Answer:
y = -3x+6
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = -3x +b
Substitute the point into the equation
-6 = -3*4+b
-6 =-12+b
Add 12 to each side
-6+12 =-12+12+b
6=b
y = -3x+6
Which function has an inverse that is also a function?
A: (-1,-2),(0,4),(1,3),(5,14),7,4)
B: (-1,2),(0,4),(1,5),(5,4),(7,2)
C: (-1,3),(0,4),(1,14),(5,6),(7,2)
D: (-1,4),(0,4),(1,2),(5,3),(7,1)
Answer:
Option (C)
Step-by-step explanation:
Option (A):
(-1, -2),(0, 4), (1, 3), (5, 14), (7, 4)
In these ordered pairs (4, 4) and (7, 4) have the same y-value.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (B):
(-1, 2), (0,4), (1, 5), (5, 4), (7, 2)
(-1, 2) and (7, 2) have the same output values for input values -1 and 7.
This function is not a one-to-one function.
Therefore, this function will have no inverse function.
Option (C).
(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)
For every input value there is a different output value in these pairs.
So the function is one-to-one function.
Therefore, inverse of this function will be a function.
Option (D).
(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)
Here (-1, 4) and (0, 4) show the same y-value which shows, the given function is not a one-to-one function.
Therefore, inverse of this function will not be a function.
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to 6 decimal places as needed
1 meter ≈ 3.28 feet
1 Liter ≈ 0.26 gallons
1 kilogram ≈ 2.20 pounds
33.777 yd ≈ __________ km
Answer:
33.777 yd = 0.030886 km
Step-by-step explanation:
==>Given:
33.777 yd
==>Required:
Convert 33.777 yd to km to 6 decimal places, using the metric and U.S systems.
==>Solution:
To convert, note that 1 km = 1093.6133 yd.
Thus,
1 km = 1093.6133 yd
x km = 33.777 yd
Cross multiply
1 × 33.777 = 1093.6133 × x
33.777 = 1093.6133x
Divide both sides by 1093.6133, to solve for x
33.777/1093.6133 = x
0.03088569 = x
x ≈ 0.030886 (to 6 decimal places)
Therefore, 33.777 yd = 0.030886 km
I’m Confused On The Question
No clue how to graph this any help would be greatly appreciated
Answer:
First, you can graph the y-intercept. The y-intercept would be (0,3) or in your equation, the number 3. Next, you could create a table by substituting values for x such as 1, 2, 3, or 4. This will give you easy numbers to graph. Instead of creating a table, perhaps you want to graph this by plotting the slope. Since the slope is 3/2, is means that it is going up, because the number is positive. An easy way to start would be starting at your y-intercept, (0,3), you could go two to the right and three up. That is a point. Then you could go the way down; two to the left and three down. Finally, you can draw a line connecting the points together.
I hope this helped you! Have a great rest of your day!
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16.
a. Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
-mu is greater than or equal to $108.50
mu is greater than $108.50
mu is less than $108.50mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
Ha: -
-mu is greater than or equal to $108.50
mu is greater than $108.50mu is less than $108.50
mu is less than or equal to $108.50
mu is equal to $108.50mu is not equal to $108.50
b. Test to determine if whether or not the average room price is significantly different from $108.50, using an alpha level of .05.
Reject H0
or
Fail to reject H0
Answer:
Step-by-step explanation:
H0: mu is equal to $108.50
Ha: mu is not equal to $108.50
This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.
z = x-u / sd/√n
Where x is $112, u is $108.50 sd is $16 and n is 64
z = 112-108.50 / 16/√64
z = 3.5/(16/8)
z = 3.5/2
z = 1.75
To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50
What is the value of X in equation? 1/3 X - 2/3 = - 18
Answer:
x=-52
Step-by-step explanation:
1/3x=-17 1/3
x=-52
2) Find the diameter.
4) If the diameter is equal to 3 inches ,d=
Answer:
d = 3 in
Step-by-step explanation:
Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.
3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).
Answer:
[tex]y = -3/2x + 4[/tex]
Step-by-step explanation:
[tex](2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-1}{x-2} = \frac{-5-1}{6-2}\\\\\frac{y-1}{x-2} = \frac{-6}{4} \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\\frac{4y = -6x+16}{4} \\\\y = -\frac{3}{2} x +4[/tex]
Which number is greatest? 6.23 times 10 Superscript 12 6.23 times 10 Superscript 8 6.23 times 10 Superscript negative 6 6.23 times 10 Superscript 3
The greatest number is 6.23 times 10 superscript 12.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that the number so;
A.6.23 x 10^12 is equivalent to rolling the decimal 12 times to the right.
B.6.23 x 10^8 is equivalent to rolling the decimal 8 times to the right.
C.6.23 x 10^-6 is equivalent to rolling the decimal 6 times to the left.
D.6.23 x 10^3 is equivalent to rolling the decimal 3 times to the right.
This shows the 10 has been multiplied by itself thrice.
Learn more about scientific notation here:
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which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answer:
Measuring it with a ruler and jotting down the length.
Step-by-step explanation:
If you are copying a line segment, the best way to copy it perfectly is to take the measure of the original line segment and copy down the measurement and then construct the other line segment to the exact measure.
Answer:
Brianlliest!
Step-by-step explanation:
you must measure the current line segment and copy it with the same length and make a new one
(7k-4)(7k^2+4k-1) mulityply the polynomials
Answer:
49k^3 -23k -4
Step-by-step explanation:
The distributive property is your friend.
[tex](7k-4)(7k^2+4k-1)=7k(7k^2+4k-1)-4(7k^2+4k-1)\\\\=49k^3+28k^2-7k-28k^2-16k+4\\\\=49k^3+k^2(28-28)+k(-7-16)-4\\\\=\boxed{49k^3-23k-4}[/tex]
A circle is shown. Angles 3 and 4 intersect an arc with a measure of 106 degrees. Angles 1 and 2 intersect an arc with measure 58 degrees. Is the measure of ∠1 equal to the measure of ∠2? Why?
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
Answer:
yes, because they intercept the same arc
Step-by-step explanation:
The sum of two odd integers is an even integer.
1. True
2. False
Answer:
True.
Step-by-step explanation:
Try out some numbers:
3 + 3 = 6
5 + 5 = 10
11 + 11 = 22
What is the height, X, of the equilateral triangle ? (Help)
Answer:
A. 7√3 in
Step-by-step explanation:
We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:
tan60° = x/7
x = 7tan60°
x = 7√3
Answer:
It's A
Step-by-step explanation:
A simple random sample of 44 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.51 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?
Answer:
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the population mean is significantly less than 5.4.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5.4\\\\H_a:\mu< 5.4[/tex]
The significance level is 0.05.
The sample has a size n=44.
The sample mean is M=5.31.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.51.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.51}{\sqrt{44}}=0.077[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{5.31-5.4}{0.077}=\dfrac{-0.09}{0.077}=-1.171[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=44-1=43[/tex]
This test is a left-tailed test, with 43 degrees of freedom and t=-1.171, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.171)=0.124[/tex]
As the P-value (0.124) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population mean is significantly less than 5.4.
This result suggest we may be making a Type II error, where a true alternative hypothesis does not have enough evidence to be supported.
If the same outcome would have been obtained with a bigger sample size, the power of the test is bigger and there is a higher probability of rejecting the null hypothesis.
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is: Compute E(Y) Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is:
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
Answer:
The expected value E(Y) is
[tex]E(Y) = 0.85[/tex]
The expected amount of the surcharge is
[tex]E(100Y^2) = 165[/tex]
Step-by-step explanation:
Let Y be the number of moving violations for which the individual was cited during the last 3 years.
The given probability mass function (pmf) of Y is
y | P(Y)
0 | 0.50
1 | 0.20
2 | 0.25
3 | 0.05
Compute E(Y)
The expected value E(Y) is given by
[tex]E(Y) = \sum Y \cdot P(Y) \\\\E(Y) = 0 \cdot 0.50 + 1 \cdot 0.20 + 2 \cdot 0.25 + 3 \cdot 0.05 \\\\E(Y) = 0.85[/tex]
Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.
The expected amount of the surcharge is given by
[tex]E(100Y^2) = 100E(Y^2)[/tex]
Where
[tex]E(Y^2) = \sum Y^2 \cdot P(Y) \\\\E(Y^2) = 0^2 \cdot 0.50 + 1^2 \cdot 0.20 + 2^2 \cdot 0.25 + 3^2 \cdot 0.05\\\\E(Y^2) = 1.65[/tex]
So, the expected amount of the surcharge is
[tex]E(100Y^2) = 100E(Y^2) \\\\E(100Y^2) = 100 \cdot 1.65 \\\\E(100Y^2) = 165[/tex]
Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of $176.47 on groceries, $78.66 for phone, and $62.37 on gas. Estimate his monthly total for groceries, phone, and gas by first rounding to the nearest $10.
Answer:
Yearly budget= $3840
Monthly budget= $320
Step-by-step explanation:
His budget will be calculated first by rounding off to the nearest$10 all his monthly spending.
For groceries= $176.47
Round off=$ 180.00
For phone =$ 78.66
Round off = $80.00
For gas = $62.37
Round off= $60.00
His total round off = $180+$80+$60
His total round off = $320
Before the round off, his total spending was $176.47+$78.66+$62.37
= $317.5
So his monthly budget should be $320
And yearly budget =$ 320*12
Yearly budget= $3840
3.A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly
Answer:
Probability of answering 5out of 10 correctly= 0.246
Step-by-step explanation:
Total question answered= 2
Question answered correctly= 1
Probability of answered correctly= 1/2
Probability of answered correctly= 0.5
Probability of answered incorrectly = 0.5
Probability of answering 5out of 10 correctly= 10C5(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 10!/5!5!(0.5)^5(0.5)^5
Probability of answering 5out of 10 correctly = 252(0.03125)(0.03125)
Probability of answering 5out of 10 correctly= 0.246
Which of the following is not a congruence theorem or postulate? A. SSS B. SAS C. SSA D. AAS
Answer:
SSA the only other right one missing is ASA
Round 2826 to the nearest hundred.
Answer:
2800
Step-by-step explanation:
2826 to the nearest hundred is 2800
Want Brainliest get this correct What is the sum of the fractions below?
If you average your costs over your total production, you get the average cost, written C: C(x, y) = C(x, y) x + y . Find the average cost for the cost function C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−0.01(x + y).
Answer:
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
Step-by-step explanation:
Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.
If total cost = C(x, y)
Average cost = C(x, y) ÷ (x+y)
For this question, total cost function is
C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾
The average cost is simply this total cost function divided by the total number of units produced.
Average cost
= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)
If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.
Hope this Helps!!!
evaluate 25.1 * 2.51 in two decimal places
Answer:
63.00
Step-by-step explanation:
25.1 × 2.51
Multiply.
= 63.001
Round to two decimal places.
63.00
Answer:
63.00
Step-by-step explanation:
when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00
For the rational function f(x)=x-2/3x^2+x-2, solve f(x)=2
Answer:
When f(x) = 2, x = 1/2, -2/3
Step-by-step explanation:
Step 1: Set equation equal to 2
[tex]2 = \frac{x-2}{3x^2 +x -2}[/tex]
Step 2: Multiply both sides by denominator
2(3x² + x - 2) = x - 2
Step 3: Distribute
6x² + 2x - 4 = x - 2
Step 4: Isolate everything to one side
6x² + x - 2 = 0
Step 5: Factor
(2x - 1)(3x + 2) = 0
Step 6: Find roots
x = 1/2, -2/3
Given h(x)=5x-5, find h(2)
Answer:
5
Step-by-step explanation:
h(2)=5(2)-5
5 x 2 = 10
10 - 5 = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The function is given below.
h(x) = 5x - 5
Then the value of the function at x = 2 will be
h(2) = 5 (2) - 5
h(2) = 10 - 5
h(2) = 5
The value of the function h(x) = 5x - 5 at x = 2 will be 5.
More about the value of expression link is given below.
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Which of the following is the missing side length that completes the
Pythagorean triple below?
5, 12,
Answer:
13
Step-by-step explanation:
We can find the missing side length by using the pythagorean theorem
a² + b² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
So, 13 is the missing side length.
A very large batch of components has arrived at a distributor. The batch can be characterized as acceptable only if the proportion of defective components is at most .10. The distributor decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. Let X denote the number of defective components in the sample. What is the distribution of X? Justify your answer.
Required:
What is the probability that the batch will be accepted when the actual proportion of defectives (p) is:_______
a, 0.01
b. 0.05
c. 0.10
d. 0.20
e. 0.25
Answer:
c. 0.10
Step-by-step explanation:
Hello!
To accept a batch of components, the proportion of defective components is at most 0.10.
X: Number of defective components in a sample of 10.
This variable has a binomial distribution with parameters n=10 and p= 0.10 (for this binomial experiment, the "success" is finding a defective component)
The distributor will accept the batch if at most two components are defective, symbolically:
P(X≤2)
Using the tables for the binomial distribution you can find the accumulated probability for a sample of n=10 with probability of success of p= 0.10 and number of successes x= 2
P(X≤2)= 0.9298
I hope this helps!
The product of two whole numbers is 1000. If neither of the numbers is a multiple of 10, what is their sum?
Answer:
133
Step-by-step explanation:
1000 = 2 * 2 * 2 * 5 * 5 * 5
To not have a multiple of 10, you cannot have 2 and 5 as factors of the same number.
One number is 2^3 = 8.
The other number is 5^3 = 125.
8 * 125 = 1000, so the two do multiply to 1000.
Neither 8 nor 125 is a multiple of 10.
8 + 125 = 133
Answer:
133
Step-by-step explanation:
We are given that the product of two numbers is 1000. Let's first list out the factors of 1000 (factors are numbers that evenly divide into 1000):
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
We see that the pairs are:
(1, 1000)
(2, 500)
(4, 250)
(5, 200)
(8, 125)
(10, 100)
(20, 50)
(25, 40)
An easy way to see if a number is divisible by 1000 is to check is it has a zero at the end. Notice that all of the pairs have at least one number that ends with at least 1 zero except (8, 125), so this is the pair of numbers we're looking for.
The sum is thus 8 + 125 = 133.
~ an aesthetics lover
can someone help me plzz!
Answer:
126.6Option A is the right option.
Step-by-step explanation:
Sum of angles in triangle= 180°
[tex]85 + 53 + m < a = 180 \\ or \: 138 + m < a = 180 \\ or \:m < a = 180 - 138 \\ m < a = 42[/tex]
Applying sine rule:
[tex] \frac{sin \: a \: }{a} = \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: b}{b} = \frac{sin \: c}{c} \\ \frac{sin \: (85)}{b} = \frac{sin(42)}{85} \\ 85 \: sin \: (85) = \: b \: sin \: (42) \\ b = \frac{85 \: sin \: (85)}{sin \: 42} \\ ac = 126.6[/tex]
Hope this helps....
Good luck on your assignment...
To dilute a solution that is 40% saline, a chemist combines it with a solution that is 15% saline. How much of each solution should she use if she needs 150 mL of a solution that is 25% saline? Hint: solve by using system of equations
Answer:
60 ml of 40% saline and 90 ml of 15% saline
Step-by-step explanation:
We can call the amount of 40% solution x and the amount of 15% solution y.
x + y = 150 -- (1)
0.40x + 0.15y = 150 * 0.25 -- (2) --- 150 * 0.25 = 37.5
40x + 15y = 3750 (Multiply (2) by 100 to get rid of decimals)
15x + 15y = 2250 -- (3) (Multiply (1) by 15)
25x = 1500 (Subtract (3) from (1)
x = 60
y = 150 - 60 = 90
Answer:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution
Step-by-step explanation:
We can solve this problem with the following system of equations:
[tex] 150*0.25 = x*0.4 + y *0.15[/tex] salt
[tex] 150*(1-0.25)= x(1-0.4) +y(1-0.15)[/tex] water
With x the ml of solution for 40% concentration and y the ml of solution at 15% of concentration
From the salt condition we have:
[tex] 37.5= 0.4 x +0.15 y[/tex]
We can solve for x and we got:
[tex] x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]
And replacing into the water condition we have:
[tex] 112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]
Solving for y we got:
[tex] 112.5= 56.25 -0.225 y+0.85 y[/tex]
[tex] y = \frac{112.5-56.25}{0.625}= 90[/tex]
And then solving for x we got:
[tex] x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]
So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution