A right triangular prism is shown.
A right triangular prism is shown. The right triangles have sides with lengths 15 and 8. The hypotenuse has a length of 17. The height of the prism is 15.
What is the volume of the prism?
900 cubic units
1,020 cubic units
1,800 cubic units
2,312 cubic units
Answers
Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.
What precisely is volume?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.
Here,
The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.
The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.
=> B = (1/2)bh = (1/2)(8)(15) = 60
The prism's height is specified as 15 inches.
As a result, the prism's capacity is:
=> 900 cubic units are equal to V = Bh = 60(15).
Therefore, the response is 900 cubic units.
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Answer:
900 cubic units
Step-by-step explanation:
Related Questions
An unfair coin with Pr[H]=23 is flipped. If the flip results in a head, then a marble is selected from an urn containing 6 red, 9 white, and 10 blue marbles. If the flip results in a tail then a marble is selected from an urn containing 10 red and 1 white marbles. If the marble selected is white, then what is the probability that a flip resulted in a head?
Answers
The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.
Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.
Using Bayes' theorem, we have:
Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]
Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.
Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:
Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]
= (9/25)*0.23 + (1/11)*0.13
= 0.0888 + 0.0118
= 0.1006
Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.
Therefore,
Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508
Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).
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in exercises 1-8 solve the inequality graph the solution
1. 6x < -30
Answers
Step-by-step explanation:
x<-5 is the answer
1.
6x=-30
2.
x=-5
3.
x<-5
A geometric sequence has first term 5 and common ratio 2. the sum of the first n terms of the sequence is 163 835. What is n ? [Answer format: integer, no units]
Answers
First term in a geometric sequence is 5, and common ratio is 2. The sum of the first n terms of the sequence is 163,835.
The following formula can be used to calculate the sum of the first n terms of a geometric sequence:
Sn = a (1 - rn) over (1 - r),
where
a is the first term,
r is the common ratio, and
n is the number of terms.
So, Sn = a (1 - rn) over (1 - r) => 163835 = 5 (1 - 2n) over (1 - 2).
Simplifying it, we have
163835 = 5 (1 - 2n) over (-1)
=> 163835 = -5 + 10n
=> 163840 = 10n
=> n = 16,384.
Therefore, the value of n is 16,384.
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A shopkeeper bought 26 apples from a fruit vendor for $37.70.How much did each apple cost?
Answers
Answer: 1.45 Cents per (Rounded to the nearest cent)
Step-by-step explanation:
26 apples = $37.70
We want what one apple costs individually. The best way to do this is to divide both sides by 26.
1 apple = 37.70/26
1 apple = 1.45 Cents
PLEASE HELP!!
20 POINTS
A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost f(m)
is a function of the number of miles m
that the car is driven.
Plan A: f(m)= 0.12+75
Plan B: f(m)+0.35
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
Answers
Answer: At 250 miles, plan B is the most cost effective.
Step-by-step explanation:
Answers are under the questions below.
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
Plan A will charge .12 per mile plus a one time fee of $75.
Equation is y = .12x + 75 with the $75 being the y intercept or one time fee.
Plan B will charge .35 per mile with no one time fee.
Equation is y = .35x with the y intercept being (0) zero.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
Initially the Plan A will be more expensive because of the one time fee, even though the rate is .12 per mile, which is much less than Plan B.
Plan B charges .35 per mile, but will eventually catch up in cost.
At approximately 326 miles the cost of each plan will equal at $114.13.
After 326 miles, Plan B will cost more than Plan A.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
Plan A, substitute 250 miles for x
Cost = .12 (250) + 75
Cost = $105
Plan B, substitute 250 miles for x
Cost = .35 (250)
Cost = $87.50
At 250 miles, plan B is the most cost effective, saving $17.50.
graph is attached.
10 * x = 425
81729 / y = 898.12
What is X and Y?
I WILL GIVE BRAINLY IF U DONT USE CALCULATOR
Answers
The value of X is 42.5 and Y is 90.98.
How to solve equations?
To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:
Simplify both sides of the equation by combining like terms and following the order of operations.
Add or subtract the same value from both sides of the equation to isolate the variable term.
Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.
Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.
Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:
[tex]10x/10 = 425/10[/tex]
Simplifying the left side of the equation gives:
[tex]x = 42.5[/tex]
Therefore, X is 42.5.
To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:
[tex]81729 = 898.12 \times Y[/tex]
Simplifying the right side of the equation gives:
[tex]Y = 81729 / 898.12[/tex]
[tex]Y = 90.98[/tex]
Therefore, Y is 90.98.
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Which of the following statements most accurately describes the relationship between cultured yeast preparation conditions and fermented alcohol yield, based on passage data?Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield.A is correct. Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, with 10% glucose (not 12%, as in Broth C) and 8% yeast inoculate (not 10%, as in Broth B). Therefore, increasing neither glucose concentration nor percentage yeast inoculate led to more production of alcohol, so neither of those parameters showed a positive correlation with alcohol yield.
Answers
Based on the passage data, the most accurate statement describing the relationship between cultured yeast preparation conditions and fermented alcohol yield is: "Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield."
What this means is that increasing the concentration of glucose or percentage of yeast inoculate did not lead to more production of alcohol. The data in Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, which had 10% glucose and 8% yeast inoculation. Broth C, which had a higher concentration of glucose at 12%, did not result in a higher yield of alcohol. Similarly, Broth B, which had a higher percentage of yeast inoculate at 10%, did not lead to a higher yield of alcohol.
Therefore, it can be concluded that neither glucose concentration nor percentage of yeast inoculates was positively correlated with fermented alcohol yield.
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Sleep researchers know that some people are early birds (E), preferring to go to bed by 10 P.M. and arise by 7 A.M., while others are night owls (N), preferring to go to bed after 11 P.M. and arise after 8 A.M. A study was done to compare dream recall for early birds and night owls. One hundred people of each of the two types were selected at random and asked to record their dreams for one week. Some of the results are presented below. Group Mean Median Standard Deviation No dreams 5 or more dreams Early birds 7.26 6.0 6.94 0.24 0.55
Night owls 9.55 9.5 5.88 0.11 0.69 A) The researchers believe that night owls may have better dream recall than do early birds. Use the data provided to carry out a test of the hypotheses about the mean number of dreams recalled per week. Do the data support the researchers' belief? (5 pts) B) Compute a 92% confidence interval about the mean number of dreams recalled per week. (You do NOT need to re check the conditions) (5pts)
Answers
The answer is: A) The data support the researchers' belief that night owls have better dream recall than early birds. B) we can be 92% confident that the true difference in mean number of dreams recalled per week between night owls and early birds is between 1.87 and 2.63.
A) These are the alternative and null hypotheses:
H0: μE = μN (the mean number of dreams recalled each week is the same for early birds and night owls) (the mean number of dreams recalled per week is the same for early birds and night owls)
Ha: μE < μN (the mean number of dreams recalled each week is smaller for early birds than for night owls) (the mean number of dreams recalled per week is lower for early birds than for night owls)
Using the following formula, we can run a two-sample t-test with unequal variances:
t = [(sN2 / nN) + (sE2 / nE)] / sqrt[(xN - xE)]
where nN and nE are the sample sizes for night owls and early birds, respectively, and xN and sN and xE and sE are the sample means and standard deviations for night owls and early birds, respectively.
When we enter the values, we obtain:
t = (9.55 - 7.26) / sqrt[(5.88^2 / 100) + (6.94^2 / 100)] = 5.01
The data are consistent with the researchers' hypothesis that night owls are more capable of remembering their dreams than early birds.
B) We can use the following formula to determine the confidence interval:
CI is equal to (xN - xE) t/2 * sqrt[(sN / nN) + (sE / nE)].
where t/2 is the t-value for the required level of confidence and degrees of freedom, and xN, xE, sN, sE, nN, and nE are the same as previously (198 in this case).
With a t-value of 1.75 and a 92% confidence level (from a t-distribution with 198 degrees of freedom), we get:
CI is equal to (9.55 - 7.26) 1.75 * sqrt[(5.88 - + 6.94 / 100)] = (1.87, 2.63) (1.87, 2.63)
The genuine difference between night owls and early birds in terms of the average number of dreams recalled per week is therefore between 1.87 and 2.63, with a 92% confidence interval.
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Select THE TWO values of that are solutions to the equation (* - 5) (7x - 21) = 0.
Answers
According to the zero product property, if the product of two factors is equal to zero, then at least one of the factors must be zero.
So, we can set each factor equal to zero and solve for x:
(*) - 5 = 0 or 7x - 21 = 0
Solving for (*) in the first equation, we get:
(*) = 5
Solving for x in the second equation, we get:
7x = 21
x = 3
Therefore, the two values of x that are solutions to the equation are x = 3 and (*) = 5.
Step 1 of 3
a.
About 180,000 terawatts of solar power reaches Earth’s surface.
Out of which about 0.06% is used by plants for photosynthesis.
Thus 108 terawatts of solar power is used by plants for photosynthesis.
Of this energy, about ends up stored in plant matter
Thus 1.08 terawatts of energy get stored in plant matter.
Consider the following facts
Therefore,
Therefore joules of energy get stored in plant matter each second.
Answers
The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
Step 1: Calculation of joules of energy stored in plant matter each secondGiven that, 1.08 terawatts of energy gets stored in plant matter for photosynthesis in a second.Therefore, 1.08 × 1012 watts of energy gets stored in plant matter each second. Also, the energy stored in plants matter in Joules = Watts × seconds (Joule is the unit of energy)1.08 × 1012 watts of energy stored in plant matter in a second.1 watt-second = 1 JouleEnergy stored in plant matter in a second = 1.08 × 1012 watts × 1 second = 1.08 × 1012 Joules Answer: The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
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8. Points P, Q, whose abscissae are 2 and 2+h, are taken on the curve y = 2x^2+1. Find the gradient of the chord PQ. To what value does this gradient approach as h decreases towards the value zero?
Answers
The gradient of the chord PQ is 2h + 8
What is the gradient of the chord?Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.
Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).
Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).
The gradient of the chord PQ is given by:
(m) = Δy /Δx
(m) = (2h^2+8h+9 - 9) / (2+h - 2)
(m) = (2h^2+8h) / (h)
(m) = 2h + 8
As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.
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How do you work this out?
Anyone help please .
Answers
Answer:
x=5/4 or x=5/9
pls mark me brainliest
Answer:
x=5/4 (for the first x),x=5/9 (for the second x)
It takes 120 unit cubes to completely fill a rectangular prism. The prism is 10 unit cubes high. What are the other possible dimensions of the rectangular prism?
Answers
the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:
V = l × w × 10
We are also given that the prism requires 120 unit cubes to fill completely, which means:
V = l × w × 10 = 120
Dividing both sides by 10, we get:
l × w = 12
Now we need to find pairs of positive integers l and w that multiply to 12. These are:
1 × 12
2 × 6
3 × 4
Therefore, the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.
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I need help with this
Answers
Therefore , the solution of the given problem of function comes out to be he function's average rate of change over the range 3 x 4 is 4.
Describe function.There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.
Here,
Calculate the difference between the function values at
=> x = 4 and x = 3, then split by the difference in x-values,
which is 4 - 3 = 1, to determine the average rate of change of the function over the range 3 x 4.
We can see from the table that f(4) = -5 and f(3) = -9. As a result, the following function numbers are different:
=> f(4) - f(3) = (-5) - (-9) = 4
=> 4 - 3 = 1 represents the x-value disparity.
Therefore, the function's average rate of change over the period 3 x 4 is:
Average rate of change is equal to
=> (f(4)-f(3))/(4-3) = 4/1 = 4.
Consequently, the function's average rate of change over the range 3 x 4 is 4.
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A company is buying new computers. The company needs no more than 220 desktops and at least 50 laptops. A total of at least 200 computers must be bought. Write a system of linear inequalities to represent the constraints of this situation. Let x represent the number of desktops, and let y represent the number of laptops.
Answers
x ≤ 220 (no more than 220 desktops)
y ≥ 50 (at least 50 laptops must be bought)
(a) In the figure below, m CED=50° and m AB = 140°. Find m CD.
(b) In the figure below, m VYW=36 and m VX = 62. Find m VW
Answers
a) Measurement of arcCD is 40°
b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]
50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]
36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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the graph represents the number of different tacos ordered for an office lunch. in total, how many tacos were ordered?
Answers
Answer:
do you have the graph to solve it?
1. If f = {(0,2), (-3,2), (2,5)} and g = {(3,4), (1,5), (-1,2)}, Find: f+g
Answers
Answer:
Step-by-step explanation:
F = (-1,9)
G = (-3,11)
Are the given functions y1 and y2 linearly independent or linearly dependent on the interval (0, 1) and why? Choose the correct statement below. Yi = cscº(t) - cot? (t), y2 = 9a. Since yi = - 42 on (0, 1), the functions are linearly independent on (0,1). b. Since yı = 5y2 on (0,1), the functions are linearly independent on (0,1). c. Since yı = 3y2 on (0,1), the functions are linearly dependent on (0,1). d. Since yi = - Žy2 on (0, 1), the functions are linearly dependent on (0,1).
Answers
The given functions [tex]y_1[/tex] and [tex]y_2[/tex] are linearly dependent on the interval (0, 1)
(a) Since [tex]y_1 = -42[/tex] on (0,1), the functions are linearly independent on (0,1).
This option does not make sense because [tex]y_1[/tex] is not always -42 on the interval (0,1).
(b) Since [tex]y_1 = 5y_2[/tex] on (0,1), the functions are linearly independent on (0,1).
This option is not correct because if we substitute y1 with 5y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex], we get [tex]5c_2 y_2 + c_2 y_2 = 0,[/tex] which means we can write [tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
(c) Since [tex]y_1 = 3y_2[/tex] on (0,1), the functions are linearly dependent on (0,1)."
To see why, we can substitute [tex]y_1[/tex] with [tex]3y_2[/tex] in the equation [tex]c_1 y_1 + c_2 y_2 = 0[/tex]:
[tex]c_1 (3y_2) + c_2 y_2 = 0[/tex]
Simplifying this, we get:
[tex](3c_1 + c_2) y_2 = 0[/tex]
Since [tex]y_2[/tex] is not equal to 0 for any value of t in the interval (0,1), this means that [tex]3c_1 + c_2[/tex] must equal 0. This is a non-trivial solution for [tex]c_1[/tex] and [tex]c_2[/tex], which means that [tex]y_1[/tex] and[tex]y_2[/tex] are linearly dependent on the interval (0,1).
(d) Since[tex]y_1 = -1/2 y_2[/tex]on (0,1), the functions are linearly dependent on (0,1).
This option is also correct because if we substitute [tex]y_1[/tex] with -1/2 y2 in the equation [tex]c_1 y_1 + c_2 y_2 = 0,[/tex] we get [tex]-1/2 c_2 y_2 + c_2 y_2 = 0[/tex], which means we can write[tex]y_1[/tex]as a constant times [tex]y_2[/tex], so they are dependent.
Therefore, the correct answer is either option d, and the functions [tex]y_1[/tex] and [tex]y_2[/tex] are dependent on the interval (0,1).
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pls help find y. 4x+5y-y+3x
Answers
Answer:
7x+4y
Step-by-step explanation:
combine like terms
Answer:
4?
Step-by-step explanation:
use the relationships in the diagram to solve for t. Justify your solution with a definition or theorem
Answers
Answer:
The value of t = 18
Step-by-step explanation:
202 = 2t + 5 + t + 3t - 2 + 5t +1 Combine like terms
202 = 11t + 4 Subtract 4 from both sides
198 = 11[tex]\frac{11x}{11}[/tex]x Divide both sides by 11
[tex]\frac{198}{11}[/tex] = 18
Is the question the value of t or the length of each side?
Each side
2t + 5
2(18) + 5
41
T
18
3T - 2
3(18) - 2
52
5T + 1
5(18) + 1
91
91 + 52 + 18 + 41 = 2002
Helping in the name of Jesus.
Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?
Answers
The conic section that formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle
When a plane intersects the central axis of a double-napped cone at a 90° angle, the resulting conic section is a circle.
To understand why this is the case, we can first consider the properties of a double-napped cone. A double-napped cone is formed by rotating a straight line, called the generatrix, around an axis that intersects the line at a fixed point, called the vertex. The resulting surface consists of two parts, each of which is a circular cone.
Now, let us imagine a plane that intersects the central axis of the double-napped cone at a 90° angle. Since the central axis of the cone is perpendicular to the base, the plane must intersect both cones at their widest point, which is also their center. At this point, the cone has a circular cross-section, which means that the plane intersects the cone in a circle.
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Answer:
circle
got it right on edg
A triangle has a base that measures 6.4 feet. Its height measures 5 feet. How many square feet is the area of the triangle?
Answers
Answer:
16 feet
Step-by-step explanation:
Area of triangle = 1/2(a x b)
A = 1/2(6.4 x 5)
A = 32/2
A = 16 feet
A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm
Answers
the area of the shaded region is approximately 37.68 cm².
define area of circleThe area of a circle is the amount of space that is enclosed by the circle in a two-dimensional plane. It is defined as the product of the square of the radius (r) of the circle and the mathematical constant pi (π), which is approximately equal to 3.14159.
The area of the larger circle is:
A1 = π(4 cm)² = 16π cm²
The area of the smaller circle is:
A2 = π(2 cm)² = 4π cm²
To find the area of the shaded region, we subtract A2 from A1:
A1 - A2 = 16π cm²- 4π cm² = 12π cm²
To round the final answer to the nearest hundredth, we can use the approximation π ≈ 3.14:
12π cm² ≈ 12 × 3.14 cm² ≈ 37.68 cm²
Therefore, the area of the shaded region is approximately 37.68 square centimeters.
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A farmer sells cows for $350 each and chickens for $75 apiece. At market, he sold 11 animals for a total of $2475. How many of each animal were sold?
Answers
Answer:
Let's use algebra to solve this problem.
Let's start by defining some variables to represent the number of cows and chickens the farmer sold. Let c be the number of cows and h be the number of chickens. We know that the farmer sold a total of 11 animals, so:
c + h = 11 (Equation 1)
We also know that the total amount of money the farmer received was $2475. The amount he received from selling cows was $350 times the number of cows, or 350c. The amount he received from selling chickens was $75 times the number of chickens, or 75h. So:
350c + 75h = 2475 (Equation 2)
Now we have two equations with two unknowns. We can solve for one variable in terms of the other in the first equation:
c + h = 11
c = 11 - h
We can substitute this expression for c into the second equation:
350c + 75h = 2475
350(11 - h) + 75h = 2475
Simplifying and solving for h:
3850 - 350h + 75h = 2475
-275h = -1375
h = 5
So the farmer sold 5 chickens. We can substitute this value of h back into the first equation to find c:
c + h = 11
c + 5 = 11
c = 6
Therefore, the farmer sold 6 cows and 5 chickens.
Calvin ordered scissors. Each pair of scissors weighs 0. 34 kg. A box of scissors weighs
64. 6 kg. How many pairs of scissors come n each box?
Answers
190 pairs of scissors came in each box.
This is an example of a word problem. As a model, a word problem depicts circumstances from the actual world that may be converted into phrases.
Weight of each pair of scissors = 0.34 kg
Weight of a box of scissors = 64.6 kg
Therefore, pairs of scissors in each box = Weight of a box of scissors ÷
Weight of each pair
= 64.6 ÷ 0.34
= 190 pairs.
Hence, 190 pairs of scissors came in each box.
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Understanding and Interpreting Confidence Intervals a Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college. She finds a 95% confidence interval for the mean systolic blood pressure to be (108.6, 120.3) mm Hg. Which statement below incorrectly conveys the meaning of the confidence interval? She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. O She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. Hint Assistance Used Use the definition of a 95% confidence interval.
Answers
The Statement 1: She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. This statement is accurate and conveys the meaning of a 95% confidence interval.
The confidence interval is the range of values within which a statistical parameter is estimated to be accurate with a certain level of confidence.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college.
Statement 2: She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. This statement is inaccurate because the confidence interval obtained from the sample cannot be generalized to the entire population of students.
The correct statement should mention that the confidence interval is only for the random sample.Statement 2 is the incorrect statement.
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what is the equation for pattern 2
Answers
Therefore , the solution of the given problem of equation comes out to be the number of dots is filled in below table.
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a single formula that separates 12 into two parts and can be used to assess received from y + 7, normalization in this case yields b + 7.
Here,
Given : A table with number of dots can be filled by this:
Here are the number of dots in each pattern:
Pattern Number of dots
1 4
2 7
3 10
4 13
5 16
6 19
7 22
8 25
9 28
10 31
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57
Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The test statistic based on the number of students who preferred to get out early equals
Group of answer choices
1.825
0.67
0.82
3.65
Answers
The test statistic based on the number of students who preferred to get out early equals 3.65.
What is a test statistic?A test statistic is a numerical summary of the sample data that is employed to determine the strength of the evidence for a hypothesis. It is a quantitative measure that compares the observed data to the hypothesis. The t-value, Z-score, F-value, and chi-squared value are examples of common test statistics. In statistical hypothesis testing, a test statistic is used to make decisions about whether or not to reject the null hypothesis.
Based on the given problem, the number of students who preferred to get out of class early is 80, while the number of students who preferred a 10-minute break is 40. Hence, the number of students who had no preference is 30.
Now, we will find the test statistic based on the number of students who preferred to get out of class early as follows:
Test Statistic = (Observed Value - Expected Value) / Standard Deviation
To find the observed value, we need to calculate the proportion of students who preferred to get out of class early in the sample as follows:
Proportion of students who preferred to get out of class early = 80 / (150-30)= 80 / 120= 0.67
Therefore, the observed value is 0.67.
To find the expected value, we need to assume that there is no difference in students' preferences, and the proportion of students who preferred to get out of class early is the same as the proportion of students who preferred a 10-minute break.
Expected value = Proportion of students who preferred to get out of class early * Total number of students= 0.5 * 150= 75
Therefore, the expected value is 75.
To find the standard deviation, we need to use the formula for the standard deviation of a proportion as follows:
Standard Deviation = √[(p*q) / n]
where p is the proportion of students who preferred to get out of class early, q is the proportion of students who preferred a 10-minute break, and n is the total number of students.
Standard Deviation = √[(80/120)*(40/120) / 150]= √(0.1778 / 150)= 0.048
Therefore, the standard deviation is 0.048.
Now, we will substitute the values in the formula for the test statistic as follows:
Test Statistic = (0.67 - 0.5) / 0.048= 3.65
Therefore, the test statistic based on the number of students who preferred to get out early equals 3.65.
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Whatis the value of # y_ When y = 5 and x = 10?
Answers
The value of y when x=36 is 31/3.
According to the question,
x varies directly with 3y+5
Thus,
[tex]x = k(3y+5)[/tex]
where K is any positive integer.
Now, from the question,
y=5/3 when x=10
Thus,
[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]
Now we can use k to find the value of y when x=36:
[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]
In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.
Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.
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Complete Question:
If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36
