The numbers that are less than 3/7 are 1/8 and 3/10, while the numbers that are greater than 3/7 are 1/2 and 2/3. The decimal 0.102, which is equivalent to 51/500 as a fraction, is also less than 3/7.
To determine which of the given numbers are less than 3/7, we can convert them to fractions and compare them to 3/7.
12.5% is equivalent to 0.125 as a decimal or 1/8 as a fraction. To compare 1/8 and 3/7, we can convert them to a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite 1/8 as 7/56 and 3/7 as 24/56. Therefore, 1/8 is less than 3/7.
0.3 is equivalent to 3/10 as a fraction. To compare 3/10 and 3/7, we can also convert them to a common denominator. The least common multiple of 10 and 7 is 70, so we can rewrite 3/10 as 21/70 and 3/7 as 30/70. Therefore, 3/10 is less than 3/7.
50% is equivalent to 0.5 as a decimal or 1/2 as a fraction. To compare 1/2 and 3/7, we can convert 3/7 to a fraction with a denominator of 2. Multiplying the numerator and denominator of 3/7 by 2 gives us 6/14. Therefore, 1/2 is greater than 3/7.
2/3 is already a fraction, and we can compare it directly to 3/7. Multiplying the numerator and denominator of 3/7 by 3 gives us 9/21, and we can see that 2/3 is greater than 3/7.
0.102 is a decimal that is less than 1, but it can also be written as a fraction. To do so, we can place the decimal over 1 followed by the appropriate number of zeros. This gives us 102/1000, which can be simplified to 51/500. To compare 51/500 and 3/7, we can convert them to a common denominator. The least common multiple of 500 and 7 is 3500, so we can rewrite 51/500 as 357/3500 and 3/7 as 1500/3500. Therefore, 51/500 is less than 3/7.
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8. The scatter plot shows the relationship between the number
of chapters and the total number of pages for several books.
Use the trend line to predict how many pages would be in a
book with 19 chapters.
Pages
11
1220+----
1200
180+
160-
(140+
120-
100+
80
60+
40+
20+
Chapters
0 2
4 6 8 10 12 14 16 18 20
Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.
Step-by-step explanation:
Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.
A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.
This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).
Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.
For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:
y = 50(19) + 200
y = 950
So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.
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If st - sv, m∠sut - w + °10, and m∠suv =3w, what is m∠sut
If st - sv, m∠sut - w + °10, and m∠suv =3w, the measure of angle SUT is 52.5°.
Given the information provided, we can set up the following equations:
1) m∠SUT + m∠SUV = 180° (since they are supplementary angles)
2) m∠SUT = w + 10°
3) m∠SUV = 3w
Now we can substitute equations (2) and (3) into equation (1):
(w + 10°) + (3w) = 180°
Combining like terms, we get:
4w + 10° = 180°
Now, subtract 10° from both sides:
4w = 170°
Finally, divide both sides by 4:
w = 42.5°
Now we can find m∠SUT by substituting the value of w back into equation (2):
m∠SUT = 42.5° + 10°
m∠SUT = 52.5°
So, the measure of angle SUT is 52.5°.
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o produto de dois números é 54 seu MMC é 18 Qual o MDC desse número?
Porfavor explique
Answer:
o MDC de 6 e 9 é 3.
O produto de dois números é 54 e o seu MMC é 18. Precisamos encontrar o MDC desses dois números.
Primeiro, encontramos os dois números cujo produto é 54: 6 e 9.
Então, fatoramos cada número em seus fatores primos: 6 = 2 x 3 e 9 = 3 x 3.
O MDC de 6 e 9 é o produto dos fatores primos comuns, elevados à menor potência. Neste caso, o único fator primo comum é 3, elevado à primeira potência.
Portanto, o MDC de 6 e 9 é 3.
Which of the following options doesn't have the same value as the others explain? 10/100, 10%, 1/10, 0.01
Answer:
it should be 1/10 if that helps you
Answer:
0.01 does not have the same value as the others.
Step-by-step explanation:
10/100, 10%, and 1/10 is all the same. 0.01 is NOT the same because it is equal to 1/100, or 1% while the others were all equal to 10%. To figure this out, you must multiply 0.01 by 100 (or move the decimal point one space to the right two times) and we will get 1. This means that 0.01 is 1% which is also equal to 1/100, therefore it does not obtain the same value as the others.
A machine has an initial cost of $40,000 and operating costs of $3500 each year. Its salvage value decreases by $4,000 each year. The machine is now 4 years old.
Assuming an effective annual interest rate of 12%, what is the cost of owning and operating the machine for one more year.
The cost of owning and operating the machine for one more year is approximately $11,160.71.
To calculate the cost of owning and operating the machine for one more year, we need to consider both the operating costs and the decrease in salvage value.
The operating costs for one more year will be $3,500.
To calculate the decrease in salvage value, we need to know the salvage value of the machine after 4 years of use. If the salvage value decreased by $4,000 each year, then after 4 years the salvage value will have decreased by $16,000. Therefore, the salvage value of the machine after 4 years is:
Salvage value after 4 years = Initial salvage value - Total decrease in salvage value
Salvage value after 4 years = $40,000 - $16,000
Salvage value after 4 years = $24,000
To calculate the cost of owning and operating the machine for one more year, we need to consider the difference between the salvage value at the end of the additional year and the salvage value after 4 years. Assuming a straight-line depreciation model, the salvage value of the machine after one more year will be:
Salvage value after one more year = Salvage value after 4 years - (4 x $4,000)
Salvage value after one more year = $24,000 - $16,000
Salvage value after one more year = $8,000
To calculate the cost of owning and operating the machine for one more year, we need to calculate the present value of the difference between the salvage values, plus the operating costs for one more year. Assuming an effective annual interest rate of 12%, the present value can be calculated using the formula:
PV = FV / (1 + r[tex])^n[/tex]
where PV is the present value, FV is the future value, r is the effective annual interest rate, and n is the number of years.
The future value of the salvage value difference plus the operating costs for one more year is:
FV = Salvage value after one more year - Salvage value after 4 years + Operating costs for one more year
FV = $8,000 - $24,000 + $3,500
FV = -$12,500
(Note that the negative value indicates a cost.)
Plugging in the values, we get:
PV = -$12,500 / (1 + 0.12[tex])^1[/tex]
PV = -$11,160.71
Therefore, the cost of owning and operating the machine for one more year is approximately $11,160.71.
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Answer this question please ( Marking best answer brainiest )
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%.400 trials: 44/400 = 0.11 = 11%.The more trials, the closer the experimental probability should be to the theoretical probability.
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The holiday health club has reduced its annual membership by 10%. if jorge sanchez purchases a years membership and pays $270, what is the regular membership fee?
The regular membership fee of the Holiday Health Club is $300.
Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:
0.9x = 270
Solving for x, we get:
x = 270/0.9
x = 300
Hence, the regular membership fee of the Holiday Health Club is $300.
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Vanessa's team played 8 games of basketball. During those 8 games her team's score was: 68, 76, 63, 58, 64, 75, 78 and 78.
What is the mean absolute deviation?
Please help!! Please answer it correctly too!!!! Whoever gets it correct gets brainliest!! and then I will give them 154 points!!!! please!!
The mean absolute deviation is 6.25.
To find the mean absolute deviation (MAD), we first need to find the mean of the scores:
Mean = (68 + 76 + 63 + 58 + 64 + 75 + 78 + 78) / 8 = 69.5
Next, we need to find the absolute deviation of each score from the mean. The absolute deviation is the absolute value of the difference between the score and the mean.
For example, the absolute deviation of the first score (68) is:
|68 - 69.5| = 1.5
We can calculate the absolute deviation for each score:
|68 - 69.5| = 1.5
|76 - 69.5| = 6.5
|63 - 69.5| = 6.5
|58 - 69.5| = 11.5
|64 - 69.5| = 5.5
|75 - 69.5| = 5.5
|78 - 69.5| = 8.5
|78 - 69.5| = 8.5
To find the MAD, we take the average of the absolute deviations:
MAD = (1.5 + 6.5 + 6.5 + 11.5 + 5.5 + 5.5 + 8.5 + 8.5) / 8 = 6.25
Therefore, the mean absolute deviation is 6.25.
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Which expression represents the surface area of the prism?
Choose 1 answer:
Choose 1 answer:
(Choice A)
2
⋅
6
+
12
+
8
+
8
2⋅6+12+8+82, dot, 6, plus, 12, plus, 8, plus, 8
A
2
⋅
6
+
12
+
8
+
8
2⋅6+12+8+82, dot, 6, plus, 12, plus, 8, plus, 8
(Choice B)
2
⋅
3
+
3
⋅
8
2⋅3+3⋅82, dot, 3, plus, 3, dot, 8
B
2
⋅
3
+
3
⋅
8
2⋅3+3⋅82, dot, 3, plus, 3, dot, 8
(Choice C)
3
+
3
+
12
+
8
+
8
3+3+12+8+83, plus, 3, plus, 12, plus, 8, plus, 8
C
3
+
3
+
12
+
8
+
8
3+3+12+8+83, plus, 3, plus, 12, plus, 8, plus, 8
(Choice D)
12
+
12
+
12
+
3
+
3
12+12+12+3+312, plus, 12, plus, 12, plus, 3, plus, 3
D
12
+
12
+
12
+
3
+
3
12+12+12+3+3
Options A and C are ruled out because they don't even represent legitimate expressions for a prism's surface area. [tex]12 + 12 + 12 + 3 + 3.[/tex]Thus, option D is correct.
What is the surface area of the prism?The expression that represents the surface area of the prism depends on the dimensions of the prism. However, we can use the formula for the surface area of a rectangular prism, which is:
Surface Area [tex]= 2lw + 2lh + 2wh[/tex]
where l is the length, w is the width, and h is the height of the prism.
Looking at the answer choices:
A)[tex]2.6 + 12 + 8 + 8 = 28.6[/tex]
B)[tex]2.3 + 3.8 = 6.1[/tex]
C)[tex]3 + 3 + 12 + 8 + 8 = 34[/tex]
D)[tex]12 + 12 + 12 + 3 + 3 = 42[/tex]
We can eliminate options A and C because they are not even valid expressions for the surface area of a prism.
Option B is a valid expression for the surface area, but it is not simplified.
Option D is also a valid expression for the surface area, and it is simplified.
Therefore, the answer is (D) [tex]12 + 12 + 12 + 3 + 3.[/tex]
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G
Given: ABCD is a trapezoid.
BA CD
CA
Prove: BD
Proving Trapezoid Theorems
C
Pretests
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
ZBAD
Statements
ZCDA
Reasons
BD = CA is proved using the Pythagorean theorem.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
From the trapezium ABCD,
BA = CD ______(A)
Now,
We can have two triangles:
ΔABD and ΔACD
Using the Pythagorean theorem.
BD² = AB² + AD² _____(1)
And,
CA² = CD² + AD² ______(2)
From (1), (2), and (A).
BD² = BA² + AD²
CA² = BA² + AD²
This means,
BD² = CA²
BD = CA
Proved
Thus,
BD = CA can be Proven as above.
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Answer:
Step-by-step explanation:
After a teacher handed out
m packs of notebooks with c notebooks in each pack, he has 13 notebooks left. how many notebooks did he originally have?
The teacher originally had [tex]m*c + 13[/tex] notebooks.
How many notebooks the teacher originally had?If the teacher handed out m packs of notebooks with c notebooks in each pack, then the total number of notebooks that he gave out would be [tex]m*c[/tex].
If he gave out m packs of notebooks with c notebooks in each pack and has [tex]13[/tex] notebooks left, then the total number of notebooks he originally had would be:
[tex]m*c + 13[/tex]
Therefore, the expression for the total number of notebooks originally had by the teacher is [tex]m*c + 13[/tex].
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A cylinder has a height of 4 in and a base circumference of 12. What is the approximate volume of the cylinder? Round to the nearest whole number.
Answer: 48 inches
Step-by-step explanation:
Solve 2^{3-x} + 2^{x+1} =17
Log x + log (x+3) = 1
To solve the equation [tex]2^{3-x} + 2^{x+1} = 17[/tex] and the equation log x + log (x+3) = 1, We get the solution to the system of equations is x = 2. To check if x = 2 satisfies the first equation [tex](2^{3-x} + 2^{x+1} = 17).[/tex]
Solve the first equation, [tex]2^{3-x} + 2^{x+1} = 17.[/tex] Rewrite the equation as[tex]2^{3-x} = 17 - 2^{x+1}.[/tex] Take the logarithm of both sides (base 2): [tex]3-x = log2(17 - 2^{x+1})[/tex]. Rewrite the equation as [tex]x = 3 - log2(17 - 2^{x+1}).[/tex]
Solve the second equation, log x + log (x+3) = 1. Combine the logarithms: log(x(x+3)) = 1. Remove the logarithm by taking the exponent of both sides: x(x+3) = 10. The equation: x^2 + 3x = 10. Rearrange to form a quadratic equation:[tex]x^2 + 3x - 10 = 0.[/tex]
Factor the quadratic equation: (x+5)(x-2) = 0. Set each factor to zero: x+5 = 0 or x-2 = 0. Solve for x: x = -5 or x = 2. The solutions. Check if x = -5 satisfies the first equation [tex](2^{3-x} + 2^{x+1} = 17).[/tex]([tex]2^{3-x} + 2^{x+1} = 17)[/tex]. If it does not, discard it.
The solution to the system of equations is x = 2.
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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm. ii, Construct M the midpoint of XZ where XYZ= 60o. iii, Measure YM.
i) The angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm is constructed.
ii) M the midpoint of XZ where XYZ= 60 is constructed.
iii) The measure of YM is 6.3 cm
Firstly, you are asked to construct an angle XYZ where XY= 8.3 cm and YZ= 11.9 cm. To construct an angle, we need to follow a few steps.
Draw a line segment XY of length 8.3 cm.
At point Y, draw a ray YZ extending in the direction of Z.
Using a compass, draw an arc of radius 11.9 cm from point Y, intersecting the ray YZ at point Z.
The angle XYZ is the angle formed by the line segments XY and YZ.
Now, you need to construct the midpoint M of XZ. The midpoint of a line segment is the point that divides it into two equal parts. To construct the midpoint, we follow these steps:
Draw a line segment XZ joining points X and Z.
Using a compass, draw an arc of radius greater than half of XZ from point X.
Using the same radius, draw another arc from point Z intersecting the first arc at point P.
Draw a line through points X and P, and another line through points Z and P. These two lines will intersect at the midpoint M of line segment XZ.
Finally, you are asked to measure angle YM. To measure an angle, we use a protractor.
Draw a line segment YM.
Place the protractor at point Y with the base line of the protractor aligned with line segment YZ.
Read the angle measurement where line segment YM intersects the protractor.
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All juniors and seniors at a high school were surveyed about whether they had ever had a summer job. This graph shows the data from the survey. PART A Based on the graph, what is the total number of students who were surveyed?
The total number of students who were surveyed is 575
The graph likely displays a horizontal axis and a vertical axis.
In this graph, the horizontal axis may indicate two categories, such as "juniors" and "seniors," and the vertical axis shows the number of students in each category who responded "yes," "no," or "not sure."
To find the total number of students surveyed, we need to look for the bar that represents the entire group of juniors and seniors. Typically, this bar will be labeled as "total," "all," or something similar. Once we locate this bar, we can add up the number of students represented by the bar. The value will be displayed on the vertical axis, and it should correspond to the sum of the bars for juniors and seniors separately.
=> 100 + 200 + 125 + 150 = 575
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The point R(-2, 9) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point, R′?
The coordinates of the resulting point, R′ are R' = (-9, -2)
What are the coordinates of the resulting point, R′?From the question, we have the following parameters that can be used in our computation:
The point R(-2, 9) is rotated 90° clockwise around the origin.
This means thar
R = (-2, 9)
Rotation rule = 90° clockwise around the origin.
The rotation rule of 90° clockwise around the origin is
(x,y) becomes (y,-x)
So, we have
R' = (y, -x)
Substitute the known values in the above equation, so, we have the following representation
R' = (-9, -2)
Hence, the coordinates of the resulting point, R′ are R' = (-9, -2)
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Three stages at a music festival are arranged in a triangle. The distances between the centers of each stage are given: Stage A and Stage B: 100 yards Stage B and Stage C: 135 yards Stage C and Stage A: 210 yards List the interior angle measures formed at the center of each stage in descending order (largest to smallest). â
Answer:
BCA
Step-by-step explanation:
The interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.
Let's label the stages A, B, and C. To find the interior angles at each stage, we can use the Law of Cosines:
cos(A) = (b^2 + c^2 - a^2) / 2bc
cos(B) = (c^2 + a^2 - b^2) / 2ca
cos(C) = (a^2 + b^2 - c^2) / 2ab
where a, b, and c are the distances between the centers of the stages.
Using the given distances, we have:
a = 100, b = 135, c = 210
cos(A) = (135^2 + 210^2 - 100^2) / (2*135*210) ≈ 0.309
cos(B) = (210^2 + 100^2 - 135^2) / (2*210*100) ≈ -0.692
cos(C) = (100^2 + 135^2 - 210^2) / (2*100*135) ≈ -0.905
To find the interior angles, we can take the inverse cosine (also known as arccosine) of each value:
A ≈ 71.7 degrees
B ≈ 133.4 degrees
C ≈ 175.0 degrees
So the interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.
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The marginal cost function, in dollars per item, for producing the x th item of a certain brand of bar stool is given by MC(x)=20−0. 5 x , 0≤ x≤ 100. The fixed cost is $200. Estimating the total cost of producing 100 bars tools using the left-rectangle approximation with five rectangles, we conclude that the total cost is approximately $
The total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.
The marginal cost function for producing the x-th item of a certain brand of bar stool is given by MC(x) = 20 - 0.5x, where 0 ≤ x ≤ 100. To estimate the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles, we first need to calculate the width of each rectangle.
The width of each rectangle is (100 - 0) / 5 = 20.
Now, we will evaluate the marginal cost function at the left endpoints of each rectangle:
MC(0) = 20 - 0.5(0) = 20
MC(20) = 20 - 0.5(20) = 10
MC(40) = 20 - 0.5(40) = 0
MC(60) = 20 - 0.5(60) = -10
MC(80) = 20 - 0.5(80) = -20
Next, multiply each value by the width (20) and sum the results to approximate the variable cost:
Variable cost ≈ 20(20) + 10(20) + 0(20) + (-10)(20) + (-20)(20) = 400 + 200 - 200 - 400 = 0
Finally, add the fixed cost of $200 to the variable cost:
Total cost ≈ $200 + $0 = $200
So, the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.
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Determine all of the characteristics of the hyperbola with equation:
(x+12)^2/36-(y-15)^2/100=1
The characteristics of the hyperbola with equation (x+12)²/36-(y-15)²/100=1 are:
Center: (-12, 15)Transverse axis length: 2a = 12Conjugate axis length: 2b = 20Distance from center to foci: c ≈ 11.66Foci: (-12, 26.66) and (-12, 3.34)Vertices: (-18, 15) and (-6, 15)How to explain the hyperbolaComparing the given equation with the standard form, we have:
(h, k) = (-12, 15)
a² = 36
b² = 100
Taking the square root of a² and b², we get:
a = 6
b = 10
c² = 36 + 100
c² = 136
c ≈ 11.66
The foci of the hyperbola are located at (-12, 15 + 11.66) and (-12, 15 - 11.66), which are approximately (-12, 26.66) and (-12, 3.34).
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1,2 2.1 2.2 2.3 20 Tilly wants to deposit money into her banking account at FNB bank: R3,50 + R1,00 per R100 is charged for an over the counter deposit. When an own ATM is used for deposits, R1,00 per R100 (First 2 free per month) is charged and for ATM withdrawals at own bank R6,50 +R1,00 per R100 is charged Determine the service fee which Tilly will incur, when: R700 is deposited over the counter? R700 was deposited as follows: R100 on Monday, R200 on Tuesday, and (3) R400 on Saturday during the first week of the month. R500 is withdrawn at an ATM? (2) (2) [14]
Service fee for the over the counter deposit of R700: R10.50
Service fee for the ATM withdrawal of R500: R11.50
To determine the service fee that Tilly will incur for the given transactions,
Over the Counter Deposit of R700:
Tilly is depositing R700, the fee will be:
Fee = R3.50 + (R1.00 per R100) x (R700 / R100)
= R3.50 + R7.00
= R10.50
Therefore, the service fee for the over the counter deposit of R700 is R10.50.
ATM Withdrawal of R500:
The fee for an ATM withdrawal at own bank is calculated as R6.50 + R1.00 per R100.
Since Tilly is withdrawing R500, the fee will be:
Fee = R6.50 + (R1.00 per R100) x (R500 / R100)
= R6.50 + R5.00
= R11.50
Therefore, the service fee for the ATM withdrawal of R500 is R11.50.
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Please help with these Please explain if possibile
By using Pythagoras' theorem, triangle 3 and 4 is a right triangle, and others are not.
What is the triangle?
A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees.
What is right-angled triangle?
A right-angled triangle is one with one of its interior angles equal to 90 degrees, or any angle is a right angle.
According to the given information:
The Pythagorean theorem states that " In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides"
Let's check fig (3)
[tex]15^{2} =12^{2} +9^{2}[/tex]
225 = 144 + 81
225 = 225
both sides are equal, Therefore it is a right-angled triangle.
Let's check fig (4)
[tex]48.5^{2}=39^{2}+32.5^{2}[/tex]
2352.25 = 1521 + 1056.25
2352.25 ≠ 2577.25
Both sides are not equal, Therefore it is not a right-angled triangle.
Let's check fig (5)
[tex]11^{2}=9^{2}+\sqrt{115} ^{2}[/tex]
121 = 81 + 115
121 ≠ 196
Both sides are not equal, Therefore it is not a right-angled triangle.
Let's check fig (6)
[tex]16^{2} = 10^{2} + (2\sqrt{39}) ^{2}[/tex]
256 = 100 + 156
256 = 256
both sides are equal, Therefore it is a right-angled triangle.
Hence figure 3 and 6 is right angle triangle, others are not.
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Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
The type of transformation shown is a vertical transformation
Determining the type of transformation shown.In mathematics, a vertical translation refers to a transformation of a function or graph that involves moving it up or down along the y-axis without changing its vertical transformation.
From the attached figure, we can see that the polygons are moved up or down to map them to one another
This means that the transformation is a vertical transformation
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Complete question
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
Vertical translation
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
24. Anna, Berta, Charlie, David and Elisa baked biscuits at the weekend. Anna baked 24, Berta
25, Charlie 26, David 27 and Elisa 28 biscuits. By the end of the weekend one of the children had
twice as many, one 3 times, one 4 times, one 5 times and one 6 times as many biscuits as on
Saturday. Who baked the most biscuits on Saturday?
(A) Anna (8) Berta (C) Charlie (D) David (E) Elisa
At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.
To determine who baked the most biscuits on Saturday, we need to calculate how many biscuits each child had at the end of the weekend.
Anna had 24 biscuits, Berta had 25, Charlie had 26, David had 27, and Elisa had 28.
Let's start with the child who had twice as many biscuits as on Saturday. We can divide their total number of biscuits by 2 to get the number they had on Saturday.
If we try this calculation for each child, we find that only Elisa's total number of biscuits (28) is evenly divisible by 2. Therefore, Elisa must be the child who had twice as many biscuits as on Saturday, meaning she had 14 biscuits on Saturday.
We can use a similar process to determine how many biscuits each child had on Saturday:
- The child who had three times as many biscuits as on Saturday must have had a total of 42 biscuits, which means they had 14 biscuits on Saturday.
- The child who had four times as many biscuits as on Saturday must have had a total of 56 biscuits, which means they had 14 biscuits on Saturday.
- The child who had five times as many biscuits as on Saturday must have had a total of 70 biscuits, which means they had 14 biscuits on Saturday.
- The child who had six times as many biscuits as on Saturday must have had a total of 84 biscuits, which means they had 14 biscuits on Saturday.
Now we can add up the number of biscuits each child had on Saturday:
- Anna had 24 biscuits.
- Berta had 25 biscuits.
- Charlie had 26 biscuits.
- David had 27 biscuits.
- Elisa had 14 biscuits.
Therefore, David baked the most biscuits on Saturday with 27.
To determine who baked the most biscuits on Saturday, we need to consider the information given about the multiplication factors (twice, 3 times, 4 times, 5 times, and 6 times) and the initial number of biscuits baked by each child.
1. Anna baked 24 biscuits.
2. Berta baked 25 biscuits.
3. Charlie baked 26 biscuits.
4. David baked 27 biscuits.
5. Elisa baked 28 biscuits.
Now, let's apply the multiplication factors and see which child had the most biscuits at the end of the weekend:
1. Anna: 24 x 2 = 48
2. Berta: 25 x 3 = 75
3. Charlie: 26 x 4 = 104
4. David: 27 x 5 = 135
5. Elisa: 28 x 6 = 168
At the end of the weekend, Elisa had the most biscuits (168). So, the answer is (E) Elisa baked the most biscuits on Saturday.
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According to "7-Year-Old Girl Gets New Hand from 3-D Printer," which is the best explanation of why Faith needs a prosthetic hand?
She needs extra help holding onto paper, bicycle handlebars, and other objects.
She has been waiting for the opportunity to design her own hand.
The waiting list was too long for other types of treatment.
She lost her left hand due to a condition at birth
Faith needs a prosthetic hand because she lost her left hand at birth and requires assistance holding objects.
Why does Faith need a prosthetic hand in "7-Year-Old Girl Gets New Hand from 3-D Printer"?According to the article "7-Year-Old Girl Gets New Hand from 3-D Printer," Faith is a young girl who was born with a condition that caused her to lose her left hand. As a result, she has difficulty holding onto objects such as paper and bicycle handlebars. Faith had been waiting for an opportunity to design her own prosthetic hand, but the waiting list for other types of treatment was too long. Fortunately, a team of students and educators at a local university were able to create a prosthetic hand for her using a 3-D printer. The new hand will allow Faith to have greater independence and mobility, and she is excited to be able to participate in activities she was previously unable to do. This story is an example of how technology can be used to improve the lives of individuals with disabilities and provide them with greater opportunities to participate fully in everyday life.
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The radius of a circle is 10 meters what is the area
Answer:
100π or ≈ 314.1592
Step-by-step explanation:
Area of a circle formula: A = πr²
A = π(10)²
A = π(100)
A = 100π ≈ 314.1592
Answer:
100pi
Step-by-step explanation:
pi*radius^2=area
pi*10^2=100pi
Please Help Fast!!!!!!!!!!!!!!!!!!!!!!!!!
The number of solutions that are there for the pair of equations for lines Q and S is zero solution (no solution) because the lines are parallel with no point of intersection.
What is no solution?In Mathematics and Geometry, no solution is sometimes referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
This ultimately implies that, a system of equations would have no solution when the line representing each of the equations are parallel lines and have the same slope i.e both sides of the equal sign are the same and the variables cancel out.
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please help ASAP (can give brainliest)
Answer:
134° + (2x)° = 180°
(2x)° = 46°
x = 23
So angles 1, 2, 3, and 4 all measure 23°.
Determine the distance between the points (−3, −6) and (5, 0).
The distance between the points (-3, -6) and (5, 0) is 10 units.
What is the Pythagorean theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
To determine the distance between two points in a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula for two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}
Given the two points (-3, -6) and (5, 0), we can plug in the values into the distance formula as follows:
x₁ = -3, y₁ = -6 (coordinates of the first point)
x₂ = 5, y₂ = 0 (coordinates of the second point)
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}
= √{(8)² + (6)²}
= √{(64) + (36)
= √100
= 10
Hence, the distance between the points (-3, -6) and (5, 0) is 10 units.
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Pls help me find the exponent
Answer:
1.6 × 10^4
Step-by-step explanation:
how many five-digit positive integers exist where the digits are non increasing from left to right? (for example, 87743 and 10000 fulfill the conditions. 78987 and 33429 do not.)
There are 715 five-digit positive integers where the digits are non-increasing from left to right.
Here, we have to find the number of five-digit positive integers where the digits are non-increasing from left to right, you can think of this as selecting five digits (from 0 to 9) with repetition allowed, while ensuring that the selected digits are arranged in a non-increasing order.
This is essentially a combinations with repetition problem.
For each digit, there are 10 choices (0 to 9). Since repetition is allowed, you can use a stars and bars approach, where you place 4 bars among 10 possible positions (one for each digit choice) to separate the digits into groups.
The number of ways to arrange 5 digits with repetition allowed is given by the formula:
Number of arrangements = (n + k - 1) choose k,
where n is the number of digits (10 choices) and k is the number of bars (4). Plugging in the values:
Number of arrangements = (10 + 4 - 1) choose 4 = 13 choose 4 = 715.
So, there are 715 five-digit positive integers where the digits are non-increasing from left to right.
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