Thus, the circumference of Ryan’s new spherical basketball is found as: 52.752 in.
Explain about the circumference:The perimeter of a polygon, including a square or rectangle, is the distance around it (P). On the opposing hand, the circumference of a circle is the distance around it (C). As a result, the circular circumference is the length of a circle's edge in linear terms.
Given data:
Volume of ball = 295.6 cubic inches.As the ball is in the shape of sphere.
Let r be the radius of sphere:
Volume of sphere = 4/3 * π * r³
295.6 = 4/3 * 3.14 * r³
r³ = (295.6 * 3)/(4*3.14)
r³ = 70.60
r = 8.40 in
circumference = 2 * π * r
circumference = 2 * 3.14 * 8.40
circumference = 52.752 in
Thus, the circumference of Ryan’s new spherical basketball is found as: 52.752 in.
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The probability that it is going to rain tomorrow is 1/7. What are the odds in favor of it raining tomorrow
The odds in favor of it raining tomorrow are 1 to 6.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
To find the odds in favor of it raining tomorrow, we need to calculate the ratio of the probability that it will rain to the probability that it won't rain. The probability that it won't rain is 1 - 1/7 = 6/7.
So, the odds in favor of it raining are:
Probability of raining / Probability of not raining
= (1/7) / (6/7)
= 1/6
Therefore, the odds in favor of it raining tomorrow are 1 to 6.
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Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions? They are both 1 standard deviation above their respective means. They are both 1 standard deviation below their respective means. They are both 2 standard deviations below their respective means. The score of 40 is 2 standard deviations below its mean, while the score of 45 is only 1 standard deviation below its mean.
The correct answer is: They are both 1 standard deviation away from their means, but in opposite directions. The first score is 1 standard deviation below mean, while second score is 1 standard deviation above the mean.
What is standard deviation?Standard deviation is a measure of the deviation or spread from the mean (mean) of a set of data values.
More specifically, the standard deviation is calculated by taking the square root of the variance of the data. Variance is the mean square of the difference of each data point from the mean.
The first score of 40 from a distribution with a mean of 50 and a standard deviation of 10 is 1 standard deviation below the mean, because it is (50-40)/10 = -1 standard deviation from the mean.
The second score of 45 from a distribution with a mean of 50 and a standard deviation of 5 is 1 standard deviation above the mean, because it is (45-50)/5 = -1 standard deviation from the mean.
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The image shows line p
For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one-to-one, give an example showing why.
(a) Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7, 8}. f: P(A) → P(A). For X ⊆ A, f(X) = A-X. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A. Prove with a proof.
(b) A = {a, b, c}, h: P(A) → P(A). For X ⊆ A, h(X) = X ⊕ {a}.
the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
To determine if the function f: P(A) → P(A), where f(X) = A-X, is onto, one-to-one, neither, or both, we need to consider the following:
Onto: A function is onto if every element in the codomain has a corresponding preimage in the domain. In other words, for every Y in P(A), there exists an X in P(A) such that f(X) = Y.
Let Y be any subset of A. Then, we need to find an X such that f(X) = Y. Since f(X) = A-X, we need to find an X such that A-X = Y. Solving for X, we get X = A-Y. Therefore, we can choose X = A-Y, and we have f(X) = A-(A-Y) = Y. Hence, f is onto.
Next, we need to prove that f is not one-to-one. To do this, we need to find two different sets X1 and X2 such that f(X1) = f(X2).
Hence, the function f: P(A) → P(A), where f(X) = A-X, is onto but not one-to-one.
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48. Graph the vertical line x = -2. Then name its intercept.
Answer:
There is no y intercept because the graph does not cross the y axis.
The x intercept is (-2,0)
Step-by-step explanation:
Helping in the name of Jesus.
In which of the following scenarios will conducting a paired
-test for means be appropriate? CHECK ALL THAT APPLY.
A. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
C. To test if the mean annual income of Ontarians is higher than that of British Columbians.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
F. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
G. None of the above
The appropriate scenario to conduct a paired t-test for means is when we have two related samples, and we want to test whether there is a significant difference in the means between the two samples. Hence, B, D, and E are the appropriate responses.
What is a t-test?A t-test is a statistical test used to determine whether two sets of data are significantly different from each other, based on their means. It is a parametric test, meaning it makes certain assumptions about the data, such as that it is normally distributed and that the variances of the two groups being compared are equal.
There are several types of t-tests, including the independent samples t-test, which is used when comparing two groups that are not related to each other, and the paired samples t-test, which is used when comparing two groups that are related or paired, such as before-and-after measurements from the same individuals.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
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NO LINKS!!! URGENT HELP PLEASE!!!
Please help me with 3 and 4
Answer:
3. 5.3 ft
4. 4.5 ft
Step-by-step explanation:
3.
Let's call the height of the connection point on the tree "h". We can use trigonometry to relate the angle and the length of the guy wire to "h". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the height "h", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:
sin(42) = h / 8
To solve for "h", we can multiply both sides by 8:
h = 8 sin(42)
Using a calculator, we get:
h ≈ 5.3 feet
So the height of the connection point on the tree is about 5.3 feet, to the nearest tenth of a foot.
4.
The ladder, the wall, and the ground form a right triangle, with the ladder being the hypotenuse. Let's call the height on the wall that the ladder reaches "x". We can use trigonometry to relate the angle and the length of the ladder to "x". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the height "x", and the hypotenuse is the length of the ladder, which is 5 meters. So we have:
sin(65) = x / 5
To solve for "x", we can multiply both sides by 5:
x = 5 sin(65)
Using a calculator, we get:
x ≈ 4.5 meters
So the ladder reaches a height of about 4.5 meters on the wall.
Find g(x), where g(x) is the translation 3 units left of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
We can conclude after answering the provided question that Therefore, function g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.
what is function?In mathematics, a function appears to be a connection between two sets of numbers in which each member of one set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from a set and produces output from another. The variable x has now been frequently sometimes used represent the inputs, and the flexible y is used to represent the outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a linear model in which each x-value yields a unique value of y.
So, g(x) = f(x + 3) = (x + 3)² = x² + 6x + 9.
g(x) = x² + 6x + 9
= 1(x² + 6x + 9)
= 1(x² + 6x + 9 + 9 - 9)
= 1((x + 3)² + 9 - 9)
= 1(x + 3)² + 0
Therefore, g(x) = 1(x + 3)² + 0, which is in the form a(x - h)² + k with a = 1, h = -3, and k = 0.
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What is the smallest number of cars that can tailgate in a straight line at a football game so that one car is in front of two cars,one car is behind two cars,and one car is in between 2 cars ?
Answer:
The smallest number of cars that can tailgate in a straight line at a football game is 12.
Step-by-step explanation:
Smallest Tailgate Cars Number
This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.
This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.
Answer:
3
Step-by-step explanation:
basicly one car will be in the back one in the middle and one in the front. if I'm correct then it should be 3
If a = 18 in, b = 18 in, c = 30 in, and d = 48 in, and the bases of the figure are the shaded regions, what is the lateral surface area of the geometric shape formed by this net?
A.
1,728 sq in
B.
2,808 sq in
C.
1,944 sq in
D.
1,404 sq in
The lateral surface area of the geometric shape formed by the given net is 3,780 sq in.
What is lateral surface area?The lateral surface area is the sum of the areas of the trapezoidal faces and the rectangular faces.
The area of a trapezoid is given by the formula:
A = (1/2)h(b1 + b2)
where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides.
Area of trapezoid 1 = (1/2)(30 + 18)(48) = 972 sq in
Area of trapezoid 2 = (1/2)(18 + 18)(48) = 864 sq in
The area of each rectangular face is given by the product of the length and the width.
Area of rectangular face 1 = 30 x 18 = 540 sq in
Area of rectangular face 2 = 48 x 18 = 864 sq in
Area of rectangular face 3 = 30 x 18 = 540 sq in
The total lateral surface area is the sum of the areas of all the faces:
Lateral surface area = Area of trapezoid 1 + Area of trapezoid 2 + Area of rectangular face 1 + Area of rectangular face 2 + Area of rectangular face 3
Lateral surface area = 972 + 864 + 540 + 864 + 540
Lateral surface area = 3,780 sq in
Therefore, the lateral surface area of the geometric shape formed by the given net is 3,780 sq in.
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Triangles CDE and NOP are similar.
The lengths of CD and NO are 53 inches and 212 inches.
DE is 106 inches long and NP is 318 inches. Find OP and CE.
Answer:
OP = 424: CE = 79,5
Step-by-step explanation:
I added a photo of my solution
coordinate points: (-5,-3),(-7,-11),(4,-13). give the coordinate of the fourth vertex
The coordinate of the fourth vertex is determined as (13,-23).
What is the coordinate of the fourth vertex?To find the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length.
Let's start by finding the vectors for two sides of the parallelogram. We can use the given coordinate points to find the vectors:
Vector AB = (xB - xA, yB - yA) = (-7 - (-5), -11 - (-3)) = (-2, -8)
Vector BC = (xC - xB, yC - yB) = (4 - (-7), -13 - (-11)) = (11, -2)
Since opposite sides of a parallelogram are parallel, we know that these two vectors are parallel.
To find the fourth vertex, we can add the vector AB to the endpoint of vector BC:
Vector CD = Vector BC + Vector AB = (11, -2) + (-2, -8) = (9, -10)
Now we can add this vector to point C to find the coordinates of point D:
Point D = (xC + CDx, yC + CDy) = (4 + 9, -13 - 10) = (13, -23)
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I need help with all 3 task
The volume of the cylinders are;
1. 602. 88 cm³
2. 56.52 cm³
3. 141. 3 cm³
How to determine the volumeThe formula for calculating the volume of an open cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinder.r is the value of the radius.h is the height of the cylinder.Then, we have;
Substitute the values
1. Volume = 3.14 × 4² × 12
Multiply the values after finding the square
Volume = 602. 88 cm³
2. Substitute the values
Inner radius, r = 2cm
Volume =3.14 × 1.5 ² × 8
Multiply the values, we get;
Volume = 56.52 cm³
3. Substitute the values
Inner radius = 2cm
Volume = 3.14 × 3² × 5
Multiply the values
Volume = 141. 3 cm³
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Malik described the figure shown below. He said, " Ray ST and ray UT form angle STU." Is Malik's description correct? Explain why or why not.
Answer:
If the figure shows two rays ST and UT with a common endpoint U, then Malik's description is correct. When two rays share a common endpoint, they form an angle. The angle formed by rays ST and UT would be angle STU. So, if the figure matches this description, then Malik's statement is correct.
for the following exercise, consider the following scenario: the weight of a newborn is 11 pounds. the baby gained one-half pound a month for its first year. find the linear function that models the baby's weight, w , as a function of the age of the baby, in months, t .
w(t) = _____
The linear function that models the baby's weight, w, as a function of the age of the baby, in months, t, is equals to the w(t) = 11 + (1/2)t.
The a straight line graph represents linear function. The linear function form is, y = f(x) = a + bx. It has an independent variable and a dependent variable. There is independent and dependent variables are x and y respectively. We have provide a scenario which consists the following informations,
The weight of new born baby = 11 pounds
The weight gained by new born baby in one month = 1/2 pounds
We have to determine a linear function which models the baby's weight (w pounds), as a function of the baby's age, in months (t). From the definition of linear function, we see here weight of baby is an dependent variable and month in first year is independent. So, the linear function of weight of baby is written as w(t) = 11 + (1/2)t , where t represents months in baby's first year. Hence, required function is w(t) = 11 + (1/2)t.
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Use the Standard Normal Table or technology to find the Z-score that corresponds to the following cumulative area.0.952
The cumulative area corresponds to the z-score is 1.67
What is the cumulative area?
The likelihood that a real-valued random variable, X, will assume a value less than or equal to x is represented by the cumulative distribution function of X, or simply by the distribution function of X, assessed at x.
Here, we have
Given: the following cumulative area is 0.952.
We have to find the Z-score that corresponds to the following cumulative area.
p(z<z)=0.952
p(z<1.67)=0.952
z=1.67 (from the standard normal table)
Hence, The cumulative area corresponds to the z-score is 1.67
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and with a solution pls thanks
Answer:
you didn't say which process to use while solving so I have used graphical method but I hove it's useful
a tree casts a shadow that is 20 ft long. Frank is 6 ft tall, and while standing next to the tree he casts a shadow that is 4 ft long. how tall is the tree? and how much taller is the tree than frank?
From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (show working too)
The area of remaining sheet is 536 cm²
Since, we know that the area of circle [tex]=\pi \times r^2[/tex]
Area of bigger circle [tex]=\dfrac{22}{7} \times14\times14[/tex]
[tex]=44\times14[/tex]
[tex]=616 \ \text{cm}^2[/tex]
Thus, the area of bigger circle is 616 cm²
Similar way, the area of 2 smaller circles [tex]=2\pi r^2[/tex]
[tex]=2\times\dfrac{22}{7} \times3.5\times3.5[/tex]
[tex]=44\times0.5\times0.5[/tex]
[tex]=77 \ \text{cm}^2[/tex]
Thus, the area of 2 smaller circle is 77 cm²
[tex]\text{Area of rectangle}=\text{Length}\times\text{Breadth}[/tex]
[tex]=3\times1=3 \ \text{cm}^2[/tex]
Thus, the area of rectangle is 3 cm²
Now, remaining area of sheet = Area of bigger circle − Area of both smaller circle − Area of rectangle
[tex]=616-77-3=536 \ \text{cm}^2[/tex]
Hence, area of remaining sheet is 536 cm²
Find the experimental probability that only 1 of
4 children in a family is a boy.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT HTTH TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
Experimental Probability = [?]%
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65 POINTS, NEED HELP ASAP!!!
7. True, 8. True, 9 No, because every name had an equal chance of being drawn from the jar, 10. False
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
7. True: Sampling bias: unequal chance of selection leading to unrepresentative samples.
8. True: Avoiding bias: random sampling, representative samples, and minimizing nonresponse bias.
9 No, because every name had an equal chance of being drawn from the jar.
10. False: Biased sample: unrepresentative sample due to factors like nonresponse or small sample size.
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Please help me. With problem 11 here
The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
What is expression ?An expression is a mathematical phrase that can contain numbers, variables, operators, and sometimes functions. Expressions are used to represent or calculate values, and they can be simple or complex. For example, "2 + 3" is a simple expression that can be evaluated to give the value 5, while "3x + 2y - 4" is a more complex expression that contains variables and can only be evaluated if values are assigned to the variables. Expressions can also be combined to form more complex expressions using operators like addition, subtraction, multiplication, and division.
According to the given information:To find the inverse function of g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)), we can follow these steps:
Step 1: Replace g(x) with y, so that the function becomes g'(x) = -y.
Step 2: Solve the equation for y in terms of x: y = - g'(x) = - (sqrt(x) + 6)/(1 - sqrt(x)).
Step 3: Interchange x and y: x = - (sqrt(y) + 6)/(1 - sqrt(y)).
Step 4: Solve for y in terms of x:
[tex]x = - (sqrt(y) + 6)/(1 - sqrt(y))\\x(1 - sqrt(y)) = -sqrt(y) - 6\\x - x sqrt(y) = -sqrt(y) - 6\\x + 6 = (x + 1) sqrt(y)\\(x + 6)/(x + 1) = sqrt(y)\\[/tex]
[tex]y = [ (x + 6)/(x + 1) ]^2[/tex]
Therefore, the inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is:g^-1(x) = [ (x + 6)/(x + 1) ]^2[/tex]
Note that this function is defined for all x except x = 1, where the original function g(x) is not defined. Therefore, g(x) is not invertible at x = 1.
Therefore, The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
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If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Given: T=X=U=Y
Prove: TUV ~ XYZ
The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
What is congruent?In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.
In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
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The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ
What is congruent?
Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.
To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.
Given that T=X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.
To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:
TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)
TU / TX = 1 (because T = X)
TX / XY = 1 (because U = Y)
Therefore, TU / XY = 1 * 1 = 1.
Similarly, we can compare the ratio of UV and YZ:
UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)
UV / UY = 1 (because U = Y)
UY / YZ = 1 (because T = X)
Therefore, UV / YZ = 1 * 1 = 1.
Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:
TUV ~ XYZ
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help pls show ur work
Answer:
For #17:
This is a 45-45-90 triangle. Therefore, the missing side length (x) is equal to the other leg of the triangle, which is 6.
For #18:
This is a 30-60-90 triangle. Therefore, the missing side length (m) is equal to the hypotenuse (18) divided by 2, or 9.
For #19:
This is a 30-60-90 triangle. Therefore, the missing side length (y) is equal to the hypotenuse (12) multiplied by the square root of 3, or 12√3.
For #20:
This is a 30-60-90 triangle. Therefore, the missing side length (u) is equal to the short leg (5√3) multiplied by 2, or 10√3.
For #21:
This is not a right triangle because the angles do not add up to 180 degrees.
For #22:
This is a right triangle because the angles add up to 180 degrees and one of the angles is 90 degrees.
Step-by-step explanation:
what is the value of 63,798 divided by 49?]
Answer:
1302
Step-by-step explanation:
The probability of flipping a coin and having it land on heads is 1/2. If a coin is tossed 4 times, how many times can you expect it to land on heads?
You can expect the coin to land on heads 2 times when it is tossed 4 times, on average.
cos(3x - 180°)=ー√3/2, where 0 < x180°
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
cos(3x - 180°) = cos(180° - 3x)
cos(180° - 3x) = -√3/2
-cos(3x) = -√3/2
cos(3x) = √3/2
3x = π/6
x = π/18
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
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Which expression is represented by the model below? pleaseeeee help!!! 30 points!!!!
The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
Let x= the number of busses and y= the number of vans
Create an equation representing the number of vehicles needed.
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Create an equation representing the total number of seats in vehicles for the orchestra members.
The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.
The system of equations to find the smallest number of busses the orchestra can rent is,
The total number of buses :
b + v ≤ 6
The total number of passengers.
25b + 12v ≥ 111 - - - - (2)
Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
7. Gretchen makes pillows using *
15 yards of fabric per pillow.
She has 814 yards of fabric. What
is the greatest number of pillows
Gretchen can make?
O A 4
OB 5
C 6
OD 8