Answers
The labelled parts of the circle include:
Center - CRadius - C, EDiameter - B, EChord - E, DSecant - A, BTangent - A, ECentral Angle - ∠CDBInscribed Angle - ∠BEFMinor Arc - BDMajor Arc - BEDWhat is a secant and an inscribed angle of a circle?A secant of a circle is a line that intersects the circle in two distinct points. In other words, a secant is a line that cuts through a circle. The length of a secant segment between the two points of intersection with the circle is called the length of the secant.
An inscribed angle is the angle formed in the interior of a circle by the intersection of two chords on the circle.
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Image transcribed:
CIRCLES ESCAPE Challenge
Directions A circle is given to the left. Parts of this circle are partially named below. Complete the names by dragging and placing the letters over the empty spaces. Though there could be more than one answer, each letter tile can only be used once
Center
Radius
Diameter
Chord
Secant
Tangent
Central Angle
Inscribed Angle
Minor Arc
Major Arc
Related Questions
C(x)
Recall that if the cost of producing x units is C(x), then the average cost function is C(x) = - -. An artist who
X
makes handmade earrings has fixed costs of $400 for a table at an art fair. The marginal cost (the cost of
producing one additional pair of earrings) is $7 per pair.
(a) Find the linear cost function C(x).
(b) Find the average cost function C(x).
(c) Find C(5) and interpret your answer.
(d) Find C(50) and interpret your answer.
(e) Find the horizontal asymptote of C(x), and explain what it means in practical terms.
Answers
(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).
What is the linear function?A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
According to the given information:(a) The linear cost function C(x) can be calculated by summing the fixed costs and the variable costs. In this case, the fixed cost is $400 for the table at the art fair, and the variable cost is $7 per pair of earrings. Therefore, the linear cost function C(x) can be expressed as:
C(x) = 400 + 7x
where x represents the number of pairs of earrings produced.
(b) The average cost function C(x) is calculated by dividing the total cost (C(x)) by the number of units produced (x). So, the average cost function C(x) can be expressed as:
C(x) = (400 + 7x)/x
(c) To find C(5), we substitute x = 5 into the average cost function C(x):
C(5) = (400 + 7(5))/5 = 435/5 = $87
This means that when 5 pairs of earrings are produced, the average cost per pair of earrings is $87.
(d) To find C(50), we substitute x = 50 into the average cost function C(x):
C(50) = (400 + 7(50))/50 = 850/50 = $17
This means that when 50 pairs of earrings are produced, the average cost per pair of earrings is $17.
(e) The horizontal asymptote of C(x) is determined by the behavior of the average cost function as x approaches infinity. In this case, since the average cost function is given by C(x) = (400 + 7x)/x, the horizontal asymptote is y = 7. This means that as the number of pairs of earrings produced (x) increases indefinitely, the average cost per pair of earrings approaches $7. In practical terms, this indicates that the artist's cost of producing one additional pair of earrings (marginal cost) remains constant at $7 as production levels increase, which could suggest economies of scale, where the artist may be able to produce earrings at a lower cost per pair as production volume increases. However, this may also depend on other factors such as demand, pricing strategy, and efficiency of production processes.
So, the horizontal asymptote at y = 7 indicates the long-term cost trend for the artist's earrings production. Overall, the artist should carefully consider the production volume and associated costs to optimize their profit margins. It's also worth noting that this analysis assumes that the cost function remains linear and does not account for potential nonlinearities in the artist's cost structure. Real-world cost functions may be more complex and require further analysis. Additionally, the artist should also consider other factors such as market demand, pricing, and competition when making production decisions. Consulting with a financial or business advisor may also be beneficial for making informed decisions. Always remember to consider the specific context and assumptions when interpreting mathematical models in real-world situations. It's important to thoroughly analyze all relevant factors before making any business decisions. Safety Disclaimer: Remember to always consult with a qualified professional for financial and business advice. This response is for informational purposes only and should not be taken as financial or business advice. The accuracy and applicability of this information to your specific situation should be verified by a qualified professional.
Therefore,(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).
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Write the recursive formula for the following. Do not include spaces in your answer. 100, 95, 90, 85...
Answers
Answer:
The recursive formula for the sequence 100, 95, 90, 85 is: a(n) = a(n-1) - 5 where a(1) = 100.
Suppose 239 subjects are treated with a drug that is used to treat pain in 52 of them develop nausea. Use a 0.05 significance level to test the claim that more than 20% of users to develop nausea.
Answers
There is not enough Evidence to support the claim that more than 20% of users of the pain medication will develop nausea.
To test the claim that more than 20% of users of a pain medication will develop nausea, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) would be that the proportion of users who develop nausea is less than or equal to 0.20, while the alternative hypothesis (Ha) would be that the proportion is greater than 0.20.
To conduct the test, we can use the binomial distribution since we are looking at the number of successes (subjects who develop nausea) out of a fixed number of trials (total number of subjects). We can calculate the expected number of successes under the null hypothesis by multiplying the total number of subjects (239) by the assumed proportion (0.20). This gives an expected number of 47.8 subjects who would develop nausea.
We can then use a one-sample z-test to compare the observed proportion of subjects who developed nausea (52/239 = 0.218) to the expected proportion under the null hypothesis (0.20). The test statistic is calculated as (0.218 - 0.20) / sqrt(0.20 * 0.80 / 239), which is approximately 1.08.
With a significance level of 0.05 and one-sided test, the critical value for the z-statistic is 1.645. Since the calculated test statistic (1.08) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that more than 20% of users of the pain medication will develop nausea.
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A cell phone plan costs $23.70 per month for 500 minutes of talk time. It costs an additional $0.07 per minute for each minute over 500 minutes.
To get e-mail access, it costs 10% of the price for 500 minutes of talk time.
Your bill, which includes e-mail, is the same each month for 8 months. The total cost for all 8 months is $253.92. Write and solve an equation to find the number of minutes of talk time you use each month
Answers
Therefore, the number of minutes of talk time used each month is 581.
What is minute?In terms of time measurement, a minute is a unit of time equal to 60 seconds. It is one-sixtieth of an hour and one-third of an hour. The word "minute" comes from the Latin word "minutes," meaning "small" or "minute."
Minutes are commonly used in everyday life to measure short durations of time, such as the length of a phone call or the time it takes to boil an egg. They are also used in scientific fields to measure very small-time intervals, such as in nuclear physics or astronomy. Additionally, minutes are often used in meetings and official proceedings to record the details of what was discussed and decided.
Let's first calculate the cost of 500 minutes of talk time, which is $23.70.
To get email access, it costs 10% of the price for 500 minutes of talk time, which is 0.1 x $23.70 = $2.37.
So the total cost per month is $23.70 + $2.37 = $26.07 for 500 minutes of talk time and email access.
For each additional minute over 500, it costs $0.07. Let's say you use x minutes of talk time per month, where x is greater than 500.
Then the cost for talk time would be[tex]$23.70 + ($0.07)(x - 500).[/tex]
The total cost per month, including email access, would be [tex]$2.37 + $23.70 + ($0.07)(x - 500) = $26.07 + ($0.07)(x - 500).[/tex]
Since the bill is the same each month for 8 months, the total cost for 8 months is[tex]$26.07(8) + ($0.07)(x - 500)(8) = $208.56 + ($0.07)(x - 500)(8) = $253.92.[/tex]
Simplifying, we get:
[tex]($0.07)(x - 500)(8) = $253.92 - $208.56[/tex]
[tex]($0.07)(x - 500)(8) = $45.36[/tex]
Dividing both sides by 0.56:
[tex](x - 500)(8) = 648[/tex]
[tex]x - 500 = 81[/tex]
[tex]x = 581[/tex]
Therefore, the number of minutes of talk time used each month is 581.
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Give the name (monomial, binomial,
trinomial, etc.) and the degree of the
polynomial.
10x9 18x8 + 12x6
Name? Trinomial
Degree? [?]
Answers
The degree of the polynomial is 9.
What is polynomial in maths?
In mathematics, a polynomial is an expression composed of variables (also called indeterminates) and coefficients, and involves only addition, subtraction, multiplication, and non-negative integer powers of the variables. An example of a single indefinite x-polynomial is x2 − 4x + 7.
Polynomials can be classified by the number of terms with nonzero coefficients, so a 1st polynomial is called a monomial and a 2nd polynomial is called a monomial. Binomials, tripartite polynomials are called trinomials. The term "quaternomial" is sometimes used for a fourth-order polynomial.
Determine the degree of y = 10x⁹ - 18x⁸ + 12x⁶
Degree = 9
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Your favorite team is in the soccer World Cup. You have assigned a probability of 63% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 67% of the time. When they lose the championship, they win the first game 27% of the time. The first game is over and your team has lost. What is the probability that they will win the World Cup?
Probability =
Answers
The probability that they will win the World Cup is 17.01%. This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.
What is probability?It is used to estimate the chance of winning, the chance of drawing a particular card, or the chance of rolling a particular number. It is a measure of the potential for a certain outcome to happen.
P(win WC| lost 1st game) = P (win WC ∩ lost 1st game) / P (lost 1st game)
P (win WC ∩ lost 1st game) = P (win WC) * P (lost 1st game| win WC)
= 0.63 * 0.27
= 0.1701
P (lost 1st game) = P (lost 1st game| win WC) + P (lost 1st game| lose WC)
= 0.27 + 0.73
= 1
Therefore, the probability that your team will win the World Cup is
0.1701 / 1 = 17.01%.
This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.
This is because the team that wins the championship usually wins the first game of the series 67% of the time, so if your team did not win the first game, their chances of winning the championship decreased. Therefore, the probability that they will win the World Cup is 17.01%.
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16. Given that is a standard normal random variable, find z for each situation.
a.
The area to the right of z is .01.
b. The area to the right of z is .025.
C. The area to the right of z is .05.
d. The area to the right of z is .10.
Answers
Answer:
It is A. dont ask i did that on paper
A faucet leaks 9 oz of water per minute. a) How many gallons of water are wasted in a year? (A gallon contains 128 oz.) b) If water costs $10.31 per 1000 gal, how much additional money is being spent on the water bill?
Answers
The amount of water wasted in a year is 36,960 gallons and the additional cost on the water bill due to the leaky faucet is $381.31.
(a). We know that the faucet leaks 9 oz of water per minute. There are 60 minutes in an hour and 24 hours in a day, so the total number of minutes in a day is
60 x 24 = 1440
The number of ounces of water wasted in a day is
1440 x 9 = 12,960.
To find out how many ounces of water is wasted in a year, we multiply the number of ounces wasted in a day by the number of days in a year is
12,960 x 365 = 4,734,240 oz.
To convert the number of ounces wasted in a year to gallons, we divide by the number of ounces in a gallon is
4,734,240 ÷ 128 = 36,960
(b). Water costs $10.31 per 1000 gal, so to find the cost per gallon
$10.31 ÷ 1000 = $0.01031 per gallon.
To calculate the additional cost on the water bill, we multiply the number of gallons wasted in a year by the cost per gallon is
36,960 x $0.01031 = $381.31.
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Directions: Solve by finding the difference of two squares.
1. x2 - y2 =
2. x2 - 16
3. a2 - b2
4. a2 - 25
5. x2 - 121
6. 225 - a2
7. 400 - y2
8. 900 - z2
9. 4x2 - 49
10. 16x2 - 25
11. 36x2 - 64
12. 64 - a2
13. 36x2 - 64
14. 25a2 - 16
15. 9a2 - 81
16. 49a2 - 4
17. 100x2 - 9
18. 64x2 - 25
19. 144x2 - 100
20. 25x2 - 25y2
Answers
the difference of two squares, you will use the formula. answers are (x + y)(x - y), (x + 4)(x - 4), (a + 5)(a - 5), (x + 11)(x - 11), (15 + a)(15 - a), (20 + y)(20 - y), (30 + z)(30 - z), (2x + 7)(2x - 7), (4x + 5)(4x - 5), 8(3x + 4)(3x - 4), (8 + a)(8 - a),8(3x + 4)(3x - 4), (5a + 4)(5a - 4), 9(a + 9)(a - 9), (7a + 2)(7a - 2), (10x + 3)(10x - 3), (8x + 5)(8x - 5),4(6x + 5)(6x - 5), 25(x + y)(x - y)
what is formula ?
A formula is a mathematical equation or expression that is used to solve a specific problem or perform a specific calculation. Formulas are often used in mathematics, physics, chemistry, engineering, and other fields to express a relationship between different variables or quantities.
In the given question,
Sure! To solve by finding the difference of two squares, you will use the formula:
a² - b² = (a + b)(a - b)
Using this formula, we can simplify the expressions given:
x² - y² = (x + y)(x - y)
=> (x + y)(x - y) =0
=> (x + y)=0 , (x - y)=0
=> x = -y ,x = y
x² - 16 = (x + 4)(x - 4)
=> (x + 4)(x - 4) =0
=> (x + 4)=0 , (x - 4)=0
=> x = -4 ,x = 4
a² - b² = (a + b)(a - b)
a² - 25 = (a + 5)(a - 5)
x² - 121 = (x + 11)(x - 11)
225 - a² = (15 + a)(15 - a)
400 - y² = (20 + y)(20 - y)
900 - z² = (30 + z)(30 - z)
4x² - 49 = (2x + 7)(2x - 7)
16x² - 25 = (4x + 5)(4x - 5)
36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)
64 - a² = (8 + a)(8 - a)
36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)
25a² - 16 = (5a + 4)(5a - 4)
9a² - 81 = 9(a + 9)(a - 9)
49a² - 4 = (7a + 2)(7a - 2)
100x² - 9 = (10x + 3)(10x - 3)
64x² - 25 = (8x + 5)(8x - 5)
144x² - 100 = 4(6x + 5)(6x - 5)
25x² - 25y² = 25(x + y)(x - y)
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Answer:
1. x^2 - y^2 = (x+y)(x-y)
2. x^2 - 16 = (x+4)(x-4)
3. a^2 - b^2 = (a+b)(a-b)
4. a^2 - 25 = (a+5)(a-5)
5. x^2 - 121 = (x+11)(x-11)
6. 225 - a^2 = (15+a)(15-a)
7. 400 - y^2 = (20+y)(20-y)
8. 900 - z^2 = (30+z)(30-z)
9. 4x^2 - 49 = (2x+7)(2x-7)
10. 16x^2 - 25 = (4x+5)(4x-5)
11. 36x^2 - 64 = 4(3x+4)(3x-4) or (6x+8)(6x-8)
12. 64 - a^2 = (8+a)(8-a)
13. 36x^2 - 64 = (6x+8)(6x-8) or 4(3x+4)(3x-4)
14. 25a^2 - 16 = (5a+4)(5a-4)
15. 9a^2 - 81 = 9(a+3)(a-3)
16. 49a^2 - 4 = (7a+2)(7a-2)
17. 100x^2 - 9 = (10x+3)(10x-3)
18. 64x^2 - 25 = (8x+5)(8x-5)
19. 144x^2 - 100 = 4(6x+5)(6x-5) or (12x+5)(12x-5)
20. 25x^2 - 25y^2 = 25(x+y)(x-y)
Step-by-step explanation:
:)
Find the measure of the indicated angle to the nearest degree
Answers
The measure of angle ABD is 45 degrees.
What is angle?
An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The two rays are also referred to as the sides of the angle.
Angles are measured in degrees, with a full circle being 360 degrees. Angles can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), and reflex (greater than 180 degrees and less than 360 degrees).
In the given diagram, we can see that angle ABD and angle BDC are complementary angles, which means they add up to 90 degrees.
We are asked to find the measure of angle ABD. To do this, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of angle BCD as follows:
angle BCD = 180 - angle BDC - angle CBD
Since angle BDC and angle CBD are both 45 degrees, we have:
angle BCD = 180 - 45 - 45 = 90 degrees
Now, since angle ABD and angle BCD are both complementary to angle BDC, we have:
angle ABD = angle BDC = 45 degrees
Therefore, the measure of angle ABD is 45 degrees.
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The volume, V, in hundreds of shares, of a company's stock, after being listed on the stock
exchange for t weeks, can be modelled by the relation V = 250t -5t² . Use the discriminant to
determine if the volume will ever reach
a) 275 000 shares in a week; V = 2750
b) 400 000 shares in a week
Answers
(a)the volume will reach 275000 shares in a week at two different times.
(b)the volume will reach 400,000 shares in a week at two different times.
(a) 275,000 shares in a week (V=2750), solve the equation:
what are discriminant?the part of the quadratic formula underneath the square root symbol.
[tex]250t - 5t^2 = 2750\\5t^2 - 250t + 2750 = 0[/tex]
by quadratic formula,
t = [250 ± ([tex]\sqrt{250^2 - 4(5)(2750))}[/tex]]/(2(5))
t = [250 ± [tex]\sqrt{187500}[/tex]]/10
t = [250 ± [tex]50\sqrt{3}[/tex]]/10
[tex]t = 25 ± 5\sqrt{3}[/tex]
Since both solutions are real, the volume will reach 275000 shares in a week at two different times.
(b) 400,000 shares in a week, solve the equation:
[tex]250t - 5t^2 = 4000\\5t^2 - 250t + 4000 = 0[/tex]
by discriminant formula, we have:
[tex]b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500[/tex]
the discriminant is positive but not equal to zero, the quadratic equation has two real roots. Therefore, the volume will reach 400,000 shares in a week at two different times.
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An image of a rhombus is shown.
a rhombus with a base of 20 centimeters and a height of 17.3 centimeters
What is the area of the rhombus?
692 cm2
346 cm2
173 cm2
47.3 cm2
Answers
Required area of the rhombus is 173 cm².
What is rhombus?
A rhombus is a parallelogram with four equal sides. It is also called a diamond or a lozenge. In a rhombus, opposite angles are equal, and the diagonals bisect each other at right angles. Since all sides of a rhombus are equal, its opposite sides are parallel, and its opposite angles are congruent. The area of a rhombus can be calculated by multiplying the length of one of its diagonals by the length of the other diagonal and dividing the result by 2.
Here given,the rhombus with a base of 20 centimeters and a height of 17.3 centimeters.
So, the area of the given rhombus is
[tex] \frac{1}{2} \times base \times \: height \\ = \frac{1}{2} \times 20 \times 17.3 \\ = 173[/tex]
So, Area = 173 cm²
Therefore, the area of the given rhombus is 173 cm².
Hence, the correct option is C.
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use the fundamental identities to find the value of trigonometric function
find sin theta if cos theta =2/3 and theta is in quad iv
Answers
Answer: Since cos(theta) = 2/3 and theta is in quadrant IV, we know that sin(theta) is negative. We can use the Pythagorean identity to find the value of sin(theta):
sin^2(theta) + cos^2(theta) = 1
Substituting cos(theta) = 2/3, we get:
sin^2(theta) + (2/3)^2 = 1
Simplifying, we get:
sin^2(theta) = 1 - (2/3)^2 = 1 - 4/9 = 5/9
Since sin(theta) is negative in quadrant IV, we have:
sin(theta) = -sqrt(5/9) = -sqrt(5)/3
Therefore, sin(theta) = -sqrt(5)/3.
Step-by-step explanation:
1. Give the rule of translating a point 4 units left and 8 units up.
2. After the translation, where is A located?
now reflect the figure over the y-axis. Answer the qyestuibs to fibd the coordinates of A after the reflection. 3. Give the rule for reflecting a point over the y-axis.
4. What are the cooredinates of A after the reflection?
5. Is the final figure congruent to the original figure? How do you know?
Answers
The final figure is congruent to the original figure because a reflection over the y-axis is an isometric transformation.
What is translation?A translation is a rigid transformation that moves an object without rotating or reflecting it.
What is reflection?In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.
Equation:1) Given the original coordinates of A, B, and C:
A(7, 5), B(2, 9), C(1, 3)
To translate the triangle 4 units to the left and 8 units up, we add -4 to the x-coordinates and +8 to the y-coordinates:
New coordinates for A:
x-coordinate: 7 - 4 = 3
y-coordinate: 5 + 8 = 13
Therefore, A after translation is A(3, 13).
2) To reflect A over the y-axis, we use the rule for reflecting a point over the y-axis, which is to keep the y-coordinate unchanged and change the sign of the x-coordinate:
New coordinates for A after reflection:
x-coordinate: -3
y-coordinate: 13
Therefore, A after reflection is A(-3, 13).
3) The rule for reflecting a point (x,y) over the y-axis is:
(x, y) -> (-x, y)
This means that we take the original x-coordinate, change its sign, and keep the y-coordinate the same.
4) The coordinates for A after reflection are (-3, 13).
5) Yes, the final figure after translation and reflection is congruent to the original figure. This is because both translation and reflection are rigid transformations, which means they preserve distances and angles, and therefore, they preserve the shape and size of the original figure. Translation preserves the orientation of the figure, and reflection preserves the orientation and reverses the handedness. Therefore, the new figure is congruent to the original figure.
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will give brainliest and 50 points!!
Answers
Answer:
A) 77°
B) 77°
C) 103°
Step-by-step explanation:
A) Vertical angles are congruent
B) Alternate exterior angles are congruent.
C) Angles B and C are supplemental. They add to 180°
Helping in the name of Jesus.
PLEASE HELP Write a function f(l) that determines the number of triangles in any given level of the pyramid.
Answers
The function that determines the number of triangles in any given level of the pyramid is given as n = n ×(n + 1) / 2 where 'n' represents the level of the pyramid.
What is Function?It is a rule that assigns to each input value a unique output value, based on a specific set of operations or calculations. Functions are commonly represented using function notation, such as f(x) or g(y), where the input variable (x or y) is substituted into an expression to obtain the corresponding output value.
Define pyramid?A pyramid is a geometric shape that has a polygonal base and triangular faces that meet at a common vertex. The polygonal base can be any shape, such as a square, rectangle, triangle, or polygon, and the number of triangular faces depends on the number of sides of the base. Pyramids are named according to the shape of their base, such as a square pyramid, rectangular pyramid, triangular pyramid, or pentagonal pyramid.
Args:
level (int): The level of the pyramid.
Returns:
int: The number of triangles in the given level.
if level ≤ 0:
return 0
else:
Each level of the pyramid has one large triangle at the top
and additional smaller triangles underneath it, forming a pattern
of 1 + 2 + 3 + ... triangles, where each term is the level number.
The number of triangles in a given level can be calculated as the
sum of the first 'level' numbers using the formula (n × (n + 1)) / 2.
num of triangles = (level × (level + 1)) // 2
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Which data set has 2 values for the mode?2,2,2,5,6,7,9,10
5,6,8,10,11,11,15,18
12,12,13,13,14,14,15,15,
21,22, 22,24,25,26,28,28
Answers
HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
Answers
The total area of the figure is 272.64 yd2. Hence, the answer is option (A) 272.64 yd².
It is a trapezoid with base sides of a length of 21.3 yards and 14.9 yards, a height of 12.8 yards, and a portion of the top from the perpendicular side to a right vertex of 6.4 yards. We can use the formula for the area of a trapezoid, which is A = (b1 + b2)h/2, where b1 and b2 are the base sides, and h is the height. We have b1 = 21.3 yards, b2 = 14.9 yards, and h = 12.8 yards. To find the missing length, we can use the fact that the sum of the lengths of the two portions of the top is equal to the length of the top, which is (b1 - b2) = 6.4 + 14.9 = 21.3. Solving for b2, we get b2 = 21.3 - 6.4 = 14.9. Substituting the values in the formula, we get A = (21.3 + 14.9) x 12.8 / 2 = 272.64 yd².
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The daily high temperature at Crystal Lake ranges from 10 °C to 40 °C. Fishermen are asked to report the number of fish they catch in a day. The park ranger wants to quantify the relationship between high temperatures and the average number of fish caught.
The park ranger plots the data, fits a line to represent the trend, and finds that this line can be described by the function f(x)=−3x+125, where x represents the high temperature in degrees Celsius and f(x) is the total number of fish caught.
What is the slope of the line? Explain the meaning of the slope in this situation.
Answers
Answer:
it is 10 and 40 i think
Answer:
slope = -3
Step-by-step explanation:
The function f(x) = -3x + 125 is a linear function in slope-intercept form y = mx + b. The slope, m, is -3. This means that for every increase of 1°C, 3 less fish are caught.
What is the volume of this figure?
2 m
2 m
2 m
3 m
9 m
3 m
6 m 5th grade
Answers
Which equation is equivalent to
−4(3x + 2) = x + 2(x − 1)?
A. −12x + 2 = 3x − 1
B. −12x − 8 = 2x − 2
C. −8 = 15x − 2
D. −15x = −10
Answers
Let's start by simplifying both sides of the equation:
−4(3x + 2) = x + 2(x − 1)
−12x − 8 = x + 2x − 2 (distributing the negative 4)
−12x − 8 = 3x - 2 (combining like terms)
Now we can add 12x to both sides and add 2 to both sides:
−12x − 8 + 12x + 2 = 3x - 2 + 12x + 2
−6x = 0
Finally, we can divide both sides by -6 to isolate x:
x = 0
Now we can check which of the given equations is equivalent to this solution:
A. −12x + 2 = 3x − 1 (substituting x = 0 gives 2 = -1, which is false)
B. −12x − 8 = 2x − 2 (substituting x = 0 gives -8 = -2, which is false)
C. −8 = 15x − 2 (substituting x = 0 gives -8 = -2, which is false)
D. −15x = −10 (substituting x = 0 gives 0 = 0, which is true)
So the answer is D.
Answer:
C. -8 = 15x - 2Step-by-step explanation:
First, let's solve the equation -4(3x + 2) = x + 2(x − 1):-
[tex]\mathrm{-4\left(3x+2\right)=x+2\left(x-1\right)}[/tex][tex]\mathrm{-12x-8=x+2x-2}[/tex][tex]\mathrm{-12x-8=3x-2}[/tex][tex]\mathrm{-12x-8=3x-2}[/tex][tex]\mathrm{-15x=6}[/tex][tex]\mathrm{\frac{-15x}{-15}=\frac{6}{-15}}[/tex]→ [tex]\boxed{\bf {x=-\frac{2}{5}\;\;or\:\:x=-0.4}}[/tex]
________________________
A. -12x + 2 = 3x - 1
-12(-2/5) + 2 = 3(-2/5) - 1 34/5=-11/5The sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).
________________________
B. -12x - 8 = 2x - 2
-12(-2/5) - 8 = 2(-2/5) - 2-16/5=-14/5Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).
________________________
C. −8 = 15x − 2
-8 = 15(-2/5) - 2-8=-8Sides are equal therefore, this equation is True and is equivalent to −4(3x + 2) = x + 2(x − 1).
________________________
D. -15x = -10
-15(-2/5) = -106 = -10Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).
Hence, C. -8 = 15x - 2 is the only equation equivalent to -4(3x + 2) = x + 2(x - 1).
______________________
Hope this helps!
Try to evaluate the logarithm
(a) log 0.01
Answers
Answer:
log10(0. 01)=−2
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Convert 4
3
5
cups to pints.
2 cups = 1 pint PLEASE HELP!
Answers
Answer:
4 cups=2 pint
3 cups=1.5 pint
5 cups=2.5 pints
Step-by-step explanation:
Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.
4/2=2
3/2=1.5
5/2=2.5
Let me know if you have any questions!
How much do you owe in social security and medicare tax (FICA) on a $65,000 salary?
For the above problem, how much do you owe in FICA taxes if you are self-employed?
Answers
If you earn a $65,000 salary, you would owe approximately $5,772.50 in FICA taxes.
As a self-employed individual on a $65,000 salary, you would owe $9,945.00 in FICA taxes.
Work out the area of a semicircle with radius 3 cm.
Give your answer in terms of pi
Answers
Answer:
9/2 π
Step-by-step explanation:
Area of semicircle = πr²/2
Prove that 5^31 - 5^29 is divisible by 100
5^31 - 5^29 = ___ * 100
Answers
Answer:24x5^29
Step-by-step explanation:
(5^2 -1) x5^29
(25-1)x5^29
24x5^29
Describe a sequence of transformations that turn
y = cos(x) into the graph of
y = cos(5(x + 3)) - 2
Answers
The transformations that turn y = cos(x) into the graph of y = cos(5(x + 3)) - 2 is a horizontal translation of -3 units, followed by a horizontal compression by a factor of 5, and finally a vertical translation of -2 units.
Describing a sequence of transformations that turn the functionTo transform the graph of y = cos(x) into the graph of y = cos(5(x + 3)) - 2, we can use the following sequence of transformations:
Horizontal Translation: We need to shift the graph to the left by 3 units, so we apply a horizontal translation of -3 to the original function, y = cos(x). This can be written as y = cos(x + (-3)).Horizontal Compression: We need to compress the graph horizontally by a factor of 5, so we apply a horizontal compression with a scale factor of 1/5 to the translated function. This can be written as y = cos(1/5(x + (-3))).Vertical Translation: We need to shift the graph downward by 2 units, so we apply a vertical translation of -2 to the compressed function. This can be written as y = cos(1/5(x + (-3))) - 2.Read more about transformations at
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12 There are 18 students in Ms. Avila's reading class. Ms. Avila will assign an equal number of pages for each student to read aloud from a book that contains a total of 45 pages. What is the total number of pages that each student will read aloud? Select one answer. A 2/5 B 2 1/2 C 27 D 63
Answers
The total number of pages that each student will read aloud is 2.5 pages.
How to find the number of pages each student read?There are 18 students in Ms. Avila's reading class. Ms. Avila will assign an equal number of pages for each student to read aloud from a book that contains a total of 45 pages.
Therefore, the total number of pages each student will read aloud can be calculated as follows:
We have 18 student in the class that want s to read 45 pages of book equally.
Hence,
number of pages each student will read aloud = 45 / 18 = 2.5 pages
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11. Two marbles are drawn in succession from a box containing 30 red, 20
white, and 10 blue. Find the probability that both marbles are red, if the
marbles are not replaced. Round your answer to 3 significant digits.
Answers
The probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.
What do you understand by the term Probability?Probability is a branch of mathematics that deals with the study of uncertainty and randomness. It is used to describe the likelihood or chance of a particular event occurring. Probability is expressed as a number between 0 and 1, where 0 indicates an event is impossible, and 1 indicates that the event is certain to occur.
The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes. For example, if you roll a six-sided die, the probability of rolling a four is 1/6, because there is one way to roll a four out of six possible outcomes.
When the first marble is drawn, there are a total of 30 + 20 + 10 = 60 marbles in the box. If the first marble is red, then there are 29 red marbles left out of a total of 59. If the first marble is not red, then there are still 30 red marbles left out of a total of 59.
So, the probability that the first marble is red is:
P(Red on first draw) = 30/60 = 1/2
And the probability that the second marble is red, given that the first marble was red, is:
P(Red on second draw given first marble is red) = 29/59
The probability that the second marble is red, given that the first marble was not red, is:
P(Red on second draw given first marble is not red) = 30/59
To find the probability that both marbles are red, we need to multiply the probability of getting a red marble on the first draw by the probability of getting a red marble on the second draw given that the first marble was red:
P(Both marbles are red) = P(Red on first draw) × P(Red on second draw given first marble is red)
= (1/2) × (29/59)
= 0.245
Therefore, the probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.
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Area of Compound Shapes
Calculate the area of the shaded region below.
Answers
Answer:
33.46cm²
Step-by-step explanation:
big rectangle minus little rectangle
(9.3x4.2)-(3.5x(9.3-4.8-2.9))
39.06-(3.5x1.6)
39.06-5.6
33.46