The domain is x [tex]\geq[/tex] 0. interval notation: [0,[tex]\infty[/tex])
the range is f(x)≤0, interval notation: (-[tex]\infty[/tex],0 ]
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
Find domain:
Set the term under the square root [tex]\geq[/tex]0
So, the domain is x [tex]\geq[/tex] 0. interval notation: [0,[tex]\infty[/tex])
Find range:
The range of a radical function of the form -c√(ax+b) +k is f(x)≤k
So, the range is f(x)≤0
interval notation: (-[tex]\infty[/tex],0 ]
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An artist connects stained glass pieces with lead strips. In this rectangular window, the strips
are cut so that FH = 22 in. Find JG.
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
What is a rectangle?
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 22in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (22) = JG
11 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
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A parallelogram has a base of 20 millimeters and a height that is 6 mm less than the base. Create an equation that
can be used to find the area, A, of the parallelogram in square millimeters.
Move the correct answer to each box. Not all answers will be used.
Me ayudan a resolver la numero 5 porfa
The solution to the inequality 6 + t ≤ 13 is given as follows:
t ≤ 7.
How to solve an inequality?An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.
The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.
For this problem, the inequality is given as follows:
6 + t ≤ 13
Hence the solution for variable t is found isolating it as follows:
t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)
t ≤ 7.
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all in image, please help asap
The angle that is same side exterior angle to ∠ABC is ∠EFH.
How to find angles?When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.
AD and EG are parallel to each other.
CH is a transversal line to the parallel lines.
Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.
Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.
Same side exterior angles are supplementary.
Therefore,
∠ABC and ∠EFH are same side exterior angles.
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A right triangle contains a 25° angle.
a.) If one leg is of length 5 inche, what is the length of the hyp?
b.) There are 2 answers. How is this possible?
If one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.
According to the question,
We have the following information:
A right triangle contains a 25° angle and length of one leg is 5 inches.
Now, the leg for which length is given can be opposite to given angle or adjacent to given angle. So, there are two possible for the length of hypotenuse (H).
Now, when it is opposite to the given angle:
Sin 25 = 5/H
H = Sin 25*5
H = 0.4226*5
H = 2.113 inches
Now, when it is adjacent to the given angle:
Cos 25 = 5/H
H = Cos 25*5
H = 0.9063*5
H = 4.5315 inches
Hence, if one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.
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a medical researcher is studying the effects of a drug on blood pressure. subjects in the study have their blood pressure taken at the beginning of the study. after being on the medication for 4 weeks, their blood pressure is taken again. the change in blood pressure is recorded and used in doing the hypothesis test.change: final blood pressure - initial blood pressurethe researcher wants to know if there is evidence that the drug reduces blood pressure. at the end of 4 weeks, 35 subjects in the study had an average change in blood pressure of -2.4 with a standard deviation of 5.2.find the p -value for the hypothesis test. your answer should be rounded to 4 decimal places.
Answer: 0.0099
Step-by-step explanation:
Express 2x=3y-7 in the form of ax+by+c=0 write the values
The final answer of the given quadratic equation is 2x - 3y + 7= 0.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
We have,
2x = 3y - 7
Converting the given equation in the form of ax + by + c = 0, we get
2x - 3y + 7= 0
Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.
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ben has 172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
The number of months Ben can be a member of the fitness club is 7 months .
In the question ,
it is given that Ben wants to join a fitness club ,
initial membership fees for fitness club is = $49.50
monthly fees for fitness club = $17.50
let the number of months be [tex]=[/tex] x
the total fees that Ben paid = $172
So ,according to the question
the equation to represent the situation is
49.50 + 17.50x = 172
17.50x = 172 - 49.50
17.50x = 122.5
x = 122.5/17.50
x = 7
Therefore , Ben can be a member of fitness club for 7 months .
The given question is incomplete , the complete question is
Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?
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Can anyone write the equation of the graph?
The equation of the absolute value function graph is: y = |x - 3| + 5.
What is the Equation of the Absolute Value Function?The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:
The vertex of the graph = (h, k)The value of a is determined by whether the graph opens up or opens down.The horizontal translation factor, which determines how far left or right the parent function is translated = hThe vertical translation factor, which determines how far up or down the parent function is translated = k.From the given graph, we have the following:
(h, k) = (3, 5) [the vertex]
Substitute the values into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:
6 = a|2 - 3| + 5
6 = a|-1| + 5
6 = a + 5
6 - 5 = a
1 = a
a = 1
To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:
y = 1|x - 3| + 5
y = |x - 3| + 5
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Given f(x) = -x - 1, find f(1).
Answer:
f(1) = -2
Step-by-step explanation:
f(1) = -(1) - 1
f(1) = -1 - 1
f(1) = -2
Angel bought a plant and planted it in pot near a window in his house. The plant
grew at a rate of 3 inches per month and its height at the time of purchase was 15
inches. Write an equation for H, in terms of t, representing the height, in inches, of
the plant t months after Angel bought the plant.
The required equation for height H of the plant t months after Angel bought the plant is,
H = 15 + 3t
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
t = time in months
H = total height
H= initial height+ rate of growth * time
H = 15 + 3t
So, the required equation for height H of the plant t months after Angel bought the plant is,
H = 15 + 3t
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Plot a point for some of the ordered pairs from the example problem shown at the right. Model the relationships by drawing a line from the y-axis through each point. Explain how the graphs show which relationship is proportional and which is not proportional.
Both the pairs of the points are linear.
Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.
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in a hypothesis test, we choose a 5% level of significance. which p-value is statistically significant at this level?
The value of p that is statistically significant at a 5% level of significance refers to a p-value of 0.05 or less.
The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the degree of significance, which is decided by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. The null hypothesis is anticipated to be shown as untrue or rejected if the result is statistically significant.
The symbol indicates the degree of significance (alpha). Therefore, the following definition applies to the level of significance:
Level of Significance = p (type I error) =
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What is the image of ( 0 , − 8 ) (0,−8) after a reflection over the line y = x y=x?
Answer:
(- 8, 0 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(0, - 8 ) → (- 8, 0 )
Wesley is baking three pumpkin pies. He will use a total of 5 1/4 quarts of pumpkin for the pies. If each pie contains the same amount of pumpkin, how many cups of pumpkin would each pie contain?
Answer:
Lol
Step-by-step explanation:
k
What integers are the solutions to
|x-4| < 8 and |-3x| > 12
Answer:
x-4<12 x<-4
-3x<12
-3x/-3=x
12/-3=-4
x-4+4=x
8+4=12
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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
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What transformation occurs from the graph y = x² to the graph of y = (x − 5)² + 7?
A a vertical shift up 5 units and a horizontal shift right 7.
B a vertical shift down 5 units and a horizontal shift right 7
C a vertical shift up 7 units and a horizontal shift left 5
D a vertical shift up 7 units and a horizontal shift right 5
The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
What do we mean by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.So, the transformation from:
y = x² to y = (x - 5)First, plot both graphs.
(Refer to the graph attached below)
Now, notice that the graph of the function y = (x - 5)² + 7 has shifted vertically upwards by 7 units and horizontally right by 5 units.Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
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A small park in the shape of a rectangle has dimensions 20m by 50m. a road through the park follows the diagonal of the rectangle. find the length of the road in simplest radical form.
The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].
Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m
As the road is diagonal of the rectangle.
So we have to find the length of the diagonal of the rectangle.
Formula to find the diagonal of rectangle:
Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]
length (l) = 50m
Breadth(b) = 20m
Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]
= [tex]\sqrt{2500 + 400}[/tex]
= √2900
= 10√29
Therefore the length of the road is 10√29.
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a federal report indicated that 13% of children under age 6 live in poverty in massachusetts, an increase over previous years. how large a sample is needed to estimate the true proportion of children under age 6 living in poverty in massachusetts within 2% with 99% confidence? round the intermediate calculations to three decimal places and round up your final answer to the next whole number.
Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.
The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.
We have Margin of error(E)=0.02,
Significance level([tex]\alpha[/tex])=0.01
Proportion(p)=0.13
Therefore, q is defined by =1-p
=> q =1-0.13
=>q=0.87
So, the Z-score is 2.582
Now, we know that sample size(S) is given by
=>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]
=>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]
=>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000
=>S=([885.01] / [1+1885.01]) × 1000
=>S=(0.200351)×1000
=>S=2003.51=2004 (approx)
Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.
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Question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior . question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior . question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior .
a) product of function f(x) and g(x) is 2x² - 6x - 8 and b) product of function that is in part a and an (x) is 2x³ - 4x² - 14x - 8.
Here are the three functions given:
f(x) = x -4
g(x) = 2x + 2
c(x) = x + 1
a) The product of function f(x) and g(x)
f(x). g(x) = (x -4). ( 2x + 2)
= x( 2x + 2) - 4(2x + 2)
= 2x² + 2x - 8x - 8
= 2x² - 6x -8
b) product of function f(x). g(x) and a(x)
f(x). g(x) . a(x) =( 2x² - 6x - 8 ). ( x + 1)
= x( 2x² - 6x - 8) + 1(2x² -6x - 8)
= 2x³ - 6x² -8x + 2x² - 6x -8
= 2x³ -4x² - 14x - 8
Therefore we get a) 2x² - 6x - 8 and b) 2x³ - 4x² - 14x -8.
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Use the properties of operations to multiply (8-2x) (-0.25x)
_x + _x^2
the _ is the blanks im supposed to fill in
The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)
What does the term Algebraic Expression means?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
Given the expression, we need to solve it by using the properties of basic multiplication.
= (8 - 2x)*(-0.25x)
= (8*(-0.25x)) + (-2x * (-0.25x))
= -2x + 0.5[tex]x^{2}[/tex]
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Suppose you toss a coin 100 times and get 80 heads and 20 tails. Based on these results, what is the probability that the next flip results in a tail?
The probability that the next flip results in a tail is approximately__
(Type an integer or decimal rounded to two decimal places as needed.)
The probability of the next flip result in a trail is 0.5.
Given that,
If you flip a coin 100 times and receive 80 heads and 20 tails.
We have to find what is the probability that the upcoming flip will result in a tail based on these findings.
What is probability?Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.
One is the probability of every event in a sample space.
Next flip result is independent of the past results.
P(Next flip result is tail) = 1/2 = 0.5
Therefore, The probability of the next flip result in a trail is 0.5.
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Ms. Nettleton wants to create an outdoor space for her dogs. The distance between the furthest corners is 4 feet. The width of the area is 2 feet. How long is the length of the area?
(please help)
The length of the area is 8 feet.
What is the shape of outdoor space?
We know that Square has equal length, Rectangle has opposites sides of equal length.By the given length we found that it is Rectangular outdoor space.Step-by-step explanation:
Given :
Distance between the furthest corners(Length)= 4 feet
Width(breadth) = 2 feet
Area of rectangle = Length * Breadth
= 4 * 2
=8 feet
Hence, The length of the area is 8 feet.
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alice passes through four traffic lights on her way to work, and each light is equally likely to be green or red. independent of the others. (a) what is the pmf, the mean, and the variance of the number of red lights that alice encounters?
The value for the number of red lights that Alice encounters are found.
Mean = 2; Var = 1; PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾What is meant as the independent events?The set of findings from an experiment is thought to as events in probability. There are numerous sorts of events, including independent, dependent, and mutually exclusive ones.X = no of red lights crossed by Alice.
X is Binomial distributed
In which n=4, p=0.5, q = 0.5
Mean value is found by the formula,
Mean = np
Mean = 4×0.5
Mean = 2
And, variance = npq
Var = np(1-p)
Var = 4×0.5×0.5
Var = 1
PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾
Thus, the value for pmf, the mean, and the variance of the number of red lights that Alice encounters are found.
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Which one of the following is NOT equivalent to 3/4? 16/24 15/20 6/8 24/32 PWEASE HURRY THESE ARE ALL MY POINTS
Which one of the following is NOT equivalent to 3/4?
16/24 = 2/3
15/20 = 3/4
6/8 = 2/3
24/32 = 3/4
Answer: 16/24 and 24/32 are not equivalent to 3/4
Step-by-step explanation:
Equivalent fractions represent the same value, even though they look different.
Here, when we convert every fraction to its simplest form, we can verify if they are equal.
(16/24) ÷ (8/8) = 2/3
(15/20) ÷ (5/5) = 3/4
(6/8) ÷ (2/2) = 3/4
(24/32) ÷ (4/4) = 6/7
As the simplest forms of 16/24 and 24/32 are not 3/4, they are not equivalent fractions of 3/4.
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re-write the statement 19 + 7 divided by 2 - 5
by including one pair of brackets to make the total value equal to 8
Re-write the statement 19 + 7 divided by 2 x 6 + 1 by including two pairs of brackets to make the total value equal to 2
Answer:
[19+7] / [2 x 6 + 1]
Step-by-step explanation:
[19+7] / [2 x 6 + 1]
[26] / [13]
[2]
this shows that the percentage in a normal distribution that is at most 1.65 sds above average is about 95%. explain why 1.65 is the right number of sds to use when constructing a 90% confidence interval. (6 points)
The correct number of Standard deviation to generate a confidence interval is therefore 1.65.
Given that;
This shows that the percentage in a normal distribution that is at most 1.65 standard deviation above average is about 95%.
Percentage above 1.65 SD equals 100 - 95 = 5.
Now, because of the symmetric distribution,
Percentage above 1.65 SD = % below 1.65 SD is what we can see:
Below 1.65 SD + between 1.65 SD below and 1.65 above + above 1.65 SD + % above 1.65 SD = 100%
=> 5% + between -1.65 SD below and 1.65 above + 5% = 100%
=> % between -1.65 SD and 1.65 SD above mean = (100 - 5 - 5)% = 90%
The correct number of SDs to generate a confidence interval is therefore 1.65.
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evaluate the expression 2x^3 - 14 when x=2
Answer:
-2
Step-by-step explanation:
2(2)*3-14
4*3-14
12-14
-2
Determine which equation is false, based on the solution set S:{4}.
3t = 12
3m + 7 = 14
4(4c + 1) = 68
9 = 5p − 11
Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4
The first equation is
3t = 12
t = 12/3
t = 4
The solution is {4}
The second equation is
3m + 7 = 14
3m = 14 - 7
3m = 7
m = 7/3
The solution is not {4}
The third equation is
4(4c + 1) = 68
4c + 1 = 68/4
4c + 1 = 17
4c = 17-1
4c = 16
c = 16/4
c = 4
The solution is {4}
The fourth equation is
9 = 5p - 11
5p = 9 + 11
5p = 20
p = 20/5
p = 4
The solution is {4}
Hence, Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4
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