[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-5}{h}~~,~~\underset{9}{k})}\qquad \stackrel{radius}{\underset{14}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-5) ~~ )^2 ~~ + ~~ ( ~~ y-9 ~~ )^2~~ = ~~14^2\implies (x+5)^2 + (y-9)^2=196[/tex]
Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.
Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.
The formula for the surface area of a cylinder is:
S = 2πr^2 + 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.
To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.
However, we can use Monique's estimate to estimate the values of r and h.
1001.66 = 2πr^2 + 2πrh
Dividing both sides by 2π, we get:
500.83 = r^2 + rh
We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.
For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:
500.83 = 5^2 + 5h
495.83 = 5h
h = 99.166
So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:
S = 2π(5^2) + 2π(5)(99.166)
S = 1570.8 square feet
This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.
Step-by-step explanation:
The volume of a cylinder is given by the formula v - pi^h, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?
The expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases. The cylinder can be thought of as a tube or a can. The lateral surface of the cylinder is formed by "unrolling" a rectangular shape along the circumference of the base.
There appears to be a typographical error in the given formula for the volume of a cylinder. The correct formula is:
V = π[tex]r^{2}[/tex]h
where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
Using this formula, the expression that represents the volume of the cylinder is:
V = π[tex]r^{2}[/tex]h
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in an integer overflow attack, an attacker changes the value of a variable to something outside the range that the programmer had intended by using an integer overflow.T/F
True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.
This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.
As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.
This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.
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What is the argument of z = StartFraction 1 Over 16 EndFraction minus StartFraction StartRoot 3 EndRoot Over 16 EndFraction i?
To find the argument of the complex number z = 1/16 - (sqrt(3)/16)i, we need to find the angle that the complex number forms with the positive real axis in the complex plane.
We can start by finding the magnitude of z, which is the distance between the origin and the point representing z in the complex plane:
|z| = sqrt( (1/16)^2 + (sqrt(3)/16)^2 )
= sqrt(1/256 + 3/256)
= sqrt(4/256)
= 1/4
Next, we can find the argument of z using the formula:
arg(z) = tan^(-1)(Im(z)/Re(z))
where Im(z) is the imaginary part of z, and Re(z) is the real part of z.
In this case, we have:
Re(z) = 1/16
Im(z) = -(sqrt(3)/16)
Therefore, we get:
arg(z) = tan^(-1)(Im(z)/Re(z))
= tan^(-1)(-(sqrt(3)/16)/(1/16))
= tan^(-1)(-sqrt(3))
= -60° (in degrees)
So, the argument of z is -60 degrees (or -π/3 radians).
Answer:
A
Step-by-step explanation:
Evaluate the expression when x = 7 (4x + 9) - 4(x - 1) + x use the answer choices in the diagram
Answer:
The answer is 20
Step-by-step explanation:
when x=7
(4x+9)-4(x-1)+x
(4(7)+9)-4(7-1)+7
28+9 -4(6)+7
37+7-24
44-24
=20
armer abe has a budget of $300 to build a rectangular pen to protect his rambunctious sheep. he decides that three sides of the pen will be constructed with chain-link fence, which costs only $1 per foot. farmer abe decides that the fourth side of the pen will be made with sturdier fence, which costs $5 per foot. find the dimensions of the largest area the pen can enclose.
Let x be the length of the pen and y be the width of the pen.
The total cost of the pen is given by:
Cost = 3x + 5y = 300
3x + 5y = 300
3x = 300 - 5y
x = (300 - 5y)/3
The area of the pen is given by:
Area = xy = (300 - 5y)/3 * y
a plumber works twice as fast as his apprentice. after the plumber has worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later. how many hours would it have taken the plumber to do the entire job by himself?
If after the plumber has worked alone for 3 hours, his apprentice joins him and working together they complete the job 4 hours later, it would take the plumber 9 hours to do the entire job by himself.
Let's start by assigning some b to represent the rate at which each person works. Let's say that the plumber's rate is P (in units of job per hour) and the apprentice's rate is A (also in units of job per hour). Since the plumber works twice as fast as the apprentice, we can write:
P = 2A
Next, let's think about how much work can be done in a certain amount of time. If the plumber works alone for 3 hours, he completes 3P units of work. When the apprentice joins him, they work together for another 4 hours to complete the entire job, which is a total of 7 hours of work. So, the amount of work done in those 4 hours is:
4(P + A)
We also know that the total amount of work is 1 (since it's one complete job). Putting this all together, we can write an equation:
3P + 4(P + A) = 1
We can simplify this to:
7P + 4A = 1
But we also know that P = 2A, so we can substitute that in:
7(2A) + 4A = 1
Simplifying this, we get:
18A = 1
So, A = 1/18. This means that the apprentice can complete 1/18 of the job in one hour. Since the plumber works twice as fast, he can complete 2/18 of the job (or 1/9) in one hour.
To find out how long it would take the plumber to do the entire job by himself, we can use the formula:
Time = Work / Rate
The entire job is 1, and the plumber's rate is 1/9. So:
Time = 1 / (1/9) = 9 hours
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a slide caliper has 32 divisions per inch and a vernier of 8 divisions per major division. for this instrument the smallest resolution and uncertainty are:
The smallest resolution for this instrument is 1/256 inches.
This is also the instrument's uncertainty, as it represents the smallest measurable increment.
Let's first understand the terms mentioned:
Slide caliper:
A measuring instrument with a main scale and a vernier scale for taking precise measurements.
Divisions per inch:
The number of equal divisions on the main scale in one inch.
Vernier:
A short auxiliary scale that slides along the main scale, allowing for more precise readings.
Divisions per major division:
The number of equal divisions on the vernier scale that correspond to one division on the main scale.
Now, let's determine the smallest resolution and uncertainty for this instrument.
Calculate the main scale resolution
Main scale resolution = 1 inch / 32 divisions per inch = 1/32 inches
Calculate the vernier scale resolution
Vernier scale resolution = Main scale resolution / Vernier divisions per major division = (1/32 inches) / 8 = 1/256 inches.
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Gemma can't type 350 words in five minutes how many words can she type in 3/4 of an hour
Answer:
Gemma can type 3150 words in 3/4hr
Step-by-step explanation:
350 word------>five minutes
x words------->3/4hr
convert 3/4hr-minutes
3/4×60=45minutes
x word =350×45/5
x word=3,150 words
A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
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pls pls help. just need the answer
The value of k is given as follows:
k = 5.
How to obtain the value of k?The function in the context of this problem is defined as follows:
f(x) = x³ + kx - 6.
We have that x - 1 is a factor of the function, meaning that, by the Factor Theorem:
f(1) = 0, x - 1 = 0 -> x = 1.
Hence, applying the numeric value, the value of k is obtained as follows:
1 + k - 6 = 0
k - 5 = 0
k = 5.
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the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3. the probability there are 8 occurrences in 10 minutes is . a. .0771 b. .0241 c. .1126 d. .9107
The probability of having 8 occurrences in 10 minutes is approximately 0.0241, which means the answer is (b).
The number of occurrences of an event in 10 minutes as a Poisson distribution with mean lambda = 5.3.
The probability of having 8 occurrences in 10 minutes is:
[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8![/tex]
where X is the random variable representing the number of occurrences of the event in 10 minutes.
Using a calculator, we can evaluate this expression:
[tex]P(X = 8) = (e^(-5.3) * 5.3^8) / 8! ≈ 0.0241[/tex]
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What are the cross-products of the proportion 6/40 = 9/60? Is the proportion TRUE?
54 and 2,400; the proportion is false.
54 and 540; the proportion is true.
360 and 360; the proportion is true.
Therefore, the answer is: 360 and 360; the proportion is true.
54 and 540; the proportion is true.
360 and 360; the proportion is true.
To find the cross-products of the proportion 6/40 = 9/60, we multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
So we have:
6 × 60 = 360
9 × 40 = 360
The cross-products are 360 and 360.
To check if the proportion is true, we compare the cross-products. If they are equal, then the proportion is true; otherwise, it is false.
Since the cross-products are equal, the proportion is true.
Therefore, the answer is:
360 and 360; the proportion is true.
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3(x + y) = y
If (x, y) is a solution to the equation above and
y = 0, what is the ratio * ?
The answer to this question is x:0
Which of the following ratios is in proportion to the ratio 3:4? (choose any that work)
5:6
12:14
12:16
6:7
4:5
6:8
Answer: 12:16
Step-by-step explanation: If you simply the ratio by dividing each side by 4 you are left with 3:4
Answer: 12:16,6:8
Step-by-step explanation:
simplify
12:16=3:4
6:8=3:4
14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?
Answer:
Speed= 500ml/hr
total distance= 2800 m
total time = d/t
2800/500= 5.6hrs
Step-by-step explanation:
in a recent basketball game, shenille attempted only three-point shots and two-point shots. she was successful on 20% of her three-point shots and 30% of her two-point shots. shenille attempted 30 shots. how many points did she score?(2013 amc 12a
The probability of a score for a recent basketball game, shenille attempted only three-point shots and two-point shots is 18 points in the game. The answer is Option B.
Let x be the number of three-point shots and y be the number of two-point shots attempted by Shenille.
Then, we have:
x + y = 30 (total number of shots attempted)
Let's solve for one of the variables. For example, we can solve for x by subtracting y from both sides of the equation:
x = 30 - y
Now, we can express Shenille's points in terms of x and y:
Points = 3x + 2y
Substituting x = 30 - y, we get:
Points = 3(30 - y) + 2y
Points = 90 - y
Shenille's success rate for three-point shots is 20%, so the number of successful three-point shots she made is 0.2x. Similarly, the number of successful two-point shots she made is 0.3y.
Total points scored = (0.2x)(3) + (0.3y)(2)
Substituting x = 30 - y, we get:
Total points scored = (0.2(30 - y))(3) + (0.3y)(2
Total points scored = 18 + 0.4y
Now we need to maximize the total points scored by Shenille. Since she attempted 30 shots in total, we have:
y = 30 - x
Substituting this into the equation for total points, we get:
Total points scored = 18 + 0.4(30 - x)
Total points scored = 30 - 0.4x
This is a linear function, which is maximized at its endpoint. The maximum value of this function occurs at x = 0, which means Shenille attempted all two-point shots. In this case, y = 30, and the total points scored would be:
Total points scored = 0 + 0.3(30)(2)
Total points scored = 18
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The question is -
In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on 20% of her three-point shots and 30% of her two-point shots. Shenille attempted 30 shots. How many points did she score?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
A rectangular plece of paper with length 28 cm and width 14 cm has two semicircles cut out of it, as shown below. Find the area of the paper that remains. Use the value 3.14 for 1, and do not round your answer. G ✓6 14 cm 0 00 H cm X 2023 McGraw Hill LLC As Rights Reserve
The area of the paper remains is 238.14 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the paper that remains, we use the formula below.
Formula:
Area of the paper that remains(A) = Area of the rectangle(LW)-Area of the two semi circles [π(W/2)²]A = LW- [π(W/2)²]................ Equation 1Where:
L = Length of the rectangleW = Width of the rectangle = Diameter of the semi circleFrom the diagram in the question,
Given:
L = 28 cmW = 14 cmSubstitute these values into equation 1
A = (28×14)-[3.14(14/2)²A = 392-153.86A = 238.14 cm²Hence, the area is 238.14 cm².
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A=P(1+r/n)^nt Find how long it takes for $1400 to double if it is invested at 7% interest compounded monthly. Use the formula A = P to solve the compound interest problem. TE The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)
It will take 10 years to double the amount.
Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,
[tex]A = P(1+r/n)^{nt}[/tex]
[tex]2800 = 1400(1+0.0058)^{12t}[/tex]
[tex]2= (1.0058)^{12t[/tex]
㏒ 2 = 12t ㏒ (1.0058)
0.03 = 12t (0.0025)
12t = 120
t = 10
Hence, it will take 10 years to double the amount.
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From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.
fuel efficiency of manual and automatic cars, part i. each year the us environmental protection agency (epa)releases fuel economy data on cars manufactured in that year. below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? assume that conditions for inference are satisfied.
Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
What is the explanation for the above response?
To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.
The t-test statistic is calculated as follows:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the values from the given statistics, we get:
t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))
t = -3.31
Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.
Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.
Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
identify the following equations as increasing linear, decreasing linear, positive quadratic, negative quadratic, exponential growth, or exponential decay.
(please help )
The types of equations in the question based on the values of the base, the slope and leading coefficients of the equations are;
11. Exponential growth
12. Exponential growth
13. Decreasing linear
14. Positive quadratic
15. Increasing linear
16. Exponential growth
17. Exponential decay
18. Exponential decay'
19. Positive quadratic
20. Linear increasing
21. Exponential growth
22. Negative quadratic
23. Negative quadratic
24. Exponential decay
What is an equation?An equation is a statement that indicates that of two expressions are equivalent, by joining them with an '=' sign.
11. The exponential equation is; y = (5/2)ˣ
The growth or decay factor, which is the base is; (5/2) > 1, therefore, the equation is an exponential growth equation
12. The exponential equation is; y = (1/4) × 3ˣ
3 > 1, therefore the equation is an exponential growth function
13. The equation y = -2·x -10 is a linear equation with a negative slope of -2, indicating that the value of y is decreasing as x increases, therefore, the equation is decreasing linear
14. The equation, y = 2·x² + 5·x - 7, which is a quadratic equation
The leading coefficient, 2, is positive, therefore, the equation is a positive quadratic equation
15. The equation y = 4·x - 3 has a positive slope, of 4, therefore, it is an increasing linear equation
16. The exponential equation (2/5)·9ˣ, with 9 > 1, is an exponential growth equation
17. The equation 3·(1/4)ˣ, with (1/4) < 1, is an exponential decay equation
18. The equation 2·(0.1)ˣ, with 0.1 < 1, is an exponential decay equation
19. The equation y = (x + 2)² is a quadratic equation
(x + 2)² = x² + 4·x + 4
The leading coefficient is 1, therefore, the equation is a positive quadratic equation
20. The linear equation 4·x + y = 7 with a positive slope of +4 indicates that the y-value of the function is increasing as the x-value of the equation is increasing, therefore, the function is an increasing linear equation
21. The exponential equation, y = 2·5ˣ, with 5 > 1, and 2 > 0, is an exponential growth equation.
22. The equation y = -(x - 3)² is a quadratic equation. The minus sign in front of the expression (x - 3) indicates that the leading coefficient, obtained by expansion, is negative
y = -(x - 3)² = -(x² - 6·x + 9) = -x² + 6·x - 9
The leading coefficient is -1, therefore the equation negative quadratic
23. The equation, y = -6·x² -5·x + 4, with a leading coefficient of -6 is a negative quadratic equation
24. The exponential equation, y = (1/7)·(3/8)ˣ, with (1/7) > 0 and (3/8) < 1 is an exponential decay equation
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brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
a client is receiving an iv solution of 2 grams of medication diluted in 100 ml of normal saline over a one hour time period. how many mg of medication is the client receiving per minute? (enter numeric value only. if rounding is required, round to the nearest whole number.)
The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.
Here 2g of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,
Concentration of 1 ml = 2/100 = 0.02 g/ml
It is delivered over a period of 1 hour. So, the amount delivered per minute will be,
Amount per minute = Volume/ time = 100/60 = 1.67 ml
Amount of medication in 1.67 ml = Volume × Amount per ml
= 1.67 × 0.02 = 0.334 g
So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.
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Keyana puts beads at the ends of her braids. On a single braid, she places 7 beads that are
each 1.03 centimeters long. Then she adds a final bead that is 0.9 centimeter long. The
expression below can be used to find the total length of the beads on one of Keyana's braids.
7 x 1.03 +0.9
What is the total length of the beads on one braid?
A 7.3 centimeters
B.8.11 centimeters
C.9.19 centimeters
D: 10.0 centimeters
The total length of the beads on one braid is 8.11 centimeters
What is the length?Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.
To find the total length of the beads on one braid, we need to evaluate the expression:
7 x 1.03 + 0.9
Multiplying 7 by 1.03 gives us:
7 x 1.03 = 7.21
Then, adding 0.9 gives us:
7.21 + 0.9 = 8.11
Therefore, the total length of the beads on one braid is 8.11 centimeters.
So, the correct answer is B.8.11 centimeters.
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please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
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A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? (5 points)
1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each
1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each
The volume of the rectangular prism is 1.6 cubic inches.
Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have
L = 1/5 × x
W = 1/5 × y
H = 1/5 × z
where x, y, and z are integers.
Since the rectangular prism is completely packed with 200 cubes, we have
x × y × z = 200
We want to find the volume of the rectangular prism, which is given by
V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z
Substituting x × y × z = 200, we get
V = 1/125 × 200 = 8/5 = 1.6 cubic inches
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The given question is incomplete, the complete question is:
A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the volume of this rectangular prism
Please help thank you
The values of sine, cosine, and tangent of the angle 'θ' are: sinθ = [tex]\frac{1}{2}[/tex],
cosθ = [tex]\frac{\sqrt{3}}{2}[/tex] and tanθ = [tex]\frac{1}{\sqrt{3} }[/tex] .
How to find trignometric ratios far an angle?To begin, determine the angle for which you wish to compute trigonometric ratios. Let's call the angle "θ".
Find the lengths of the sides of the right triangle that correspond to the angle "θ". Choose the trigonometric ratio you wish to calculate: sine (sin), cosine (cos), or tangent (tan).
Now, using the proper trigonometric formula, determine the needed ratio:
sin θ [tex]= \frac{Opposite side}{Hypotenuse }[/tex]
cos θ [tex]= \frac{Adjacent side }{Hypotenuse}[/tex]
tan θ [tex]= \frac{Opposite side }{Adjacent side}[/tex]
In the given problem, values for angle θ are-:
opposite side = 4 and Adjacent side = 4[tex]\sqrt{3}[/tex]
Using Pythagorean theorem to find the value of hypotenuse:
[tex]hypotenuse = \sqrt{(opposite^2 + adjacent^2)}[/tex]
[tex]hypotenuse=\sqrt{4^{2}+(4\sqrt{3})^2 } =\sqrt{16+48} =\sqrt{64} =8[/tex]
Now, putting values to find required trignometric ratios-:
sin θ[tex]= \frac{Opposite side}{Hypotenuse }=\frac{4}{8 }=\frac{1}{2}[/tex]
cos θ[tex]= \frac{Adjacent side }{Hypotenuse} =\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}[/tex]
tan θ [tex]= \frac{Opposite side }{Adjacent side}=\frac{4}{4\sqrt{3}}=\frac{1}{\sqrt{3} }[/tex]
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If you’re are doing a gift exchange, and everyone has to spend at least 10 dollars but less than 20 dollars, what inequality represents the situation?
A. 10 > x > 20
B. 10 ≤ x < 20
C. 10 ≥ x ≥ 20
D. 10 < x < 20
The correct inequality to represent the situation where everyone has to spend at least 10 dollars but less than 20 dollars in a gift exchange is 10 ≤ x < 20. (option b).
The correct inequality to represent the situation is B. 10 ≤ x < 20. This inequality reads "x is greater than or equal to 10, but less than 20". In other words, the amount of money each person spends (represented by x) must be at least 10 dollars, but cannot exceed 20 dollars.
To understand why this is the correct inequality, let's break it down. The symbol ≤ means "less than or equal to", and the symbol < means "less than". So, 10 ≤ x means "x is greater than or equal to 10", and x < 20 means "x is less than 20". Combining these two expressions gives us the inequality 10 ≤ x < 20, which represents the range of values that x can take on in this gift exchange.
Hence the correct option is (b).
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4. A bag of candy has 22 twix, 14 reeces, and 16 hersheys. Give a reduced ratio of non-twix to ALL candy.
Answer: 30/52 or 58%
Step-by-step explanation:
The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3
Answer: 15 non-twix to 26 total candy
Step-by-step explanation:
non twix: 14+16=30
all candy: 22+14+16=52
30:52
simplify
15:26