5. Select all the choices that apply to a triangle with angles measures 30°, 60°, and 90°. obtuse acute Oright 000000000 scalene isosceles SSA ASA SAS sss
Answers
The following applies to the given triangle:acute, right, scalene.SSA and SSS do not apply to a triangle with angles measures 30°, 60°, and 90° because SSA is the ambiguous case and SSS is the congruence case which applies only to non-right triangles. ASA and SAS apply to non-right triangles only.
The angles measures of a triangle with 30°, 60°, and 90° are as follows:Explanation:Given angles measures of a triangle are 30°, 60°, and 90°.To identify the different types of the triangle and to know which of the following apply to it: Obtuse, Acute, Right, Scalene, Isosceles and SSA, ASA, SAS, sss, we use the following:We have the Pythagorean theorem:In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.Let us apply the Pythagorean theorem to the given triangle.The hypotenuse is the side opposite the right angle (90°). So, the hypotenuse is the longest side of the triangle. Thus, hypotenuse is opposite to the largest angle of the triangle.∴ The largest angle in the given triangle is 90°.The length of the sides opposite the angles 30° and 60° are 'a' and 'b' respectively and the length of the hypotenuse is 'c'.So, from the Pythagorean theorem we have
:c² = a² + b²∴ c² = (a/2)² + (a√3/2)²= a²/4 + 3a²/4 = 4a²/4= a²a = c/2andc² = a² + b²∴ b² = c² - a²= (c/2)² + (a√3/2)²= c²/4 + 3a²/4 = 3c²/4= (√3/2)c²b = c/2 × √3
The length of the sides of the given triangle with angles 30°, 60°, and 90° are a, b and c respectively: Therefore, the triangle is a right triangle because it has a 90° angle.The sides are in a ratio of 1 : √3 : 2. Therefore, the triangle is a scalene triangle.The angles are in the ratio of 1 : 2 : 3. Therefore, it is an acute triangle.Therefore, the following applies to the given triangle:acute, right, scalene.SSA and SSS do not apply to a triangle with angles measures 30°, 60°, and 90° because SSA is the ambiguous case and SSS is the congruence case which applies only to non-right triangles. ASA and SAS apply to non-right triangles only.
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Related Questions
Prove That There Are No Integers, A,B∈Z Such That A2=3b2+2015.
Answers
Step 1: Suppose, for the sake of contradiction, that there are integers A and B such that A2 = 3B2 + 2015. Let N = A2. Then, N ≡ 1 (mod 3).
Step 2: By the Legendre symbol, since (2015/5) = (5/2015) = -1 and (2015/67) = (67/2015) = -1, we know that there is no integer k such that k2 ≡ 2015 (mod 335).
Step 3: Let's consider A2 = 3B2 + 2015 (mod 335). This can be written as A2 ≡ 195 (mod 335), which can be further simplified to N ≡ 1 (mod 5) and N ≡ 3 (mod 67).
Step 4: However, since (2015/5) = -1, it follows that N ≡ 4 (mod 5) is a contradiction.
Therefore, there are no integers A, B such that A2 = 3B2 + 2015.
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Which table made this graph?
Answers
Answer:
IV
Step-by-step explanation:
The Y column is the same, and so is the graph.
Let T. R² → R³ be a linear transformation such that T(1, 0, 0) = (-1, 2, 4), T(0, 1, 0) = (3, 1, -2), and T(0, 0, 1)=(2, 0, -2). Find the indicated image T(0, 1, -3)
Define T: P₅ → P₄ by T(p)=p' What is the kernel of T? (Use a0, a1, a2, ... arbitrary constant coefficients of 1, x, x², ... respectively.) ker(T) = {p(x)= __ :a1 ∈ R}
Answers
In this problem, we are given a linear transformation T: R² → R³, and the images of the standard basis vectors are provided. We need to determine the image of a specific vector and find the kernel of the transformation. Additionally, we are asked to define another transformation T: P₅ → P₄ and find its kernel.
To find the image of the vector (0, 1, -3) under the transformation T: R² → R³, we can express (0, 1, -3) as a linear combination of the standard basis vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1) and use the linearity of the transformation. We multiply each basis vector by its corresponding image under T and sum them up to obtain the image of (0, 1, -3).
For the transformation T: P₅ → P₄ defined as T(p) = p', where p' is the derivative of the polynomial p, the kernel of T consists of all polynomials p(x) such that T(p) = p' = 0. In other words, the kernel of T is the set of all constant polynomials, where the coefficients a1, a2, ... can be any arbitrary real numbers.
To find the image of (0, 1, -3) under T: R² → R³, we use the linearity of the transformation. We have T(0, 1, -3) = T(0(1, 0, 0) + 1(0, 1, 0) - 3(0, 0, 1)). Applying linearity, we obtain T(0, 1, -3) = 0T(1, 0, 0) + 1T(0, 1, 0) - 3T(0, 0, 1). Substituting the given images, we get T(0, 1, -3) = 0(-1, 2, 4) + 1(3, 1, -2) - 3(2, 0, -2) = (3, -5, 2).
For the transformation T: P₅ → P₄ defined as T(p) = p', where p' is the derivative of p, the kernel of T consists of all polynomials p(x) for which the derivative p'(x) equals zero. In other words, the kernel of T contains all constant polynomials p(x) of the form p(x) = a₀, where a₀ is an arbitrary constant coefficient. Therefore, the kernel of T is represented as ker(T) = {p(x) = a₀ : a₀ ∈ R}.
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1.81 find some values of z. find the value normal variable that satisfies each of the following conditions. (if you use table a, report the value of that comes closest to satisfying the condition.) in each case, sketch a standard normal curve with your value of marked on the axis. a. 68% of the observations fall below b. 75% of the observations fall above
Answers
The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.
A. To find the value of z that corresponds to 68% of the observations falling below, we can use the z-score formula. The z-score formula is z = (x-μ)/σ, where x is the value we are looking for, μ is the mean of the normal distribution, and σ is the standard deviation. Using this formula and a standard normal table, we can find that the value of z is 0.84. This means that 68% of the observations fall below z = 0.84. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 0.84 marked on the x-axis.
B. To find the value of z that corresponds to 75% of the observations falling above, we can use the same formula and a standard normal table. We can find that the value of z is 1.15. This means that 75% of the observations fall above z = 1.15. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 1.15 marked on the x-axis.
The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.
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a 'scooped' pyramid has a cross-sectional area of x 4 at a distance x from the tip. what is its volume if the distance from tip to base is 5?
Answers
The volume of the 'scooped' pyramid is approximately 26.6667 cubic units.
To find the volume of the 'scooped' pyramid, we first need to determine the area of its base. Since the cross-sectional area of the pyramid is x 4 at a distance x from the tip, we can assume that the area at the tip is zero. This means that the area of the base is 4 times the area at a distance of 5 from the tip (since the distance from tip to base is 5).
Therefore, the area of the base is 4x4 = 16 square units. To find the volume, we can use the formula for the volume of a pyramid, which is:
Volume = (1/3) x Base Area x Height
In this case, the height of the pyramid is 5 units. So, we can substitute the values we have:
Volume = (1/3) x 16 x 5
Volume = 26.6667 cubic units
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Which function is the best represented by the graph?
Answers
Answer:
B
Step-by-step explanation:
An elevator ascends, or goes up, at a rate of 750 feet per minute. Is the height to which the elevator ascends proportional to the number of minutes it takes to get there?
Answers
Answer:
Yes
Step-by-step explanation:
We know this because the proportion can be used to find another answer.
Example:
How many feet did the elevator ascend in 0.25 minutes?
750 x
---------- = ----------
1 0.25
750(0.25) = 1x
187.5 = x
***Sorry about the format. Hope this helps!
Validation of the model and answering the question "what are my options" occur in the ___ phase of the IDC.
A. choice
B. design
C. intelligence
D. implantation
Answers
Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.
The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.
In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.
In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.
Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.
The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.
Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.
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(7) Explain why 198: 1,287 and 2: 13 are equivalent ratios.
Your answer
I
Answers
Answer:
Because they are both multiplied.
Step-by-step explanation:
198 divided by 99 is 2
1287 divided by 99 is 13
2:13 :)
Use the simplex algorithm to find the optimal solution to the following LP (solve manually): maxz= 36x1+30x2−3x3−4x4
s.t. x1+x2−x3≤5
6x1+5x2−x4≤10
∀xi≥0
Answers
The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.
maximize: z = c1x1 + c2x2 + ... + cnxn
subject to
a11x1 + a12x2 + ... + a1nxn ≤ b1
a21x1 + a22x2 + ... + a2nxn ≤ b2
am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i
In our case,
the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x
subject to:
x1 + x2 - x3 ≤ 5
6x1 + 5x2 - x4 ≤ 10
xi ≥ 0 for all i
We can rewrite the constraints as follows:
x1 + x2 - x3 + x5 = 5 (adding slack variable x5)
6x1 + 5x2 - x4 + x6 = 10 (adding slack variable x6)
Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:
x1 = x7
x2 = x8
x3 = x9
x4 = x10
The objective function becomes:
z = 36x7 + 30x8 - 3x9 - 4x10
Now we have the problem in standard form as:
maximize: z = 36x7 + 30x8 - 3x9 - 4x10
subject to:
x7 + x8 - x9 + x5 = 5
6x7 + 5x8 - x10 + x6 = 10
xi ≥ 0 for all i
To apply the simplex algorithm, we initialize the simplex tableau as follows:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0 | 36 | 30 | -3 | -4 | 0 |
---------------------------------------------------------------------------
x5| 0 | 1 | 0 | 1 | 1 | -1 | 0 | 5 |
---------------------------------------------------------------------------
x6| 0 | 0 | 1 | 6 | 5 | 0 | -1 | 10 |
---------------------------------------------------------------------------
Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:
Iteration 1:
1. Choose the most negative coefficient in the 'z' row, which is -4.
2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).
3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.
Ratios: 5/0 = undefined, 10/(-4) = -2.5
4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.
5. Perform row operations to
make all other elements in the pivot column zero.
After performing these steps, we get the updated simplex tableau:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0.4 | 36 | 30 | -3 | 0 | 12 |
---------------------------------------------------------------------------
x5| 0 | 1 | -0.2 | 1 | 1 | -1 | 0 | 5 |
---------------------------------------------------------------------------
x10| 0 | 0 | 0.2 | 1.2 | 1 | 0 | 1 | 2.5 |
---------------------------------------------------------------------------
Iteration 2:
1. Choose the most negative coefficient in the 'z' row, which is -3.
2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).
3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.
Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5
4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.
5. Perform row operations to make all other elements in the pivot column zero.
After performing these steps, we get the updated simplex tableau:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0.8 | 34 | 30 | 0 | 4 | 0 |
---------------------------------------------------------------------------
x5| 0 | 1 | -0.4 | 0.6 | 1 | 5 | -2 | 10 |
---------------------------------------------------------------------------
x9| 0 | 0 | 1 | 6 | 5 | 0 | -5 | 12.5 |
---------------------------------------------------------------------------
Iteration 3:
No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:
z = 0
x1 = x7 = 0
x2 = x8 = 10
x3 = x9 = 0
x4 = x10 = 0
x5 = 10
x6 = 0
Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.
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Which shows a quadratic function?
Answers
Answer:
Step-by-step explanation:
from table , we can see that ,
quadratic equation gives same solution for positive and negative numbers .
According to this we can se that option 1 is a quadratic equation
Mr. Ailey gave his class
45
45 minutes to read.
Davida reads
27
3
4
27
4
3
pages in that time.
At what rate, in pages per hour, did Davida read?
Answers
Answer:
Answer: 37 pages per hour
Step-by-step explanation:
37 pages per hour
Step-by-step explanation:
Given that :
Time Given to read = 45 minutes ; 45 / 60 = 0.75
Number of pages readable ad by Davida within the given time frame = 27 3/4 pages
David's reading rate in pages per hour :
Number of pages read / time taken (hrs)
[27 3/4] ÷ (45/60)
[111 / 4] ÷ (45/60)
(111 / 4 ) * (60/45)
(111 * 60) / (4 * 45)
6660 / 180
= 37 pages per hour
4. What are the Z-scores for the following Confidence Interval levels? Remember, you MUST account for both tails of the curve, positive and negative, when identifying each. That means you will need to do a little math to obtain the correct z-value. 3 Points 68%= 85% = 99% =
Answers
In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.
Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.
We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)
Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!
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What is the area of a rectangle with a length of 5 inches and a with of 2 inches
Answers
Answer:
10 inches
Step-by-step explanation:
Does someone mind helping me with this? Thank you!
Answers
The number of seconds that it would take the thermometer to hit the ground would be 22 seconds.
How to find the time taken ?The equation for the height of the falling thermometer is h(t) = -16t² + initial height. We know that the initial height is 7,744 feet, and we want to find when the thermometer hits the ground, or when h(t) equals zero.
Setting h(t) to zero gives us:
0 = -16t² + 7744
Solve this equation for t:
16t² = 7744
t² = 7744 / 16 = 484
So, t = √(484) = 22 seconds
It will take 22 seconds for the thermometer to hit the ground.
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What is AAS ASA SSS SAS?
Answers
The rules AAS, ASA, SSS and SAS are congruence rule of triangle and the each rules has been explained
The rules AAS, ASA, SSS and SAS are congruence rule of triangle
SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent
SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to the two sides and one included angles between the sides of the other triangle, then both triangles are congruent
ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent
AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent
Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle
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A thick cylindrical shell with inner radius of 10 cm and outer radius of 16 cm is subjected to an internal pressure of 70MPa. Find the maximum and minimum hoop stresses.
Answers
The cylindrical shell is subjected to an internal pressure of 70MPa. The shell's inner radius is 10 cm, and the outer radius is 16 cm. The maximum and minimum hoop stresses in the cylindrical shell are determined below.
For an element of thickness dr at a distance r from the center, the hoop stress is given by equation i:
σθ = pdθ...[i]Where, p is the internal pressure.
The thickness of the shell is drThe circumference of the shell is 2πr.
Therefore, the force acting on the element is given by:F = σθ(2πrdr)....[ii]
Let σmax be the maximum stress in the shell. The stress at radius r = a, which is at the maximum stress, is given by:σmax = pa/b....[iii]
Here a = radius of the shell, and b = thickness of the shell.
According to equation [i], the hoop stress at radius r = a is given by:σmax = pa/b....[iii].
Substitute the given values:σmax = 70 × 10^6 × (16 - 10)/(2 × 10) = 56 × 10^6 Pa.
The minimum hoop stress in the shell occurs at the inner surface of the shell. Let σmin be the minimum stress in the shell.σmin = pi/b....[iv].
According to equation [i], the hoop stress at radius r = b is given by:σmin = pi/b....[iv]Substitute the given values:
σmin = 70 × 10^6 × 10/(2 × 10) = 35 × 10^6 Pa.
Therefore, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa.
A thick cylindrical shell with an inner radius of 10 cm and an outer radius of 16 cm is subjected to an internal pressure of 70MPa. Maximum and minimum hoop stresses in the cylindrical shell can be determined using equations and the given data. σθ = pdθ is the formula for hoop stress in the cylindrical shell.
This formula calculates the hoop stress for an element of thickness dr at a distance r from the center.
For the cylindrical shell in question, the force acting on the element is F = σθ(2πrdr).
Let σmax be the maximum stress in the shell. According to equation [iii], the stress at the radius r = a, which is the maximum stress, is σmax = pa/b.σmax is calculated by substituting the given values.
The maximum hoop stress in the shell is 56 × 10^6 Pa according to this equation.
Similarly, σmin = pi/b is the formula for minimum hoop stress in the shell, which occurs at the inner surface of the shell.
The minimum hoop stress is obtained by substituting the given values into equation [iv].
The minimum hoop stress in the shell is 35 × 10^6 Pa.As a result, the maximum and minimum hoop stresses in the cylindrical shell are 56 × 10^6 Pa and 35 × 10^6 Pa, respectively.
Thus, the maximum hoop stress in the shell is 56 × 10^6 Pa and the minimum hoop stress is 35 × 10^6 Pa. These results are obtained using equations and given data.
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A teacher is making identical supply kits with 92 crayons, 46 pieces of paper, and 23 glue sticks. what is the greatest number of supply kits the teacher can make with no items leftover?
Answers
The greatest number of supply kits the teacher can make with no items leftover are 23 packets.
What are prime numbers?Any natural number greater than one that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is any natural number greater than one that is not prime. For instance, the number 5 is a prime because there are only two ways to represent it: as the product 1 5 and as 5 1.
What is factors?A number or algebraic expression known as a factor evenly divides another number or expression, leaving no remainder. As an example, 12 is a factor of 3 and 6 since 12 3 = 4 and 12 6 = 2, respectively.
Given that,
Supply kit contains 92 crayons, 46 pieces of paper and 23 glue sticks
Factors of 92:
1, 2, 4, 23, 46 and 92.
Factors of 46:
1, 2, 23, and 46.
Factors of 23:
23 is a prime number
Then the greatest common factor GCF (92, 46, 23) = 23
Therefore, number of supply kits the teacher can make with no items leftover are 23 packets.
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The real estate agent earns 12% commission on all sales. Last month the agent sold homes for a total of $350,000. How much money did the agent earn in commission?
Answers
Answer: 42000
Step-by-step explanation:
10% =35000
1% =3500 × 2 = 7000 + 35000 42000
Answer:
tep-by-step explanation:
10% =35000
1% =3500 × 2 = 7000 + 35000 42000
Step-by-step explanation:
Find the x-intercepts of the parabola with
vertex (1,20) and y-intercept (0,16).
Answers
Answer:
the x intercepts are \((1-\sqrt{5} ,0) , (\:1+\sqrt{5},0 )\)
Explanation:
vertex (1,20) and y-intercept (0,16)
equation used f(x) = a(x - h)² + k where (h,k) is vertex.
16 = a(0 - 1)² + 20
16 = a + 20
a = -4
f(x) = a(x - h)² + k ......this is vertex to find equation of parabola.
f(x) = -4(x-1)² + 20
f(x) = -4(x-1)² + 20
f(x) = -4x²-8x-4+20
f(x) = -4x²+8x+16 .....if simplified.
To find x intercepts, y must be 0,
4x²+8x+16 =0
\(x_{1,\:2}=\frac{-8\pm \sqrt{8^2-4\left(-4\right)\cdot \:16}}{2\left(-4\right)}\)
\(x_1=\frac{-8+8\sqrt{5}}{2\left(-4\right)},\:x_2=\frac{-8-8\sqrt{5}}{2\left(-4\right)}\)
\(x=1-\sqrt{5},\:x=1+\sqrt{5}\)
So, the x-intercepts of the parabola vertex (1,20) and y-intercept (0,16) are \((1-\sqrt{5} ,0) , (\:1+\sqrt{5},0 )\)
Solve. 8x² + 5 = 35 Round to the nearest hundredth. Enter your answers in the boxes. The solutions are approximately and .
Answers
Answer:
x=1.94
x = - 1.94
Step-by-step explanation:
8x² + 5 = 35
Subtract 5 from each side
8x² + 5-5 = 35-5
8x² = 30
Divide each side by 8
8x² /8 = 30/8
x² = 15/4
Take the square root of each side
sqrt( x²) = ±sqrt(15/4)
x = ±sqrt(15/4)
x=1.93649
x = - 1.93649
To the nearest hundredth
x=1.94
x = - 1.94
Answer:
1.94
Step-by-step explanation:
\(8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\\)
≈ ±1.94
Does this graph represent a proportional relationship? Explain
this is a test please help
Answers
Answer:
No
Step-by-step explanation:
the line has to be straight for it to be a proportional relationship..
Answer: No.
Step-by-step explanation: It has to start from the Origin (which is the two arrows crossing on the bottom left corner, 0,0) and it needs to be in a straight line in order to be proportinal.
(12,-18),(7,-9) find the slope of this equation
Answers
Answer: 1.8
Step-by-step explanation:
(-18-(-9))/(12-7)=-9/5
A couple is thinking about having 3 children. Assume that each child is equally likely to be a girl or a boy. What is the probability that exactly 2 of the children are girls?
A. 0.125
B. 0.25
C. 0.375
D. 0.5
Answers
Answer:
O.375
Step-by-step explanation:
We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set. There is a 50/50 chance of having a girl or a boy, and there are three children. For now we'll use B to represent a boy and G for a girl. It goes as follows:
(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)
I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)
Count the total number of combinations (9). Next, count the number that include exactly 2 girls (4). With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy. 4/9 is in simplest form, so all you have to do is find the percentage 44.444%
Answer:
C or 37.5
the histogram represents the number of absences for 15 students. how many students had between 6 and 15 absences?
Answers
Carlos spent 25 hours helping his neighbor build a fence. The neighbor paid Carlos $187.50 for his work. How much money would Carlos earn if he worked for 30 hours?
Answers
Answer:
225 dollars
Step-by-step explanation:
Money earned by working for 25 hours =187.50
Money earned by working for 1 hour=187.50/25=7.5
Money earned in 30 hours =7.5*30=225 dollars
Answer:
225 dollars
Step-by-step explanation:
187.5÷25=7.5
7.5×30=225
A crayon company recently changed its labels. It currently has a total of 80,553 crayons in stock, 45,695 of which have the new label. How many crayons with the old label does the company have in stock?
Answers
Answer:
34858
Step-by-step explanation:
You would subtract 80553 by 45695 and you would get your answer.
Answer:
vh
Step-by-step explanation:
bkkjggjgjrtyyuuiiiiiuiki
Ariel made 108 cupcakes. If 32 of them are chocolate, what percent of the cupcakes are vanilla?
Answers
Answer:
About 70%
Step-by-step explanation:
Subtract the number of chocolate cupcakes from the total cupcakes.
108-32=76
76 cupcakes are vanilla.
Divide 76/108
76/108
70.3%
About 70% of the cupcakes are vanilla.
(I don't know if you are allowed to use a calculator in your class, but I did)
what can you conclude from picard’s theorem? (i ) d y d t =t cos−1 y, y(0) =1 (i i ) d y d t = t y , y(0) =y0 (i i i ) d y d t = 1 t 2 y2 , y(0) =0 (i v) d y d t =y2/3, y(0) =0
Answers
Picard's theorem states that a first-order ordinary differential equation of the form y' = f(x, y) with an initial condition y(x0) = y0 has a unique solution if the function f(x, y) is continuous and satisfies the Lipschitz condition with respect to y in some region containing the initial point (x0, y0).
For the given differential equations, we can apply Picard's theorem to determine whether they have unique solutions.
(i) The function f(x, y) = t cos^-1(y) is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, 1), so by Picard's theorem, the equation has a unique solution.
(ii) The function f(x, y) = tx is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, y0), so by Picard's theorem, the equation has a unique solution.
(iii) The function f(x, y) = 1/(t^2*y^2) is not continuous at (0, 0), so we cannot apply Picard's theorem to determine whether the equation has a unique solution.
(iv) The function f(x, y) = y^(2/3) is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, 0), so by Picard's theorem, the equation has a unique solution.
Learn more about Picard's theorem here: brainly.com/question/30906464
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PLease please please help quick
Answers
Answer:
B
Step-by-step explanation:
Same as last. multiple 8 into the entire equation.
Answer:
-80x+28y-56
4(-20x+7y-14)
Step-by-step explanation: