
It is H
Function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x
Equation of a parabola in vertex form: Equation of a parabola in vertex form is given by,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
Given in the graph,
Vertex of the parabola → (3, -9) Parabola passes through the origin (0, 0).Equation of the graph with vertex (3, -9) will be,
y = a(x - 3)² - 9
Since, the parabola passes through (0, 0),
0 = a(0 - 3)² - 9
0 = 9a - 9
a = 1
Substitute the value of 'a' in the equation of the parabola,
y = 1.(x - 3)² - 9
y = x² - 6x + 9 - 9
y = x² - 6x
Hence, the function representing the graph will be f(x) = x² - 6x
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Ruby has $2.10 in nickels and dimes.
She has three as many dimes as nickels. How many nickels and dimes does she have?
Answer:
$
Step-by-step explanation:
Unit conversion is the conversion of one unit to another unit with its standard conversion.
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
The number of nickels is 5.
The number of dimes is 15.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
Now,
Let,
Dimes = 3x
Nickels = x
Now,
The total number of cents.
10(3x) + 5x = 180
30x + 5x = 180
35x = 180
x = 5.14
x = 5
Now,
3x = 3 x 5 = 15
Thus,
The number of nickels is 5.
The number of dimes is 15.
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a function is shown f(x) = 2/3x +3 what is the value of f (6)?
Answer:
The answer is 28/9
Step-by-step explanation:
Step one
Given information
We are given that the function is
[tex]f(x) = 2/3x +3[/tex]
And we are expected to find f(6), that is substitute the value of x with 6
Step two:
[tex]f(6)= 2/3(6)+3\\\\f(6)=2/18+3\\\\f(6)=1/9+3\\\\f(6)=1+27/9\\\\f(6)= 28/9[/tex]
