Create a rational inequality for which -2 < x < 1 is the solution.
(Use the chart to show work)
Answers
A rational inequality for which -2 < x < 1 is the solution is (3x - 1)/(x + 2) > 2.
What is a rational equation?An inequality that incorporates one or more rational expressions—that is, expressions that can be expressed as the quotient of two polynomial expressions—is referred to as a rational inequality. The same techniques used to resolve other kinds of inequalities, such as graphing, testing intervals, or algebraic manipulation, can also be used to resolve rational inequalities. The denominator of a rational expression cannot, however, equal zero, hence extra care must be made to identify and rule out any values of the variable that would do so, as these values would render the expression undefinable.
A rational inequality for which -2 < x < 1 is the solution is:
(3x - 1)/(x + 2) > 2
In the equation when,
For x -2, the inequality holds because both the denominator and the numerator are negative.
When -2 x 1, the inequality is true since both the denominator and the numerator are positive.
When x > 1, the denominator and numerator are both positive, but the expression's value is less than 2, rendering the inequality untrue.
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Related Questions
Brody has pulled 27 marbles from a large bag, and 12 of them are red. What is the experimental probability that the next marble selected from the bag will be red?
Answers
Answer:
Step-by-step explanation:
4/9
By the number of red marbles taken out, we expect that 12/27=4/9 of the marbles are red. Therefore, the probability of the next marble being red is 4/9.
Cual es el término general de la sucesión 4, 9, 14, 19, 24
Answers
Ll término general de la sucesión 4, 9, 14, 19, 24 es an = 5n - 1.
Progresión aritméticaLa sucesión 4, 9, 14, 19, 24 es una progresión progresión aritméticacon una diferencia común de 5.
El término general de una progresión aritmética se puede encontrar utilizando la fórmula:
an = a1 + (n - 1)d
donde:
an = el término general que se desea encontrar
a1 = el primer término de la progresión
n = la posición del término que se desea encontrar
d = la diferencia común de la progresión
En este caso, a1 = 4 y d = 5. Para encontrar el término general para cualquier posición n, podemos sustituir estos valores en la fórmula y simplificar:
an = a1 + (n - 1)dan = 4 + (n - 1)5an = 4 + 5n - 5an = 5n - 1Por lo tanto, el término general de la sucesión 4, 9, 14, 19, 24 es an = 5n - 1.
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An airline has a new plane with 120 seats and a new route from panama city, FL to New York city, NY. The function F(x) models the profit the airline makes, where x is the cost per seat. The table of values for function f(x) is shown
Answers
The correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.
What is Correlation Coefficient?The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient.
To calculate the correlation coefficient between x and f(x), we need to calculate several quantities first:
mean of x:
[tex]$\overline{x}[/tex] = {50+35+60+65+70+75+80}{7} = {435}/{7}
= 62.14
mean of f(x):
[tex]$\overline{f(x)}[/tex]= {1,272 + 1,884.5 + 2,322 + 2,584.5 + 2,672 + 2,584.5 + 2,322}/{7}
= 2,112.86
and, standard deviation of x:
[tex]$s_x[/tex]=[tex]\sqrt{\frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n-1}}[/tex]
= [tex]= \sqrt{\frac{(50-62.14)^2 + (35-62.14)^2 + (60-62.14)^2 + (65-62.14)^2 + (70-62.14)^2 + (75-62.14)^2 + (80-62.14)^2}{6}} \\\approx 17.27$[/tex]
and, standard deviation of f(x):
[tex]$s_{f(x)} = \sqrt{\frac{\sum_{i=1}^n (f(x_i) - \overline{f(x)})^2}{n-1}}[/tex]
= (1,272-2,112.86)² + (1,884.5-2,112.86)² + (2,322-2,112.86)² + (2,584.5-2,112.86)² + (2,672-2,112.86)²+ (2,584.5-2,112.86)² + (2,322-2,112.86)²}/ 6
= 385.09
Now, covariance of x and f(x):
[tex]$cov(x,f(x)) = \frac{\sum_{i=1}^n (x_i - \overline{x})(f(x_i) - \overline{f(x)})}{n-1}[/tex]
= {(50-62.14)(1,272-2,112.86) + (35-62.14)(1,884.5-2,112.86) + (60-62.14)(2,322-2,112.86) + (65-62.14)(2,584.5-2,112.86) + (70-62.14)(2,672-2,112.86) + (75-62.14)(2,584.5-2,112.86) + (80-62.14)(2,322-2,112.86)} / 6
= 762.36
Using these values, we can calculate the correlation coefficient:
[tex]$r = \frac{cov(x,f(x))}{s_x s_{f(x)}} = \frac{762.36}{17.27 \cdot 385.09} \approx 0.39$[/tex]
Therefore, the correlation coefficient between x and f(x) is approximately 0.39. This suggests a weak positive correlation between the cost per seat and the profit the airline makes.
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1.2cm radius
4cm height
Pls help me find the surface area and volume
Answers
Answer:
if its a circle
Volume - 7.20 cm
Surface area 18.1 cm
Step-by-step explanation:
Volume of a sphere = 4/3 πr^3
4/3 (3.14) 1.2^3
4/3 (3.14) 1.728
4/3 of 5.42592=
7.23456 or 7.20
Surface area of sphere = 4πr²
4(3.14) 1.2^2
4(3.14) 1.44
4 (4.5216) =
18.0864 or 18.1
please help will give brainliest
On average, Carson spends $2 of his $20 monthly allowance on library fines. When creating a circle graph of what Carson does with his money, what fraction of the circle will represent the amount he spends on library fines?
Answers
Answer:
1/10 of the circle (36° central angle).
Step-by-step explanation:
2/20 = 1/10
A circle has 360 degrees, so the central angle will be 1/10 × 360° = 36°.
a survey asked 215 people what alternative transportation modes they use. the results are below. 144 walk 102 use the bus 105 ride a bicycle 78 walk and use the bus 65 walk and ride a bicycle 45 ride the bus and ride a bicycle 34 said they use all three modes of transportation. how many people don't use any alternate transportation
Answers
The number of people who don't use any alternative transportation mode is 18 people.
To find the number of people who don't use any alternative transportation mode we can use the principle of inclusion and exclusion (PIE) method.
adding the number of people who use each mode:
walk = 144
bus = 102
bicycle = 105
Next, subtract the number of people who use two modes:
walk and bus = 78
walk and bicycle = 65
bus and bicycle 45
adding people who use all three modes:
all three modes of transportation = 34
Therefore, the total number of people who use at least one alternative mode of transportation is:
= 144 + 102 + 105 - 78 - 65 - 45 + 34
= 197
To find the number of people who don't use any alternative transportation. we need to subtract the number of people who use at least one alternative mode of transportation from the total number of people in the survey:
= 215 - 197
= 18
Therefore, The number of people who don't use any alternative transportation mode is 18.
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Please help
What was the balance before the ATM withdrawal on June 5?
Answers
Answer: 586.20
Step-by-step explanation:
you add the balance on june 5th with the amount withdrawed to get the past balance
Maia was baking cupcakes for a party. She mixed 4 drops of red food coloring for every 6 drops of yellow food coloring to dye her icing orange. Circle the ratios of food coloring drops that would create the same orange color and justify your choices.
2 red to 3 yellow 40 yellow to 100 red 44 red to 66 yellow 24 red to 26 yellow 28 red to 42 yellow
Answers
The ratios that would create the same orange color as Maia's ratio of [tex]2:3[/tex] are [tex]2[/tex] red to [tex]3[/tex] yellow, [tex]44[/tex] red to [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.
What are the ratios?The ratio of 4 drops of red food coloring to 6 drops of yellow food coloring can be simplified to 2:3 by dividing both numbers by 2. This means that for every 2 drops of red food coloring, Maia used 3 drops of yellow food coloring to create orange icing.
Let's evaluate each of the given ratios:
2 red to 3 yellow: This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
40 yellow to 100 red: We can simplify this ratio by dividing both numbers by 20, giving us 2 yellow to 5 red. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.
44 red to 66 yellow: We can simplify this ratio by dividing both numbers by 22, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
24 red to 26 yellow: We can simplify this ratio by dividing both numbers by 2, giving us 12 red to 13 yellow. This ratio is not equivalent to Maia's ratio of 2:3, so it would not create the same orange color.
28 red to 42 yellow: We can simplify this ratio by dividing both numbers by 14, giving us 2 red to 3 yellow. This ratio is equivalent to Maia's ratio of 2:3, so it would create the same orange color.
Therefore, the ratios that would create the same orange color as Maia's ratio of [tex]2:3[/tex] are [tex]2[/tex] red to [tex]3[/tex] yellow, [tex]44[/tex] red to [tex]66[/tex] yellow, and [tex]28[/tex] red to [tex]42[/tex] yellow.
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A rectangular prism has a volume of 12,500 cubic inches and is 50 inches tall.
Which equation can be used to find B, the area of the base of the prism?
Group of answer choices -
A. 12500=50B
B. 12500=B/50
C. 12500=50/B
D. 50=12500B
Answers
The for the given volume of 12,500 cubic inches for rectangular prism, the base area will be estimated by equation: A. 12500=50B.
Explain about the rectangular prism:A rectangular prism is one of the more typical shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. The other surfaces are also rectangles because the bases are rectangles. These are a rectangular prism's characteristics:
two parallel rectangular basesCongruent as well as parallel rectangles on three facestotal of six rectangular facesGiven:
volume of rectangular prism = 12,500 cubic inches
Height h = 50 inches.
Let the base area be B.
Then,
volume of rectangular prism = B*h
12500 = B*50
12500 = 50B (required equation)
B = 12500/50
B = 250 unit sq.
Thus, the for the given volume of 12,500 cubic inches for rectangular prism, the base area will be estimated by equation: A. 12500=50B.
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[tex]9x^2-4(y+2x)^{2}[/tex]
Answers
Answer:
Step-by-step explanation:
by identity a²-b² =(a-b)(a+b)
9x² = (3x)²
4(y+2x)² = 2²(y+2x)² = (2(y+2x))²=(2y+4x)²
so : a = 3x and b = 2y+4x
put a and b in this identity a²-b² =(a-b)(a+b) ....continu
In one part of the world, the number of a certain species of forest wildflowers is expected to grow according to the
function f graphed below. In another area of the world, the same species is expected to grow according to the the
function g represented by the data in the table. The values for x in each function represent time, in decades.
what function has the greater initial value
in a third area, the number of flowering plants is expected to grow according to the following description the initial count is 1500 and for each decade moving forward the count will increase by 200. Will this model be linear or exponential what is the model that relates the number of plants h to the number of decades x
Answers
Answer:
f(x) has the greater initial value.
linear; h(x) = 200x + 1500
Step-by-step explanation:
f(0) = 1000
g(0) = 750
Therefore, f(x) has the greater initial value.
In the third area, the model is linear and the function would be:
h(x) = 200x + 1500
I NEED HELP ON THIS ASAP!!
Answers
The area of triangle XYZ when using YZ as the base, can be found to be 24 square units.
How to find the area ?To find the area of triangle XYZ, we can use the Shoelace Theorem (also known as the Surveyor's Formula). Given the coordinates of the vertices, the area of the triangle is:
Area = (1/2) x |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|
Plugging in the coordinates:
Area = (1/2) x |(2(9 - 1) + 10(1 - 5) + 6(5 - 9))|
Area = (1/2) x |(2(8) - 10(4) + 6(-4))|
Area = (1/2) x |(16 - 40 - 24)|
Area = (1/2) x |-48|
Area = 24 square units
The area of triangle XYZ is 24 square units.
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50 Points!!! Are collinear lines real? If so, explain.
Answers
Answer:
You may see many real-life examples of collinearity such as a group of students standing in a straight line, a bunch of apples kept in a row, next to each other, etc. In geometry, two or more points are said to be collinear, if they lie on the same line.
Step-by-step explanation:
Hope this helps!=D
solve |3x-.5|>1.5, |3x-.5|=1.5,|3x-.5|<1.5
Answers
Solve and get |3x - 0.5| > 1.5: x < -0.333 or x > 1, The solution to |3x - 0.5| = 1.5 is: x = 0 or x = 1, The solution to |3x - 0.5| < 1.5 is: -0.333 < x < 0.833
Depending on whether the expression contained in the absolute value is positive, negative, or zero, there are three scenarios that need to be taken into account in order to system of equations the absolute value inequalities involving |3x - 0.5|.
Example 1: (3x - 0.5) > 0
The absolute value expression in this situation is reduced to 3x - 0.5. We thus have:
3x - 0.5 > 1.5
When we solve for x, we get x > 1.
Example 2: (3x - 0.5) < 0
The absolute value expression in this situation is -(3x - 0.5), which is equivalent to -3x + 0.5. We thus have:
-3x + 0.5 > 1.5
The result of solving for x is: x -0.333
Example 3: (3x - 0.5) = 0
The equation for the absolute value in this situation is |0|, which equals 0. The result is either 3x - 0.5 = 1.5 or 3x - 0.5 = -1.5.
The results of each equation's x term are: x = 1 or x = 0.
As a result, the answer to |3x - 0.5| > 1.5 is either x -0.333 or x > 1.
x = 0 or x = 1 is the answer to the equation |3x - 0.5| = 1.5.
The answer to the equation |3x - 0.5| 1.5 is: -0.333 x 0.833
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What is the sum of 25 and h, divided by f cubed?
Answers
The expression for the given statement can be written as (25 + h) / f³.
What is sum?A sum is the result of adding two or more numbers together. For example, the sum of 2 and 3 is 5, which is obtained by adding 2 and 3. In mathematical notation, we can represent this as:
2 + 3 = 5
According to question:The expression for the given statement can be written as:
(25 + h) / f³
where h and f are variables.
If you have specific values for h and f, you can substitute them into the expression and evaluate it. Otherwise, you can leave the expression as it is.
The expression "(25 + h) / f³" represents the result of adding 25 to the value of h, and then dividing the sum by the cube of the value of f.
In general, if you have specific values for h and f, you can substitute them into the expression and evaluate it. If you don't have specific values for h and f, you can leave the expression as it is. This expression is an algebraic expression, which means it contains variables (h and f) and mathematical operations (+, /, and ³).
Note that division is performed before addition, so the sum of 25 and h is first calculated, and then the result is divided by f³.
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Identify the shape, explain how you found your answer.
Answers
Answer:
The shape in the image is a trapezoid. It is a quadrilateral with one pair of parallel sides.
Step-by-step explanation:
The circumference of a circle is 5π ft. What is the area, in square feet? Express your answer in terms of \piπ.
Answers
Answer: We know that the formula for the circumference of a circle is:
Circumference = 2πr
where r is the radius of the circle.
In this problem, we are given the circumference, which is 5π ft, so we can set up an equation:
5π = 2πr
Dividing both sides by 2π, we get:
r = 5/2 feet
Now that we know the radius, we can use the formula for the area of a circle:
Area = πr^2
Substituting in the value of r that we found, we get:
Area = π(5/2)^2
Area = π(25/4)
Simplifying, we get:
Area = 25π/4
Therefore, the area of the circle is 25π/4 square feet.
Step-by-step explanation:
Two groups of friends went to the local movie theater. The first group bought four large buckets of
popcorn and five boxes of candy and spent $42.75. The second group spent $25.50 on two boxes of
candy and three large buckets of popcorn.
How much would one large popcorn and one box of candy cost?
Answers
One large bucket of popcorn costs $6 and one box of candy costs $3.75.
To solve this problemLet's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :
Equation 1: 4p + 5c = 42.75 (first group's purchase)
Equation 2: 3p + 2c = 25.50 (second group's purchase)
We can use any method to solve these equations, such as substitution or elimination.
Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":
8p + 10c = 85.50 (multiplying Equation 1 by 2)
-15p - 10c = -127.50 (multiplying Equation 2 by -5)
Adding the two equations, we get :
-7p = -42
p = 6
Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:
4(6) + 5c = 42.75
24 + 5c = 42.75
5c = 18.75
c = 3.75
Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.
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a general rehydration recommendation after exercise is 2.5 cups of fluid for every 1 pound of body weight lost. using this guideline, how much fluid would vanessa need to consume to make up for the weight that was lost during her run? calculation: 2.5 cups x lbs of body weight lost
Answers
Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.
The amount of water needed to be drank is approximately 2 cups of water are required for every pound of body weight reduced.
Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.
Refilling fluid: To add fluid to something that has been drained, in particular: to replace any fluids the body has lost from dehydration. assist a patient in hydrating.
Oral rehydration solutions (ORSs), which include Pedialyte, are used to treat dehydration. ORSs, which help replace lost fluids, include the correct ratio of salt, sugar, potassium, and other minerals.
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Complete question - A general rehydration recommendation after exercise is 2.5 cups of fluid for every 1 pound of body weight lost. Using this guideline, how much fluid would Vanessa need to consume to make up for the weight that was lost during her run?
Calculation: 2 cups x lbs of body weight lost = cups of water needed
A. Approximately 4 cups of fluid
B. Approximately 8 cups of fluid
C. Approximately 6 cups of fluid
D. Approximately 10 cups of fluid
7. Vanessa asks if she should start using sports drinks. Which of the following would best answer Vanessa's question?
A. A sports drink is not beneficial for you at this time and may provide unnecessary calories.
B. A sports drink would be beneficial to replace fluid and electrolytes when exercising for less than 30 minutes.
C. A sports drink would be beneficial on days when you are exercising for over an hour at a higher intensity.
8. If Vanessa uses a sports drink in the future, how much glucose, sodium and potassium should be provided per 24 fluid ounces of sports drink?
A. No more than 30 g of glucose, 450 g of sodium and 225 mg of potassium.
B. No more than 75 g glucose, 150 mg sodium, 175 mg potassium.
C. No more than 15 g of glucose, 500 mg sodium, 200 mg potassium.
D. No more than 45 g of glucose, 225 mg of sodium and 275 mg of potassium.
the point (-2, y) is on the same line as the points (1, 2) and (7, -1). What is the value of y?
Answers
that means that the slope for all three points is the same, since all are collinear, hmmm what's the slope of (1 , 2) and (7 , -1)?
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 6 } \implies - \cfrac{1 }{ 2 }[/tex]
ahaaa!, that means from from (-2 , y) and either of those points is the same slope of -1/2, so
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1})[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{y}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-2)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ \cfrac{ -1 }{ 2 }}\implies \cfrac{-1-y}{7+2}=\cfrac{-1}{2}\implies \cfrac{-1-y}{9}=\cfrac{-1}{2} \\\\\\ -2-2y=-9\implies -2y=-7\implies y=\cfrac{-7}{-2}\implies y=\cfrac{7}{2}[/tex]
Answer:
Step-by-step explanation: (-2, y) (1, 2) and (7, -1) wat is the value of y
Noemi strings together x green beads at $0.75 each with 3 blue beads at $0.30 each. She makes a bracelet that averages $0.60 per bead. How many green beads does Noemi use?
Answers
Answer: Noemi strings together 6 green beads at $0.75 each to make the bracelet.
Step-by-step explanation:Let's start by using algebra to solve the problem. We can begin by letting x be the number of green beads that Noemi strings together. Then, the cost of the green beads will be 0.75x, and the cost of the blue beads will be 3 × 0.30 = 0.90.
The total cost of the bracelet will be the sum of the cost of the green and blue beads, which is 0.75x + 0.90. The total number of beads on the bracelet will be x + 3.
We know that the average cost per bead is $0.60. We can write this as:
(0.75x + 0.90)/(x + 3) = 0.60
Now we can solve for x:
0.75x + 0.90 = 0.60(x + 3)
0.75x + 0.90 = 0.60x + 1.80
0.15x = 0.90
x = 6
Therefore, Noemi strings together 6 green beads at $0.75 each to make the bracelet.
Pls help, its easy I just dont want to do it.
Answers
Purple-25
Red-45
Step-by-step explanation:
The green triangle :
The angle x is 65°
this is because both the sides are equal so when the other angle is 65° angle x is also 65°
The blue triangle :
The angle x is 25°
this is because both the sides are equal so when the other angle is 25° angle x is also 25°
The red triangle :
The angle x is 45°
this is because both the sides are equal so when the other angle is 45° angle x is also 45°
y=2x+35
y=9x
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answers
Answer:
To find the point of intersection between the two lines represented by the equations:
y = 2x + 35
y = 9x
We can set the two equations equal to each other and solve for x:
2x + 35 = 9x
Subtracting 2x from both sides:
35 = 7x
Dividing both sides by 7:
x = 5
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Using the second equation:
y = 9x = 9(5) = 45
Therefore, the point of intersection between the two lines is (5, 45).
Step-by-step explanation:
Answer:
x=5 and y=45; (5,45)
Step-by-step explanation:
Step One→ Solve one equation for either x or y.
Step Two→ Substitute the expression from step one into the 2nd equation.
Step Three→ Solve the second equation for the given variable.
Step Four→ Plug your solution back into the first equation.
Step Five→ Write your solution as a point.
What is the equation that represents the circle shown on the graph?
Equation
Answers
The equation of the circle is represented by [tex]x^{2} + (y-3)^{2} = 16[/tex] with radius of the circle as r = 4.
How to find the equation of the circle?
To find the equation of the circle is
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
here h is the x- coordinate of the center of the circle
k is the y- coordinate of the center of the circle
r is the radius of the circle
From the given figure,
h = 0
k = 3
r = 4
putting all the values of the above equation
[tex](x-0)^{2} + (y - 3)^{2} = 4^{2}[/tex]
[tex]x^{2} + (y-3)^{2} = 16[/tex]
Therefore the equation of the circle is
[tex]x^{2} + (y-3)^{2} = 16[/tex]
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the length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. in a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.5 inches and 95.1 inches? g
Answers
The probability that the mean of a sample of 45 boards will be between 94.5 inches and 95.1 inches, given that the length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches, can be calculated using the Central Limit Theorem. The theorem states that the distribution of sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean (μ) is 95 inches, the population standard deviation (σ) is 0.52 inches, and the sample size (n) is 45. The standard deviation of the sample mean is σ/√n = 0.52/√45 ≈ 0.0775.
To find the probability, we can use the Z-score formula:
Z = (X - μ) / (σ/√n)
For the lower limit of 94.5 inches, the Z-score is:
Z1 = (94.5 - 95) / 0.0775 ≈ -6.45
For the upper limit of 95.1 inches, the Z-score is:
Z2 = (95.1 - 95) / 0.0775 ≈ 1.29
Now, using a Z-table or calculator, find the probability for each Z-score:
P(Z1) ≈ 0 (since it is a very low Z-score)
P(Z2) ≈ 0.9015
The probability that the mean of the sample will be between 94.5 inches and 95.1 inches is the difference between these probabilities:
P(94.5 < X < 95.1) = P(Z2) - P(Z1) = 0.9015 - 0 ≈ 0.9015, or approximately 90.15%.
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tell whether segment QS is a diameter of circle c
Answers
QS is the diameter of circle
Define circleA circle is a two-dimensional geometric shape consisting of all points in a plane that are a given distance from a fixed point called the center. It is a closed shape, meaning it has no beginning or end, and every point on its perimeter is equidistant from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter
In the given circle QS bisects perpendicularly the chord PR in two equal part. so, it must pass through center of circle.
QS is passing through center.
The chord passing through center is called as diameter of circle.
Hence, QS is the diameter of circle.
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A storage box is shaped like a rectangular prism, as shown below. Skylar stored
1/2 -inch cubes in the box.
How many cubes are needed to completely fill the box?
54 cubes
108 cubes
72 cubes
27 cubes
pls explain your answer
Answers
The correct answer is that 60 cubes are needed to completely fill the box.
What are the cubes?
We can find the number of cubes needed to fill the box by dividing the volume of the box by the volume of one cube. Since the cubes are 1/2 inch on each side, their volume is (1/2)³ = 1/8 in³
To find the volume of the box, we need to multiply its length, width, and height:
Volume of box = 5 × 4 × 3 = 60 in³
Now we can divide the volume of the box by the volume of one cube to find the total number of cubes needed:
Total cubes = Volume of box / Volume of one cube
Total cubes = 60 / (1/8)
Total cubes = 480
Therefore, the correct answer is not one of the given options. However, if we divide 480 by 2 (since the cubes are 1/2 inch on each side), we get:
Total cubes = 480 / 2 = 240
And if we divide 240 by 4 (since the box has dimensions of 5, 4, and 3 units), we get:
Total cubes = 240 / 4 = 60
Therefore, the correct answer is that 60 cubes are needed to completely fill the box.
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the one-sample z-test is used when the population standard deviation is unknown. group of answer choices true false
Answers
The given statement that 'the one-sample z-test is used when the population standard deviation is unknown.' is true.
Z-test is used to test hypotheses about the population means when we don't have any information about the population standard deviation and the sample size is huge. According to the given statement, the standard error of the mean can be estimated with the help of sample standard deviation, and the test statistic can be approximated by a standard normal distribution.
In another case where the sample size is too small, T-test should be used instead of Z-test. This is encouraged because of increased efficiency.
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Ms. Khan wants to add x feet onto each side of an existing patio. The new patio would have an area of x2+14x+48 square feet.
What are the dimensions of the existing patio?
Answers
Therefore , the correct option is A Dimension of exisiting patio is 6feet by 8feet.
Ms. Khan wants to add x feet onto each side of an existing patio, then the area of the existing patio is (x-2)² square feet.
Define square feet?
In the United States, Canada, China, and the United Kingdom, the square foot is a commonly used imperial measure of area. Its emblem is a straightforward square with a vertical line cutting it in half .
The Imperial system uses a combination of feet, inches, miles, and gallons.
So,
we can write (x-2)² = x²+14x+48.
Expanding the left side gives us x²-4x+4 = x²+14x+48.
Simplifying gives us 18x = 44.
Therefore, x = 11/4.
The dimensions of the square patio are (11/4 - 2)×2 feet by (11/4 - 2)×2 feet which is equal to( 3/4)×2 feet by 6/8
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a coin is tossed twice.what is the probability of tossing heads and then tails, given that the coin already shows heads in the first toss?
Answers
The probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2.
Let's first find the sample space of this experiment, which is {HH, HT, TH, TT}. We know that the coin has already shown heads in the first toss, so we can eliminate TT from the sample space. Therefore, the new sample space becomes {HH, HT, TH}.
Out of these three possible outcomes, only one satisfies the given condition of tossing heads and then tails, which is HT. Therefore, the probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2 (i.e., one favorable outcome out of two possible outcomes).
Therefore, the probability of tossing heads and then tails, given that the coin already shows heads in the first toss, is 1/2, as there is only one favorable outcome out of the two possible outcomes in the new sample space after eliminating TT.
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