Answer:
(-1/2,-9/2)
Step-by-step explanation:
that is the coordinates for the vertex of the function y=2xsqaured+2x-4
A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. Graph a system of linear equations to find x.
Answer:
see below for a graph
x = 4
Step-by-step explanation:
The perimeter is given by the formula ...
P = 2(L +W)
The area is given by the formula ...
A = LW
We want these two values to be equal. Using "y" for both perimeter and area, and substituting the given values for L and W, we have the equations ...
y = 2(4 +x)
y = 4x
The graph of these equations (below) shows the value of x is 4.
a bag is full of poker chips . the probability of randomly selecting a red chip from the bag is 1/8. the probability of selecting a blue chip from the bag is 13/24. find the probability hint there are other colors in the bag too
Answer:
1/3
Step-by-step explanation:
Let the probability of selecting all coloured chips in the bag be 1.
If the probability of randomly selecting a red chip from the bag is 1/8 and the probability of selecting a blue chip from the bag is 13/24, then the probability of selecting both will be 1/8+13/24
1/8+13/24
= (3+13)/24
= 16/24
= 2/3
If the probability of selecting both ted and blue chip is 2/3, then the probability that there are other colors in the bag too will be expressed as 1-2/3 which is equivalent to 1/3
Final answer:
To find the probability of picking a chip that is neither red nor blue from the bag, we subtract the probabilities of picking a red or blue chip from 1. The calculation shows that the probability of selecting a different color chip is 1/3.
Explanation:
The student's question pertains to the calculation of probabilities when selecting poker chips of different colors from a bag. We are given that the probability of selecting a red chip is 1/8, and the probability of selecting a blue chip is 13/24. The aim here is to find the probability of selecting a chip of a different color. Since probabilities sum up to 1 for all possible outcomes, we would subtract the given probabilities from 1 to find the probability of selecting a chip that's neither red nor blue.
The total probability for all colors in the bag is always 1 (or 100%), which can be mathematically expressed as:
P(red) + P(blue) + P(other colors) = 1
Given P(red) = 1/8 and P(blue) = 13/24, we can substitute to find P(other colors):
P(other colors) = 1 - (P(red) + P(blue))
P(other colors) = 1 - (1/8 + 13/24)
First, we need to find a common denominator to combine the fractions:
P(other colors) = 1 - (3/24 + 13/24)
P(other colors) = 1 - 16/24
P(other colors) = 1 - 2/3
P(other colors) = 1/3
Therefore, the probability of selecting a chip that is neither red nor blue is 1/3.
Which describes a set amount of pay received by a worker over the course of a year?
tuition
expense
salary
hourly wage
Answer:
salary
Step-by-step explanation:
Salary is the term generally used to refer to the annual amount of wages.
_____
tuition is the amount paid to an educational institution for the classes they offer.
hourly wage refers to the amount earned in an hour, not a year.
expense is the name given to any expenditure, not an amount earned.
Answer:
C. Salary
Step-by-step explanation:
EDg
An organism which must obtain its food from other organisms is called a:
parasite
spore
fern
moss
Answer:
Parasite
Step-by-step explanation:
It feeds off of other organisms by living on or in the animal.
What is the answer to the problem?
Answer:
a
Step-by-step explanation:
good luck :)
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answer:
a) The function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)
Written in interval form
(-∞, -1.45) and (3.45, ∞)
- The function, f(x) is decreasing at the interval (-1.45 < x < 3.45)
(-1.45, 3.45)
b) Local minimum value of f(x) = -78.1, occurring at x = 3.45
Local maximum value of f(x) = 10.1, occurring at x = -1.45
c) Inflection point = (x, y) = (1, -16)
Interval where the function is concave up
= (x > 1), written in interval form, (1, ∞)
Interval where the function is concave down
= (x < 1), written in interval form, (-∞, 1)
Step-by-step explanation:
f(x) = x³ - 6x² - 15x + 4
a) Find the interval on which f is increasing.
A function is said to be increasing in any interval where f'(x) > 0
f(x) = x³ - 6x² - 15x + 4
f'(x) = 3x² - 6x - 15
the function is increasing at the points where
f'(x) = 3x² - 6x - 15 > 0
x² - 2x - 5 > 0
(x - 3.45)(x + 1.45) > 0
we then do the inequality check to see which intervals where f'(x) is greater than 0
Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45
(x - 3.45) | negative | negative | positive
(x + 1.45) | negative | positive | positive
(x - 3.45)(x + 1.45) | +ve | -ve | +ve
So, the function (x - 3.45)(x + 1.45) is positive (+ve) at the intervals (x < -1.45) and (x > 3.45).
Hence, the function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)
Find the interval on which f is decreasing.
At the interval where f(x) is decreasing, f'(x) < 0
from above,
f'(x) = 3x² - 6x - 15
the function is decreasing at the points where
f'(x) = 3x² - 6x - 15 < 0
x² - 2x - 5 < 0
(x - 3.45)(x + 1.45) < 0
With the similar inequality check for where f'(x) is less than 0
Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45
(x - 3.45) | negative | negative | positive
(x + 1.45) | negative | positive | positive
(x - 3.45)(x + 1.45) | +ve | -ve | +ve
Hence, the function, f(x) is decreasing at the intervals (-1.45 < x < 3.45)
b) Find the local minimum and maximum values of f.
For the local maximum and minimum points,
f'(x) = 0
but f"(x) < 0 for a local maximum
And f"(x) > 0 for a local minimum
From (a) above
f'(x) = 3x² - 6x - 15
f'(x) = 3x² - 6x - 15 = 0
(x - 3.45)(x + 1.45) = 0
x = 3.45 or x = -1.45
To now investigate the points that corresponds to a minimum and a maximum point, we need f"(x)
f"(x) = 6x - 6
At x = -1.45,
f"(x) = (6×-1.45) - 6 = -14.7 < 0
Hence, x = -1.45 corresponds to a maximum point
At x = 3.45
f"(x) = (6×3.45) - 6 = 14.7 > 0
Hence, x = 3.45 corresponds to a minimum point.
So, at minimum point, x = 3.45
f(x) = x³ - 6x² - 15x + 4
f(3.45) = 3.45³ - 6(3.45²) - 15(3.45) + 4
= -78.101375 = -78.1
At maximum point, x = -1.45
f(x) = x³ - 6x² - 15x + 4
f(-1.45) = (-1.45)³ - 6(-1.45)² - 15(-1.45) + 4
= 10.086375 = 10.1
c) Find the inflection point.
The inflection point is the point where the curve changes from concave up to concave down and vice versa.
This occurs at the point f"(x) = 0
f(x) = x³ - 6x² - 15x + 4
f'(x) = 3x² - 6x - 15
f"(x) = 6x - 6
At inflection point, f"(x) = 0
f"(x) = 6x - 6 = 0
6x = 6
x = 1
At this point where x = 1, f(x) will be
f(x) = x³ - 6x² - 15x + 4
f(1) = 1³ - 6(1²) - 15(1) + 4 = -16
Hence, the inflection point is at (x, y) = (1, -16)
- Find the interval on which f is concave up.
The curve is said to be concave up when on a given interval, the graph of the function always lies above its tangent lines on that interval. In other words, if you draw a tangent line at any given point, then the graph seems to curve upwards, away from the line.
At the interval where the curve is concave up, f"(x) > 0
f"(x) = 6x - 6 > 0
6x > 6
x > 1
- Find the interval on which f is concave down.
A curve/function is said to be concave down on an interval if, on that interval, the graph of the function always lies below its tangent lines on that interval. That is the graph seems to curve downwards, away from its tangent line at any given point.
At the interval where the curve is concave down, f"(x) < 0
f"(x) = 6x - 6 < 0
6x < 6
x < 1
Hope this Helps!!!
This question involves finding the increasing and decreasing intervals, local maximum and minimum values, and concavity of a cubic function f(x) = x3 – 6x2 – 15x + 4. These are found by taking the first and second derivative and applying various tests.
Explanation:The subject of this question is Calculus, more specifically, regarding the properties of the function f(x) = x3 – 6x2 – 15x + 4. To find the intervals where the function is increasing or decreasing, we need to find the derivative of f(x), set it to zero and solve for x to find critical points. Then we set up a number line with these critical numbers and analyze the sign of f'(x) in each interval.
The local maximum and minimum values can also be found from the critical numbers. To find where the function is concave up or down, we find the second derivative (f''(x)) and perform a similar process we did with the first derivative.
The inflection points, where the function changes its concavity, can also be found from evaluating the second derivative.
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Help me please!!!!!!!!!!!
Answer:
Step-by-step explanation:
Socratic had the answer on there I think
The National Health Statistics Reports published in 2018 reported that a sample of 360 ten-year old boys had a mean weight of 70.5 pounds with a standard deviation of 5.3 pounds. In addition a sample of 329 ten-year-old girls had a mean weight of 68.7 pounds with a standard deviation of 4.3 pounds. Can you conclude that the mean weights of ten-year-old boys and girls differ? Use ???? = 0.01.
Answer:
[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]
Since we conduct a bilateral test we have the p value given by:
[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]
Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance
Step-by-step explanation:
Information given
[tex]\bar X_{boys}=70.5[/tex] represent the mean weigth for ten year boys
[tex]\bar X_{girls}=68.7[/tex] represent the mean weigth for ten year girls
[tex]s_{boys}=5.3[/tex] represent the sample deviation for 10 year boys
[tex]s_{girls}=4.3[/tex] represent the sample standard deviation for 10 year girls
[tex]n_{boys}=360[/tex] sample size for boys
[tex]n_{girls}=329[/tex] sample size for girls
t would represent the statistic
[tex]\alpha=0.01[/tex] significance level assumed
System of hypothesis to check
We need to conduct a hypothesis in order to check if the true means are different for boys and girls, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{boys}=\mu_{girls}[/tex]
Alternative hypothesis:[tex]\mu_{boys} \neq \mu_{girls}[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X_{boys}-\bar X_{girls}}{\sqrt{\frac{s^2_{boys}}{n_{boys}}+\frac{s^2_{girls}}{n_{girsl}}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]
P value
We can assume that the degrees of freedom for this case are large enough to assume that the t distribution is approximately the normal distribution.
Since we conduct a bilateral test we have the p value given by:
[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]
Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance
Let A = {t, u, v, w}, and let S1 be the set of all subsets of A that do not contain w, and S2 the set of all subsets of A that contain w. (a) Find S1. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.)
Answer:
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
Step-by-step explanation:
Given:
A = {t, u, v, w}
S1 = set of all subsets of A that do not contain w.
S2 = set of all subsets of A that contains w.
Therefore S1 & S2 in set roster notation will be given as:
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
S2 = { {w}, {t,w}, {u,w}, {v,w}, {t,u,w}, {t,v,w}, {u,v,w}, {t,u,v,w} }
a) We can see that,
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
The problem involves finding subsets of a given set. The set S1, which includes subsets of the original set A that do not contain the element 'w', includes eight such subsets.
Explanation:The given set A contains the elements {t, u, v, w}. The set S1 consists of all the subsets of A that do not contain the element 'w'. Similarly, the set S2 consists of all the subsets of A that do contain the element 'w'.
To find S1, we can start by listing out each possible subset of A without the element 'w'. These include {}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, and {t, u, v}. So, S1 = {{}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, {t, u, v}}.
We ignore S2 as it's not relevant to the question asked.
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Use the image to answer the question. Use the drop-down menus to complete the statements. It isfor Acacia to pick a purple piece of candy compared to a green one. It isfor Eduarte to pick a pink piece of candy compared to a yellow one.
Answer:
1. less likely
2. more likely
Step-by-step explanation:
test took
Answer:
1. less likely
2. more likely
Step-by-step explanation:
Matt finds a box with dimensions 16 by 8 by 8 inches.
What volume can the box hold?
A box has a length of 16 inches, height of 8 inches, and width of 8 inches.
Use the formula V = Bh to calculate the volume of the box.
The area of the base of the box, B, is in.2.
The volume of the box is in.3.
Answer:
the box can hold a volume of 1024 inches ^3
Step-by-step explanation:
The volume of the given box is 1024 in.3.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
We are given that;
Dimension= 16*8*8 inches
Now,
To find the area of the base, we need to use the formula:
B=lw
where l is the length and w is the width. Substituting the given values, we get:
B=16×8
B=128
So, the area of the base of the box is 128 in.2.
To find the volume of the box, we substitute the values of B and h into the formula:
V=Bh
V=128×8
V=1024
Therefore, by the given prism the answer will be 1024 in.3.
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Question 4 Multiple Choice Worth 5 points)
(05.02 LC)
What is the area, in square units of the parallelogram shown below?
A
A
/
7 units
DC
5 units
25 square units
30 square units
35 square units
Answer:
35 square units.
Step-by-step explanation:
To find the area of a parallelogram, the formula is the exact same as finding the area of a rectangle. So 7 x 5 is 35.
Steph runs a vehicle body repair shop with one mechanic in Cleveland. Repair time for vehicles is exponentially distributed, with a mean of 2.8 minutes per vehicle. Customers arrive at an average rate of 15 per hour following a Poisson distribution. NOTE: calculate the measures per hour. Calculate system utilization. (Round your answer to the nearest whole percent without the percent sign.) System Utilization =
Answer:
System utilization = 0.7 or 70%
Step-by-step explanation:
Given arrival rate of customer = 15 customer/Hour
Servie rate = [tex] \dfrac{60}{2.8} customer/Hour [/tex]
Now, use the below formula to find the system utilization.
System utilization = [tex] \dfrac{\text{ Arrival rate of customer }}{\text{ Servie rate}}[/tex]
System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]
System utilization = [tex] \dfrac{15}{ \dfrac{60}{2.8}}[/tex]
System utilization = 0.7 or 70%
Can someone help me?
Answer:
1. x-2y
2. 2(13a-5)
Step-by-step explanation:
1. it's asking to expand the equation, so you should distribute the -1/2. -1/2*-2x becomes 1x or just x and -1/2*4y becomes -2y, so the answer is x-2y.
2. it's asking to factor, so you should find the greatest common factor of 26a and 10, which is 2. (a isn't on both terms, but if it was, then you would factor out the a also.) 26a/2 is 13a and -10/2 is -5, so the answer is 2(13a-5).
hope this helped!
Please go fast i only have 20 minutes left
Which statements are true about the rectangular pyramid below? Select three options. A rectangular pyramid. The rectangular base has a length of 6 centimeters and width of 4 centimeters. 2 triangular sides have a base of 6 centimeters and height of 6 centimeters. 2 triangular sides have a base of 4 centimeters and height of 4.6 centimeters. The area of the base is 24 cm2. There are four lateral faces. All the lateral faces are congruent. The total surface area of the figure is 66.4 cm2. At least one of the lateral faces has an area equal to 24 cm2.
the image isnt here, but if u use ed then u will know i hope. anything helps
Answer:
can you please post the pyramid
Step-by-step explanation:
The statements that are true concerning the rectangular pyramids include the following:
The area of the base is 24 cm²There are four lateral faces.What are the properties of a rectangular pyramid?
The properties of a rectangular pyramid include the following:
It has five faces, eight edges, and five vertices.It has four lateral triangular sides with a rectangular base.From the given rectangular pyramid, The area of the base is 24 cm² because, 6*4= 24cm²
There are four lateral faces which are triangular in shape.
Answer:
Explanation:
Answer:
Explanation:
To estimate LaTeX: \muμ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is LaTeX: \bar{x} = $73,220 x ¯ = $ 73 , 220 and the sample standard deviation is s = $4400. A 99% confidence interval for LaTeX: \mu μ is Group of answer choices
A. 73220 +/- 11440
B. 73220 +/- 568
C. 73220 +/- 431
D. 73220 +/- 28.6
Answer:
99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]
Step-by-step explanation:
Sample mean = [tex]\bar{x} =73220[/tex]
Standard deviation = s = 4400
Z at 99% confidence level = 2.57
Sample = n = 400
Formula of confidence interval :[tex]\bar{x} \pm Z \times \frac{s}{\sqrt{n}}[/tex]
Substitute the values in the formula :
So,99% confidence interval for [tex]\mu = 73220 \pm 2.57 (\frac{4400}{\sqrt{400}})[/tex]
99% confidence interval for [tex]\mu = 73220 \pm 565.4[/tex]
8^1/6 x2^x=32^1/2 work out the exact value of x
Answer:
i hope that helps......
For the given equation, the value of [tex]x[/tex] is [tex]2[/tex].
[tex]8^{\frac{1}{6}} \times 2^{x} = 32^{\frac{1}{2}}[/tex]
[tex](2^{3})^{\frac{1}{6}} \times 2^{x} = (2^{5})^{\frac{1}{2}}[/tex]
[tex]2^{\frac{1}{2}} \times 2^{x} = 2^{\frac{5}{2}}[/tex]
[tex]2^{\frac{1}{2}+x}=2^{\frac{5}{2}}[/tex]
Since, the bases are equal, we can compare the powers.
[tex]\frac{1}{2}+x=\frac{5}{2}[/tex]
[tex]x=\frac{5}{2}-\frac{1}{2}[/tex]
[tex]x=\frac{5-1}{2}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So, the value of [tex]x[/tex] is [tex]2[/tex].
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According to the U.S. Department of Transportation’s Air Travel Consumer Report, the nation’s 12 largest airlines recorded an on-time arrival percentage of 77.4% during 2001. Of interest is to estimate the mean delay time for all flights that did not arrive on time during 2013. A simple random sample of 35 late arriving flights was selected, and the mean delay time of this sample of 35 flights was 14.2 minutes, with a standard deviation (s) of 6.4 minutes. Use this information to calculate and interpret a 95% confidence interval for the mean delay time for all flights that did not arrive on time during 2013.
Answer:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
Step-by-step explanation:
Information given
[tex]\bar X=14.2[/tex] represent the sample mean for the delay time
[tex]\mu[/tex] population mean
s=6.4 represent the sample standard deviation
n=35 represent the sample size
Confidence interval
The confidence interval for the true parameter of interest is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=35-1=34[/tex]
The Confidence level is 0.95 or 95%,and the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this case is [tex]t_{\alpha/2}=2.03[/tex]
And replacing we got:
[tex]14.2-2.03\frac{6.4}{\sqrt{35}}=12.004[/tex]
[tex]14.2+2.03\frac{6.4}{\sqrt{35}}=16.396[/tex]
We are 95% confidence that the true mean for the delay time is between (12.004 and 16.396)
The traveler is disputing the claim about the variance. The hypothesis test is a right-tailed test. The result of the test does not provide enough evidence to dispute the airline's claim.
Explanation:109. The traveller is disputing the claim about the variance.
110. A sample standard deviation of 15 minutes is the same as a sample variance of 225 minutes.
112. H-o: The variance is 150 minutes or less.
113. d-f = 24
114. chi-square test statistic = 35.172
115. p-value = 0.082
116. Graph the situation:
Horizontal axis: VarianceMean: 150 minutesTest statistic: 225 minutesShade the p value: right tail117. Let a = 0.05
Decision: Fail to reject the null hypothesis
Conclusion: There is not enough evidence to dispute the airline's claim about the variance being 150 minutes or less.
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Help plz and thanks will mark you as BRAINLIEST
Answer: 36 cubic inches
Step-by-step explanation:
Una goma tiene un diámetro de 18 pulgadas. Cual es el área de la goma en pulgadas cuadradas?
Answer:
The area of the car tire = 254.57 in²
el área de la goma en pulgadas cuadradas = 254.57 in²
Step-by-step explanation:
English Translation
A car tire has a diameter of 18 inches which is the area of the tire in square inches?
A car tire is circular in nature, the area of a circle (car tire) is given as
A = πr²
where
π = pi (a constant) = (22/7)
r = radius of the circle = (diameter/2) = (18/2) = 9 inches
Area of the car tire = π×9² = 254.57 in²
Hence, the area of the car tire = 254.57 in²
Hope this Helps!!!
A disease is spreading throughout a community of 3,000 people at a rate (measured in number infected per day) proportional to the product of number of people infected and the number of people not yet infected, with constant of proportionality k = 0.004. Initially, 500 people are infected. Write an initial value problem.
Answer:
[tex]I'(t)=12I-0.004I^2, I_o=500[/tex]
Step-by-step explanation:
Population of the Community=3000
Let the number of infected=I
The number of uninfected=3000-I
The rate at which disease is spreading is proportional to the product of number of people infected and the number of people not yet infected.
[tex]\frac{dI}{dt}\propto I(3000-I) \\\frac{dI}{dt}=k I(3000-I)\\\frac{dI}{dt}=0.004 I(3000-I)\\$Let I_o$=Initial Number of Infected=500\\Therefore, the initial value problem is given as:\\I'(t)=12I-0.004I^2, I_o=500[/tex]
Which graph represents a function with a rate of change of 0.5?
On a coordinate plane, a line with negative slope goes through points (negative 1, 1) and (0, negative 1).
On a coordinate plane, a line with negative slope goes through points (negative 2, 0) and (0, negative 1).
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (1, 1).
On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
Answer: D-On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0). plz mark me brainliest.
Step-by-step explanation:
Option D. is correct. On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
Which graph represents a function with a rate of change of 0.5?
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
since
given rate of change = 0.5
slope of curve = rate of change
slope = [tex]\frac{Y_2-Y_1}{X_2-X_1}[/tex]
we have (0,-1) and (2, 0)
slope = 0+1/2-0
= 1/5
=0.5
=rate of change
Thus, On a coordinate plane, a line with positive slope goes through points (0, negative 1) and (2, 0).
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a² + 2ab + b² = 44
test test at few quarters
Answer:
Move all the terms to the left and set equal to zero.
Then set each factor equal to zero.
Step-by-step explanation:
I hope this helps
The correct answer is that the expression [tex]\(a^2 + 2ab + b^2\)[/tex] equals 44.
To solve the given mathematical expression [tex]\(a^2 + 2ab + b^2\),[/tex] we recognize that it is a perfect square trinomial. The perfect square trinomial can be factored into the square of a binomial:
[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]
Given that this expression equals 44, we can set the factored form equal to 44:
[tex]\[ (a + b)^2 = 44 \][/tex]
To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we take the square root of both sides of the equation. Remembering that the square root of 44 is not a whole number, we can express it as the product of prime factors:
[tex]\[ \sqrt{44} = \sqrt{4 \cdot 11} = \sqrt{2^2 \cdot 11} = 2\sqrt{11} \][/tex]
Therefore, we have:
[tex]\[ a + b = \pm 2\sqrt{11} \][/tex]
This equation tells us that the sum of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is either [tex]\(2\sqrt{11}\) or \(-2\sqrt{11}\).[/tex] Without additional information about [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we cannot determine unique values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], but we know that their sum must equal one of these two values.
The expression [tex]\(a^2 + 2ab + b^2\)[/tex] is indeed equal to 44, and the relationship between [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is given by [tex]\(a + b = \pm 2\sqrt{11}\).[/tex]
Which of the following expressions has a value of 3? Select all that apply.
Answer:
-6 ÷ -2 and (-1)(-3)
Step-by-step explanation:
To find which expressions have a value of 3, set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply.
Explanation:To find which expressions have a value of 3, we can set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply. Let's go through each expression:
2x - 1 = 3So, the only expression that has a value of 3 is 2x - 1 = 3 when x = 2.
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One grocery clerk can stock a shelf in 40 min. A second clerk requires 25 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?
Answer:
It would take 15.3846 minutes to stock the shelf if the two clerks worked together
Step-by-step explanation:
The first grocery clerk can stock a shelf in 40 minutes, it means that he can do 1/40 shelf per minute. At the same way, the second clerk requires 25 minutes, it means that he can do 1/25 shelf per minute
Then, if they worked together, they can stock 13 shelfs in 200 minutes, and it is calculated as:
[tex]\frac{1}{40}+\frac{1}{25} = \frac{13}{200}[/tex]
Now, using the rule of three, we need to find the minutes required to stock 1 shelf if they work at a rate of 13 shelf in 200 minutes as:
13 shelfs -------------- 200 minutes
1 shelf --------------- X minutes
Where X are the minutes required to stock 1 shelf.
So, solving for X, we have:
[tex]X=\frac{1*200}{13}=15.3846[/tex]
Finally, it would take 15.3846 minutes to stock the shelf if the two clerks worked together
Which of the following is not true in hypothesis testing? The smaller the p-value, the less evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. The larger the p value, the less evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. The smaller the p value, the more evidence the data provide against the null hypothesis and in favor of the alternative hypothesis. None of the above
Answer:
The larger the p value, the less evidence the data provide against the null hypothesis and in favour of the alternative hypothesis
Step-by-step explanation:
P Value is the probability of obtaining extreme observed results in a statistical hypothesis test, assuming that null hypothesis is correct.
High p value implies evidence in favour of null hypothesis, against alternate hypothesis.
Low p value implies evidence against null hypothesis, in favour of alternate hypothesis
So, larger p value, more evidence the data provides in favour of null hypothesis & against alternate hypothesis.The incorrect statement about hypothesis testing is that a smaller p-value indicates less evidence against the null hypothesis.
A small p-value actually provides strong evidence against the null hypothesis, prompting its rejection.
The p-value measures how unlikely the observed data is under the null hypothesis, but does not indicate the truth of the null hypothesis itself.
The statement in hypothesis testing that is not true is The smaller the p-value, the less evidence the data provides against the null hypothesis and in favor of the alternative hypothesis.
A small p-value indicates that the observed test statistic is very unlikely if the null hypothesis is true, which provides stronger evidence against the null hypothesis and in favor of the alternative hypothesis.
In fact, we generally use a significance level (commonly < 0.05) to determine if we should reject the null hypothesis. On the contrary, a larger p-value suggests less evidence against the null hypothesis, implying that we are less likely to reject it.
It's important to remember that the p-value is the probability of obtaining the observed data, or more extreme, given that the null hypothesis is true.
It does not, however, describe the probability that the null hypothesis itself is true, thus a small p-value means that the data is unlikely under the null hypothesis, leading to its potential rejection.
The circumference of the inner circle is 88 ft. The distance between the inner circle and the outer circle is 3 ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use StartFraction 22 Over 7 EndFraction
for pi.
Final answer:
The circumference of the outer circle is approximately 18.86 feet greater than the circumference of the inner circle, which has a circumference of 88 feet.
Explanation:
The circumference (C) of a circle is calculated using the formula C = 2πr, where π is Pi and r is the radius of the circle. Given that the circumference of the inner circle is 88 ft and the distance between the inner and outer circle is 3 ft, we deduce that the radius of the outer circle is 3 ft greater than the radius of the inner circle. Using the given approximation of π as 22/7, we can find the new circumference.
First, let's find the radius of the inner circle. Rearrange the formula to r = C / (2π) and substitute π with 22/7:
r = 88 / ((2 × 22)/7) = 88 / (44/7) = 88 / (6.2857) ≈ 14 ft
Now, the radius of the outer circle is r + 3 ft, which equals 17 ft. The circumference of the outer circle is then:
C = 2πr = 2 × 22/7 × 17 = 2 × 22 × 17 / 7 = 34 × 22 / 7 = 748 / 7 ≈ 106.86 ft
To find by how many feet the circumference of the outer circle is greater than the inner circle, subtract the circumference of the inner circle from that of the outer circle:
106.86 ft - 88 ft = 18.86 ft
Therefore, the circumference of the outer circle is approximately 18.86 ft greater than the circumference of the inner circle.
the points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C. What equation would represent circle C
Answer:
(x+5)² + (y-2)² =58
Step-by-step explanation:
"Your answer needs to be at least 20 characters long"
The equation of circle C will be;
⇒ (x + 5)² + (y - 2)² = 7.61²
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.
Now,
Since, The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.
Hence, The diameter of circle = √(- 2 - (-8))² + (- 5 - 9)²
= √ 6² + 14²
= √36 + 196
= √232
= 15.23
Thus, The radius of circle = 15.23 / 2
= 7.61
And, The center of the circle = (- 8 + (-2)) / 2 , (9 + (-5))/2
= (- 5, 2)
So, The equation circle C is,
⇒ (x - (-5))² + (y - 2)² = 7.61²
⇒ (x + 5)² + (y - 2)² = 7.61²
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A family plans to have three children. The wife and husband are trying to determine the probabilities of the different gender outcomes for the children.
The husband thinks that the probability that the first child is a girl is greater than the probability that the first child is a girl and the second child is a girl. The wife disagrees. She thinks that the two probabilities are equal.
The sample space of possible outcomes is listed below. B represents a boy, and G represents a girl.
Who is correct, the husband or the wife?
The husband is correct; the probability of the first child being a girl is higher than the probability of the first two being girls.
Let's list the sample space of possible outcomes for the genders of three children:
1. BBB (all boys)
2. BBG (two boys, one girl)
3. BGB (one boy, one girl, one boy)
4. BGG (one boy, two girls)
5. GBB (one girl, two boys)
6. GBG (two girls, one boy)
7. GGB (two girls, one boy)
8. GGG (all girls)
Now, let's examine the probabilities the husband and wife are discussing:
1. Husband's claim: Probability of the first child being a girl is greater than the probability of the first two children being girls.
Probability of the first child being a girl: [tex]\( \frac{4}{8} = \frac{1}{2} \)[/tex]
Probability of the first two children being girls: [tex]\( \frac{2}{8} = \frac{1}{4} \)[/tex]
The husband is correct.
2. Wife's claim: Probability of the first child being a girl is equal to the probability of the first two children being girls.
Both probabilities are [tex]\( \frac{1}{2} \)[/tex].
The wife is incorrect.
Therefore, the husband is correct in this scenario.
The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 40% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 40%. They sample 100 first-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test, they choose a 5% level of significance. What would be the null and alternative hypotheses
Answer:
Step-by-step explanation:
The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be
p = 0.4
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as
p ≠ 0.4