Step-by-step explanation:
2.1 Factoring 3x2-2x-23
The first term is, 3x2 its coefficient is 3 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -23
Step-1 : Multiply the coefficient of the first term by the constant 3 • -23 = -69
Step-2 : Find two factors of -69 whose sum equals the coefficient of the middle term, which is -2 .
-69 + 1 = -68
-23 + 3 = -20
-3 + 23 = 20
-1 + 69 = 68
A company can make a hollow rubber ball for $0.02 per square foot. each ball costs the company $1. what is the diameter of a ball to the nearest tenth of a foot?
Answer:
4.0 feet
Step-by-step explanation:
You want the diameter of a rubber ball that costs $1, if that cost is $0.02 per square foot.
AreaThe surface area of a sphere is given by ...
A = 4πr²
In terms of diameter, this is ...
A = 4π(d/2)² = πd²
CostThe cost will be ...
Cost = (cost/square foot)(area)
1.00 = 0.02(πd²)
DiameterSolving for d, we have ...
d² = 1.00/(0.02π) ≈ 15.915
d ≈ √15.915 ≈ 3.989 ≈ 4.0 . . . . feet
The diameter of the ball is about 4.0 feet.
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marbles a bag contains two red marbles, four green ones, one lavender one, four yellows, and four orange marbles. how many sets of four marbles include one of each color other than lavender?
The number of sets is 128 by using the multiplication principle.
The multiplication principle states that if there are k events, and if the first event can happen in n_1 ways, the second event can happen in n_2 ways, and so on, then the k events can happen in n_1 × n_2 × ... × n_k ways.
To find the number of sets of four marbles include one of each color other than lavender, A bag contains two red marbles, four green ones, one lavender one, four yellows, and four orange marbles.
There are two red marbles.
There are four green ones.
There are four yellows.
There are four orange marbles.
So, total of 2 + 4 + 1 + 4 + 4 = 15 marbles in the bag.
To find the total number of sets of four marbles including one of each color other than lavender, use the multiplication principle.
In this question, there are 5 events (choosing one of each color).
The first event can happen in 2 ways.
The second event can happen in 4 ways.
The third event can happen in 4 ways.
The fourth event can happen in 4 ways.
Therefore, by the multiplication principle, the total number of sets of four marbles includes one of each color other than lavender
= 2 × 4 × 4 × 4 ⇒ 128 sets.
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7 Maryam is trying to expand and simplify (n - 2)²
Here is her working.
A
(n-2)² = (n − 2)(n-2)
= n²-2n - 2n-4
= n²-4n-4
Maryam's answer is wrong.
(a) Find Maryam's mistake.
I should be
Answer[tex]n^{2} -4n+4[/tex]
Step-by-step explanation:
had to keep the minus than add a plus sign
(09.02 MC)
A quadrilateral PQRS is inscribed in a circle, as shown below:
A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 85 degrees.
What is the measure of arc PQR? (1 point)
Accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.
What is quadrilateral ?A quadrilateral is a fοur-sided pοlygοn, which is a twο-dimensiοnal geοmetric figure with straight sides. Quadrilaterals can have a variety οf shapes, sizes, and angles, but they all have fοur sides and fοur vertices (cοrners).
Since the quadrilateral PQRS is inscribed in a circle, we knοw that angle PQR is an inscribed angle οf arc PR. By the Inscribed Angle Theοrem, the measure οf an inscribed angle is equal tο half the measure οf its intercepted arc. Therefοre, the measure οf arc PQR is twice the measure οf angle PQR, which is:
2 * 85 = 170 degrees.
Therefοre, accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.
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The sum of two numbers is 67 and the difference is 13. What are the numbers?
Answer:
40 and 27
Step-by-step explanation:
Answer:Let's call the two numbers x and y.
From the problem, we know that:
x + y = 67 (equation 1)
and
x - y = 13 (equation 2)
To solve for x and y, we can use the method of elimination. We can add equations 1 and 2 to eliminate y:
(x + y) + (x - y) = 67 + 13
Simplifying this equation, we get:
2x = 80
Dividing both sides by 2, we get:
x = 40
Now we can use equation 1 to solve for y:
x + y = 67
40 + y = 67
Subtracting 40 from both sides, we get:
y = 27
Therefore, the two numbers are 40 and 27.
Step-by-step explanation:
Write a formula you can use to find the sum of the measurements of a interior angels of a polygon.Use it to find the sum of the measures of the interior angel of a polygon with 11 sides.
The sum of the measures of the interior angles of an 11-sided polygon is 1620 degrees.
The formula to find the sum of the measures of the interior angles of a polygon is:
Sum of interior angles = (n - 2) × 180 degrees
Where n: number of sides of the polygon.
Using this formula, we can find the sum of the measures of the interior angles of a polygon with 11 sides:
Sum of interior angles = (11 - 2) × 180 degrees
Sum of interior angles = 9 × 180 degrees
Sum of interior angles = 1620 degrees
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PLEASE SHOW WORK!!!!!!!!!
Based on the information provided, the probability of both events happening is 0.011 or 1.1% (option A).
How to calculate the probability in this case?The probability can be described as the proportion between the desired outcome happening and the total of possible outcomes. Using this principle, let's calculate the probability:
Probability of Gypsy finishing first: 1 / 10 = 0.1
Probability of Silver Rush finishing second: 1/ 9 = 0.11
Total probability 0.1 x 0.11 = 0.011 or 1.1% (0.011 x 100)
Therefore, the answer that matches the probability is option A.
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What is the vertex of the graph?
The calculated vertex of the graph represented in the figure is (-3, -3)
What is the vertex of the graph?Given that we have the graph
The curve on the graph is a quadratic function
As a general rule, the vertex of a graph is the minimum or the maximum point on a graph
From the graph, we have the minimum point to be
Minimum = (-3, -3)
This means that
Vertex = (-3, -3)
Hence, the vertex is (-3, -3)
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The diameter of a circle is 24 cm. Find its area to the nearest whole number.
The area of the circle given a diameter of 24 inches is 452 square centimeters
Calculatng the area of a circle.To calculate the area of a circle with a diameter of 24cm, we first need to find the radius.
The radius is half the diameter, so it would be 12cm.
Once we have the radius, we can use the formula for the area of a circle, which is A = πr².
Substituting the value of the radius into the formula gives us:
A = π(12)² = 144π
Evaluate
A = 452cm²
Hence, the area of the circle is 144π square centimeters or 452cm²
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Frank has $50 dollars to buy party supplies. He wants to buy chips and dip. He has already bought seven bags of chips that costs him $32. The dip he wants to buy has a unit cost of $2.25 per container. Write and solve an equation, or inequality, to determine the number of containers of dip Frank can buy.
Help-
Answer: 32+2.25(8)=50
Step-by-step explanation:
If you have $50 and waste $32 that leaves you with $18.
If each dip cost 2.25 you can have a total of 8 dips.
32+2.25(x)=50
32+2.25(8)=50
Can someone find the median
Answer: 17.5
Step-by-step explanation:
First find the two numbers (data values) that are in the middle. Thats 15 and 20. When you have two numbers in the middle of a data set you average them. (Buy adding 15 and 20 then dividing by 2) So the answer is 17.5
y=x^(2) Transformation: Reflects across x-axis Horizontal shift 5 units to the right Vertical shift up 4 units Vertical shrink by (1)/(2) Domain: 3,9
The domain of the function is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.
Domain of function explained.
To transform the function y=x^2 according to the given specifications, we can use the following steps:
Reflecting across the x-axis: This transformation reflects the function across the x-axis, which means that every y-coordinate is multiplied by -1. Therefore, the function becomes y = -x^2.Horizontal shift 5 units to the right: This transformation moves the entire function horizontally to the right by 5 units. To achieve this, we subtract 5 from the x-coordinate. Therefore, the function becomes y = -(x-5)^2.Vertical shift up 4 units: This transformation moves the entire function vertically up by 4 units. To achieve this, we add 4 to the y-coordinate. Therefore, the function becomes y = -(x-5)^2 + 4.Vertical shrink by (1/2): This transformation shrinks the function vertically by a factor of 1/2, which means that every y-coordinate is multiplied by 1/2. Therefore, the function becomes y = -1/2(x-5)^2 + 4.Domain: Finally, the domain of the transformed function is given as [3, 9], which means that the function is only defined for x-values between 3 and 9. Therefore, we need to restrict the domain of the function to this interval. Therefore, the final transformed function is:
Therefore the transformation is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.
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Help please and thank you
The reasons for the statements supporting the proof that ∡TV ≅ ∡ XW are given as follows;
A - Given
H - Vertical Angles
F- Angles that inscribe a half circle are congruent and 90°
C - Angle-Angle-Side Triangle Congruence
E - CPCTC
D - Reflexive Property
I - Hypotenuse Leg (H-L) Triangle Congruence
G - CPCTC
B - Arcs of a congruent angles are congruent
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". It is a theorem used in geometry to prove that two triangles are congruent.
An inscribed angle is half the measure of its intercepted arc. A half circle is a semicircle, which has an intercepted arc of 180°, so the inscribed angles are 1/2(180°) = 90° and congruent.
The reflexive property is a property of equality that states that any quantity is equal to itself. In other words, a = a. This property is used in many mathematical proofs.
The Hypotenuse-Leg (H-L) Triangle Congruence is a rule used to prove that two right triangles are congruent. If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and the corresponding leg of another triangle, then the two triangles are congruent.
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What 3-dimensional shape is formed by this net? PLS HELP
Answer:
A triangular prism.
Step-by-step explanation:
Answer: Triangular prism
Step-by-step explanation:
A triangular prism is a three dimensional shape, consisting of two triangular and three rectangular faces. Based on the image provided, and the description of a triangular prism, we can deduct this three dimensional shape is a triangular prism.
Make sure you explain why and show all your work.
In Triangle LMO, T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. Also, LT = 9, JM = 12, and OL = 32.
What is the perimeter of the Triangle TJP?
Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if
any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks,
below.
f(-2)=? f(2)=?
By using the graph, the key features of the function include the following:
The function's domain = {-∞, ∞}.The function's range = {-1, ∞}.The x-intercepts = (0, 0)The y-intercept = (0, 0)f(-2) = 3.f(2) = -1.How to determine the domain and range?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or {x|x ∈ R}.
Range = {-1, ∞}.
Based on the graph, the x-intercept and y-intercept of the function both occur at the origin (0, 0).
When x = -2, the y-value is given by:
f(-2) = 3.
When x = 2, the y-value is given by:
f(2) = -1.
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Which expression must be added to 3x - 7 to equal 0?
Answer:
To find out which expression must be added to 3x - 7 to equal 0, we need to solve the equation:
3x - 7 + a = 0
where "a" is the expression to be added.
To solve for "a", we can isolate "a" on one side of the equation by adding 7 to both sides:
3x - 7 + a + 7 = 0 + 7
Simplifying the left side, we get:
3x + a = 7
Therefore, the expression that must be added to 3x - 7 to equal 0 is:
a = -3x + 7
We can check that this is correct by substituting -3x + 7 for "a" in the original equation:
3x - 7 + (-3x + 7) = 0
Simplifying the left side, we get:
3x - 3x - 7 + 7 = 0
0 = 0
The equation is true, which confirms that the expression -3x + 7 must be added to 3x - 7 to equal 0.
Step-by-step explanation:
an electrician needs 2/5 rolls of electrical wire in each room in a house. How many rooms can he wire with 2 rolls of wire?
Answer:
The number of rooms he can wire with 3/4 of a roll of wire is 1/4.
What are proportions?
Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, an electrician needs 3 rolls of electrical wire to wire each room in a house.
Let the number of rooms he can wire with 3/4 of a roll of wire be x.
Now, the proportion is
3/1 = 3/4/x
3x=3/4
x=1/4
I don’t completely understand the question or how to work it out
Answer:
Step-by-step explanation:
[tex]\frac{3x+9}{12x} \\we \ can \ write \ 3x+9 \ as 3(x+3)\\\frac{3x+9}{12x}=\frac{3(x+3)}{3*4x}=\frac{x+3}{4x}[/tex]
Answer:
[tex]\frac{x+3}{4x}[/tex]
Step-by-step explanation:
[tex]\frac{3(x)+9}{12x}[/tex]
[tex]\frac{3(x+3)}{12x}[/tex]
What is 1/4+1/8 estimated answer
Answer:
3/8
Step-by-step explanation:
1/4+1/8
2/8+1/8
=
3/8
3/8
1+2 to equal 3, which is all the numerators above the least common denimonater 8
A $9. 00 album is marked up 6 1/4% and then is offer for 14% off. If the sales tax is 5% what is the total amount if tax that must be paid for this album
A $9. 00 album is marked up 6 1/4% and then is offered for 14% off. If the sales tax is 5%. The total amount of tax that must be paid for this album is $0.41.
Let's break this problem down into steps:
Find the markup price of the album after it is marked up by 6 1/4%.Markup price = $9.00 + 6.25% of $9.00
Markup price = $9.00 + $0.56
Markup price = $9.56
Find the sale price of the album after it is discounted by 14%.Sale price = Markup price - 14% of Markup price
Sale price = $9.56 - 14% of $9.56
Sale price = $9.56 - $1.34
Sale price = $8.22
Add the sales tax of 5% to the sale price.Tax amount = 5% of the Sale price
Tax amount = 5% of $8.22
Tax amount = $0.41
Therefore, the total amount of tax that must be paid for this album is $0.41.
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in 30 seconds, 180 cm^3 of oxygen diffuse through a porous plate. How long will it take 300cm3 of chlorine to diffuse through the same pot
Answer:
50s
Step-by-step explanation:
180cm³= 30s
300cm³=x s
Thus,
180x= 30×300
180x = 9000
x= 50s.
Hope this helps! :)
Select all ordered pairs that correspond to input-output pairs of the function y = -7x + 3,
A
(4,0)
B.
(
639)
DO
C (
853)
D. (5,32)
Select all order pairs to that correspond to input-output pairs of the function y=-7x+3
The ordered pairs that correspond to input-output pairs of the function y=-7x+3 are (5,32).
The input-output pairs of the function y=-7x+3 can be determined by plugging in the input value x into the function and solving for y. The formula y=-7x+3 can be used to calculate the output value corresponding to a given input value x. For example, if x=4, then y=-7(4)+3=-28+3=5, so the input-output pair is (4,5). Similarly, if x=5, then y=-7(5)+3=-35+3=32, so the input-output pair is (5,-32). The ordered pairs that correspond to input-output pairs of the function y=-7x+3 and (5,32).
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Which research scenario would most likely be biased against non-voters? Select all that apply.
1. a convenience sample collected at a political rally used to determine candidate preferences
2. a volunteer sample collected at a political rally used to determine candidate preferences
3. a simple random sample of all non-voters used to determine why they don’t vote
4. a simple random sample of all eligible voters, some of whom didn’t have time to vote
5. a volunteer sample collected at large department store to determine who they voted for
Research scenariο wοuld mοst likely be biased against nοn-vοters are :
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr.What is Bias?Bias in research refers tο a systematic deviatiοn frοm the truth in the results οf a study, usually due tο factοrs that affect the sampling, measurement, οr analysis οf data. A research scenariο is biased against nοn-vοters if it systematically under-represents οr misrepresents the views, οpiniοns, οr behaviοrs οf peοple whο dοn't vοte in the sample οr pοpulatiοn under study.
In the given οptiοns, the scenariοs that are biased against nοn-vοters are:
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences: A cοnvenience sample is a nοn-randοm sample that is cοmpοsed οf individuals whο are easily accessible οr available. A cοnvenience sample cοllected at a pοlitical rally is biased against nοn-vοters because it is likely tο οver-represent peοple whο are pοlitically active, mοtivated, and engaged, and under-represent peοple whο are apathetic, disengaged, οr unable tο attend the rally, including nοn-vοters.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences: A vοlunteer sample is a nοn-randοm sample that is cοmpοsed οf individuals whο self-select οr vοlunteer tο participate in the study. A vοlunteer sample cοllected at a pοlitical rally is biased against nοn-vοters because it is likely tο οver-represent peοple whο are pοlitically active, mοtivated, and engaged, and under-represent peοple whο are apathetic, disengaged, οr unable tο attend the rally, including nοn-vοters.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr: This scenariο is biased against nοn-vοters fοr similar reasοns as the previοus twο scenariοs. A vοlunteer sample cοllected at a large department stοre is likely tο οver-represent peοple whο are willing tο participate in surveys, and under-represent peοple whο are nοt interested, busy, οr unable tο participate, including nοn-vοters.Therefοre, research scenariο wοuld mοst likely be biased against nοn-vοters are :
a cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences.a vοlunteer sample cοllected at large department stοre tο determine whο they vοted fοr.To know more about bias visit :
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PLEASE HELPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer and Explanation:
1. corresponding: bottom right graph
→ the angles are in the same place in relation to the parallel lines
2. alternate interior: bottom left graph
→ the interior angles are on opposite sides of the transversal
3. alternate exterior: top left graph
→ the exterior angles are on opposite sides of the transversal
4. none of these: top middle graph
→ there are no parallel lines
Suppose X is an exponential random variable with mean μ , i.e.,
X∼μExpo(1). Invert appropriate UMP tests of H0 :μ=μ0 to find (a) a 90% confidence interval for μ of the form [∗,[infinity]); (b) a 90% confidence interval for μ of the form [0,∗]
The answer of the given question based on the exponential random variable with mean i.e. [tex]\mu o \leq \bar x + \frac{z \alpha \sigma}{\sqrt{n} }[/tex].
What is Null hypothesis?The null hypothesis is statement or assumption about population parameter that is tested for its validity using statistical methods. It is statement of no effect, no difference, or no relationship between the variables of interest,
(a) To test the null hypothesis [tex]H$ o: \mu =\mu o[/tex], we can use a one-sided test with rejection region R = [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex], is the critical value from the Standard Normal distribution that corresponds to a significance level of α = 0.10 (since we want a 90% confidence interval). If the observed sample mean falls in the rejection region R, we reject the null hypothesis and conclude that the true mean μ is greater than μ0 with 90% confidence.
To find the confidence interval of the form [∗,[infinity]), we can solve the inequality [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex] for [tex]\mu[/tex] which gives:
[tex]\mu o \leq \bar x - \frac{z \alpha \sigma}{\sqrt{n} }[/tex]
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there is a mound of g pounds of gravel in a quarry. throughout the day, 300 pounds of gravel is added to the mound. two orders of 600 pounds are sold and the gravel is removed from the mound. at the end of the day, the mound has 1400 pounds of gravel.
solve for g.
Answer:
2000 pounds
Step-by-step explanation:
Let's start with the initial amount of gravel in the mound, which is g pounds.
After 300 pounds are added, the total amount of gravel in the mound becomes:
g + 300
Then, two orders of 600 pounds are sold and removed from the mound. So, the total amount of gravel in the mound after these two orders are sold becomes:
g + 300 - 2(600) = g + 300 - 1200 = g - 900
Finally, we know that at the end of the day, the mound has 1400 pounds of gravel. So, we can set up an equation:
g - 900 + 300 = 1400
Simplifying this equation, we get:
g - 600 = 1400
Adding 600 to both sides, we get:
g = 2000
Therefore, the initial amount of gravel in the mound was 2000 pounds.
Answer:
2000 pounds
Step-by-step explanation:
sorry it took a while;)
Joey has a storage cabinet in the shape of a rectangular prism with a base length of 3 feet, a base width of 2 feet, and a height of 8 feet.
A. Joey is going to paint the lateral area and the top of the storage cabinet, but he will not paint the bottom on which it sits. What is the surface area of the storage cabinet that Joey is going to paint?
B. What is the total surface area of the cabinet, which includes the bottom?
C. Find the volume of the cabinet to determine the amount of space Joey will have to use if he wants to fill the cabinet with supplies?
Answer: 592
Step-by-step explanation:
A=2(wl+hl+hw)
A=2(8*10+12*10+12*8)=592
[tex]\sqrt { (340)^2^/^3 *\frac{1}{{(0.09)^1^/^2}}* \sqrt{81{(0.09)^1^/^2}[/tex]
use your knowledge of the decision-making process to choose the correct location for each of the three missing labels in the following diagram.
The correct locations for the three missing labels in the diagram are "Analyze the Situation" in the top-left corner, "Identify Options" in the bottom-left corner, and "Make a Decision" in the bottom-right corner. We need to apply the decision-making process to the three missing labels in the diagram.
The first missing label is for the top-left corner of the diagram. The correct location for this label is "Analyze the Situation." This is because the decision-making process begins with an analysis of the situation to understand the problem and identify any potential constraints.
The second missing label is for the bottom-left corner of the diagram. The correct location for this label is "Identify Options." This is because the decision-making process involves identifying all of the available options for solving the problem.
The third missing label is for the bottom-right corner of the diagram. The correct location for this label is "Make a Decision."
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