The total fencing used is 36 ft and the playpen would look like a square rather than a rectangle.
1) The given design uses 36 feet of fencing. Other playpens that could be made with the same amount of fencing are:
A square playpen with sides of length 9 feet (since 4 x 9 = 36)
A rectangular playpen with length 12 feet and width 6 feet (since 2 x (12 + 6) = 36)
2) The fencing used for the given design is the sum of the lengths of all four sides. From the diagram, we can see that the two shorter sides have a length of 8 feet each, and the two longer sides have a length of 10 feet each. Therefore, the total fencing used is:
2(8 ft) + 2(10 ft) = 16 ft + 20 ft = 36 ft
3) Leah's statement is not correct. A square playpen with sides of length 9 feet would require a perimeter of 4 x 9 = 36 feet, which is the same amount of fencing used for the given design. However, the shape of the playpen would be different, since the sides would all be equal in length. The playpen would look like a square rather than a rectangle.
4) Another playpen that could be made with the same amount of fencing is a rectangular playpen with length 18 feet and width 0 feet (i.e., a straight line). The perimeter would be:
2(18 ft) + 2(0 ft) = 36 ft
This playpen may not be practical for animals, but it satisfies the requirement of using 36 feet of fencing.
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Four out of 5 freshmen study algebra. How many study
algebra in a class of 400?
Answer:
4/5 ×400
0.8 × 400
=320 freshmen study algebra.
I had used fraction method.
Brad rolled a cube number cube 30 times and recorded the results in the tally chart below which what is the experimental probability of rolling a five
Which expression represents the relationship between the step number n and the total number of small squares in the pattern
The expression that represents the relationship between the step number n and the total number of small squares in the pattern is this: (n-1)^2.
How to find the right expressionFrom the given information, we can see that the pattern starts with 0 squares at step 1, and each subsequent step adds a square to the pattern. However, the lower right square is always missing. Therefore, the total number of small squares in the pattern at step n can be represented by the expression: (n-1)^2
The reason we subtract 1 from n is that we started counting from step 1, whereas the expression (n-1)^2 assumes that we start counting from 0. Then we square (n-1) to account for the number of squares in the pattern, excluding the missing square in the lower right corner.
Complete Question:
Which expression represents the relationship between the step number n and the total number of small squares in the pattern?
A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.
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If the dimensions of a prism with surface area 42 m^2 and volume 18 m^3 are enlarged by a factor of 4, what is the surface area and volume of the prism?
SA = 2lw + 2lh + 2wh = 42 m^2 ... (1)
And the volume of the original prism is given by:
V = lwh = 18 m^3 ... (2)
If you enlarge the dimensions of the prism by a factor of 4, then the new dimensions will be 4l, 4w, and 4h. The new surface area of the prism will be:
New SA = 2(4l)(4w) + 2(4l)(4h) + 2(4w)(4h)
= 32lw + 32lh + 32wh
= 32(2lw + 2lh + 2wh)
= 32(42)
= 1344 m^2
So, the surface area of the enlarged prism is 1344 m^2.
Similarly, the new volume of the prism will be:
New V = (4l)(4w)(4h)
= 64lwh
= 64(18)
= 1152 m^3
So, the volume of the enlarged prism is 1152 m^3.
Therefore, the surface area of the prism is 1344 m^2 and the volume of the prism is 1152 m^3 after the dimensions are enlarged by a factor of 4.
*IG:whis.sama_ent
Simplify 9/12x1/12=?
Answer: Exact Form:
1/16
Decimal Form:
0.0625
Step-by-step explanation:
o determine whether voters would be willing to vote for a tax increase to improve the city's parks, the park commission surveys 500 park users.
Why is this sample likely to be biased?
This sample is likely to be biased because it only includes individuals who use the city's parks, which means it may not represent the entire population of voters who would be affected by a tax increase to improve the parks.
What is sample?A sample is a subset or a smaller group of individuals or 17 that are selected from a larger population to represent the population.
According to question:The park commission's study of 500 park users is likely biassed because it only covers people who use the city's parks. This indicates that the sample does not accurately reflect the full electorate who would be impacted by a tax hike to fund park improvements.
Various people may hold various views regarding whether or not a tax increase is required to develop the parks. For instance, if they don't frequent the parks or have other priorities for their tax money, they might be less likely to approve a tax hike.
If the park commission only conducted surveys of people at specific times of day or in specific locations of the city, the sample may also be skewed. This could omit those who visit the parks at various hours or in various locations around the city.
In order to get accurate and valid results, it's crucial to utilise a representative sample that includes people from different demographic groups. A biased sample can produce results that are erroneous or misleading.
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UO
Graph each figure and classify it. Then find the area.
6. R(3,-2), S(7, -2), T(8, -6), V(1, -6)
22 unit² is the area of trapezoid .
In arithmetic, what is a polygon?
A polygon is a closed, one-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. Polygonal edges are another name for the sides of a polygon. A polygon's vertices (or corners) are the places where two sides converge.
this is trapezoid .
area of trapezoid = 1/2 * sum of parallel side * height
= 1/2 * (3 + 8 ) * 4
= 22 unit²
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Question 2
Mike deposited $3,000 in the first year of a retirement account, and then increased the deposits by $300 each year. The account earned 8.35%. What was the account value after forty years?
The account value after forty years is approximately $489,074,140.57.
What is formula for the future value of an annuity?To calculate the account value after forty years, we need to use the formula for the future value of an annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we have:
P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on
r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)
n = 40 years
To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:
S = n/2 * [2a + (n-1)d]
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = $3,000
d = $300
n = 40
Plugging these values into the formula, we get:
S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000
Thus, the aggregate sum of installments more than 40 years is $2,340,000.
We can now enter these figures into the formula for annuity future value:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
[tex]FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835[/tex]
FV = $2,340,000 * 209.251
FV = $489,074,140.57
Consequently, after forty years, the account's value is approximately $489,074,140.57.
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Find the area of the shape
The area of the composite shape are
1. Orange
2. Light blue
3. Purple
4. Green
5. Red
6. Yellow
7. Light green
8. Yellow
9. Dark blue
10. Pink
How to find the area of the composite shapesThe area of the composite shapes are solved as follows
1. rectangles
= 7 * 3 + (15 - 7) * 1.5
= 21 + 12
= 33 square cm
2.
= 39 x 4 + 0.5(39 + 26) x (18 - 4)
= 156 + 455
= 611 square m
3.
= 12 * 15 + 0.5 x 15 x 10
= 180 + 75
= 255 square ft
4.
= 15 x 7 + 0.5 x π x 3.5 x 3.5
= 105 + 19.24
= 124.2 square cm
5.
= 0.5 x 10 x 22 - 0.5 x 6 x 12
= 110 - 36
= 74 square yd
6.
= 0.5 x π x 3 x 3 + 0.5 x 6 x 11
= 14.14 + 33
= 47.1 square m
7.
= 18 x 6 - 2 x π x 2 x 2
= 108 - 25.13
= 82.8 square m
8.
= 4 x 16 + 0.5 (16 + 10) x (8 - 4)
= 64 + 52
= 116 square cm
9.
= 18 x 8 - 4 * 0.5 x 4 x 4
= 144 - 32
= 112 square cm
10.
= [0.5 (7 + (9 + 3)) x (15 + 6 - 17)] + [(17 - 6) x (9 + 3)] + [6 x 9]
= 38 + 132 + 54
= 224 square cm
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I don’t get it. I just came from a vacation
Answer:
the answer ur looking for would be B
Step-by-step
Solve the inequality for the variable: 2(3c + 15) + 4c > 100
Answer:
c > 7
Step-by-step explanation:
Now we have to,
→ Find the required value of c.
The equation is,
→ 2(3c + 15) + 4c > 100
Then the value of c will be,
→ 2(3c + 15) + 4c > 100
Applying Distributive property:
→ 2(3c) + 2(15) + 4c > 100
→ 6c + 30 + 4c > 100
Combining the like terms:
→ 10c + 30 > 100
→ 10c > 100 - 30
→ 10c > 70
Dividing the value 70 with 10:
→ c > 70 ÷ 10
→ [ c > 7 ]
Hence, the answer is c > 7.
Hello !
Answer:
[tex]\boxed{\sf c > 7 \ \ \ ||\ \ \ \sf (7,+\infty)}[/tex]
Step-by-step explanation:
We are looking for the values of c that satisfy the following inequality :
[tex]\sf 2(3c + 15) + 4c > 100[/tex]
Let's expand the left side of the inequality.
[tex]\sf 2\times 3c +2\times 15+4c > 100\\6c+30+4c > 100[/tex]
Now we will combine like terms :
[tex]\sf 10c+30 > 100[/tex]
Let's substract 30 from both sides of the inequality.
[tex]\sf 10c+30-30 > 100-30\\10c > 70[/tex]
Finally, let's divide both sides by 10.
10>0 so the inequality remains the same.
[tex]\sf\frac{10c}{10} > \frac{70}{10} \\\boxed{\sf c > 7}[/tex]
Have a nice day ;)
What is the relative frequency of students that are of the 1 to 5 class and are left handed?
Enter the answer as a percentage rounded to the nearest whole percentage
Class Left Right
1 to 5 17 25
6 to 10 23 23
10 to 12 32 48
The relative frequency of students that are of the 1 to 5 class and are left-handed is 40%.
What is relative frequency?Relative frequency is the ratio of the number of times an event occurs to the number of trials. This can be expressed as a fraction, a percentage, or a proportion.
This can be calculated using the following equation:
Relative Frequency = (Number of Left-Handed Students in 1 to 5 Class / Total Number of Students in 1 to 5 Class) x 100
Relative Frequency = (17 / (17 + 25)) x 100
Relative Frequency = 40%
This calculation shows that 40% of students in the 1 to 5 class are left-handed. This percentage can be rounded to the nearest whole percentage, giving the answer of 40%.
By comparing the relative frequency of left-handed students in the 1 to 5 class to the relative frequency in the other classes, it can be seen that the 1 to 5 class has the highest relative frequency of left-handed students.
This could be due to the developmental stage of students in this age group, as studies have shown that being left-handed is more common in children aged 5 to 10 than in adults.
Alternatively, it could be due to cultural factors, such as left-handed students feeling more comfortable in the 1 to 5 class due to the younger age group.
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Patricia is buying new kitchen cabinets, which are shaped as rectangular prisms. The cabinets are 34 inches tall, 24 inches deep, and 16 inches wide. What is the volume of the cabinets?
If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.
To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:
Height = 34 inches
Depth = 24 inches
Width = 16 inches
So the formula for the volume is:
Volume = Height x Depth x Width
Substituting the given values, we get:
Volume = 34 x 24 x 16
Volume = 16,384 cubic inches
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Write an inequality to compare -21 and -13 which temperature is warmer?
Answer:
[tex]-13 > -21[/tex]
-13 is the warmer temperature.
Step-by-step explanation:
When comparing negative numbers, the number closer to zero on the number line is greater.
(OR, the negative number that, if it was positive, would be less).
In this case, that number is -13.
We now know that -13 is greater than -21, so we can write this inequality:
[tex]-13 > -21[/tex]
In regards to temperature, greater numbers usually mean hotter temperature, so -13 is the warmer temperature.
the lifetimes of batteries created by a company are normally distributed with a mean of 105 hours and a standard deviation of 12 hours. what percentage of these batteries will last between 90.6 and 109.8 hours? state your answer as a percent rounded to the nearest hundredth, but do not include a % symbol in your answer.
Around 21.13% of the batteries will final(last) between 90.6 and 109.8 hours.
To unravel this issue, ready to utilize the standard typical conveyance by standardizing the values utilizing the equation:
z = (x - μ) / σ
where
x is the esteem we need to discover the likelihood
μ is cruel(mean), and σ is the standard deviation.
So, for the lower conclusion of the extent, we have:
z1 = (90.6 - 105) / 12 ≈ -1.20
z1 = -1.20
And for the upper conclusion of the extension, we have the:
z2 = (109.8 - 105) / 12 ≈ 0.45
z2 = 0.45
We need to discover the rate of batteries that will final(last) between these two values, which compares to the area under the typical bend between z1 and z2.
Able to utilize a standard ordinary conveyance table or calculator to discover this zone, or we will utilize the properties of the typical conveyance to inexact it.
Since the typical conveyance is symmetric around the cruel, we know that the zone between z1 and z2 is the same as the range between -z2 and -z1 (i.e., the comparing values on the other side of the mean).
So, ready to discover the range between -z2 and -z1, which compares to the rate of batteries that will final between 90.6 and 109.8 hours:
P(-z2 < z < -z1) ≈ P(z < -z1) - P(z < -z2)
Employing a standard typical dissemination table or calculator, we discover:
P(z < -1.20) ≈ 0.1151
P(z < -0.45) ≈ 0.3264
So, the rate of batteries that will final between 90.6 and 109.8 hours is rough:
P(-z2 < z < -z1) ≈ 0.3264 - 0.1151 ≈ 0.2113
Increasing by 100%, we get:
0.2113 * 100% ≈ 21.13D
44 Subsequently, roughly 21.13% of the batteries will final between 90.6 and 109.8 hours.
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JK and YA intersect at point C.
Find the measure of ZJCA.
C
123°
A
K
Angles
The measure of angle JCA is 57°
What are verically opposite angles?When two lines intersect, the opposite (X) angles are equal. This means ;
123° = JCY
and JCA = YCK ( verically opposite angles)
The sum of angle at a point is 360. This means the addition of all the angles above is 360°.
Representing angle JCA by x , therefore,
x+x +123+123 = 360°( angle at a point)
2x + 246 = 360
2x = 360-246
2x = 114
divide both sides by 2
x = 114/2
x = 57°
therefore the measure of angle JCA is 57°
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The perimeter of parallelogram ABCD is 96 cm. AD is 3 cm more than twice AB. Find the lengths of all four sides of ABCD
The lengths of all four sides of parallelogram ABCD:
AB = 15 cm, BC = 33 cm, CD = 15 cm and AD = 33 cm
Consider a parallelogram ABCD
Let's assume that x represents the length of sides AD and BC
y be the length of sides AB and CD
We know that the formula for the perimeter of parallelogram is
P = 2(length + width)
Here, AD is 3 cm more than twice AB
So we get an expression,
AD = 3 + 2(AB)
AD = 3 + 2y
x = 3 + 2y
USing above formula of perimeter, the perimeter of parallelogram ABCD would be,
P = 2(x + y)
96 = 2(3 + 2y + y)
48 = 3 + 3y
45 = 3y
y = 15 cm
And x = 3 + 2(15)
x = 33 cm
Therefore, the lengths of sides AD and BC = 33 cm and the lengths of sides AB and CD = 15 cm
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Establishing causality is often a main focus of statistical studies. What is the best type of study to conduct to establish causality? Use the situation in this task to support your answer
The best type of study is RCT randomized controlled trial.
What is statistical studies?The practise of gathering and analysing data with the purpose of identifying patterns and trends is known as statistical analysis. It is a technique for eliminating bias from data evaluation by using numerical analysis. This method is beneficial for gathering research interpretations, creating statistical models, and organising surveys and studies.
What is causality?In the false idea that there must be an underlying causal relationship because the data reveals a correlation, people frequently misunderstand and misuse the concept of causality in statistics. The best method for proving that two variables are causally related is to utillize a controlled study.
Randomised controlled trials (RCTs) are the most effective study design for proving causality. The treatment group in an RCT receives the intervention under study, whilst the control group either receives no intervention or a placebo. Participants are then randomly assigned to one of the two groups. The RCT helps to adjust for confounding variables and demonstrate a cause-and-effect relationship between the intervention and the result by randomly allocating participants.
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the graph of p(x)=2(x-4) is translated 2 units right and down 1 unit. What is the equation of the translated function q(x) in slope intercept form
The equation of the translated function q(x) in slope-intercept form is q(x) = 2x - 13.
What is the equation of the translated function q(x)The function p(x) = 2(x - 4) can be rewritten in slope-intercept form as:
p(x) = 2x - 8
To translate the graph of p(x) two units to the right and one unit down, we need to make the following adjustments to the equation:
To shift the graph two units to the right, we need to replace x with (x - 2).To shift the graph one unit down, we need to subtract 1 from the entire equation.So the equation of the translated function q(x) in slope-intercept form is:
q(x) = 2(x - 2) - 8 - 1
Simplifying, we get:
q(x) = 2x - 13
Therefore, the equation of the translated function q(x) in slope-intercept form is q(x) = 2x - 13.
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Graph the data set. {(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)} Which kind of model best describes the data?
Answer:
linear
Step-by-step explanation:
i js took the test
The kind of model that best describes the data is a linear relation
Calculating the kind of model best describes the data?From the question, we have the following parameters that can be used in our computation:
{(0, 0), (−1, −3), (−2, −6), (−3, −9), (−4, −12)}
In the above dataset, we can see that
As x increases by -1The values of y increases by -3Using the above as a guide, we have the following:
The relation has a constant rate of -3/-1
Evaluate
The relation has a constant rate of 3
Only linear relations have constant rates
Hence, the kind of model that best describes the data is a linear relation
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the time series component that reflects the random changes in a time series that are not caused by any other components, and tends to hide the existence of the more predictable components, is called:
The time series component that reflects the random changes in a time series that are not caused by any other components, and tends to hide the existence of the more predictable components, is called the "random" or "irregular" component.
It represents the noise or fluctuations in the time series that cannot be explained by any of the other components, such as trend, seasonality, or cyclical variations. The irregular component is also known as the "white noise" or "error" component, and it is typically modeled as a random process with zero mean and constant variance. It is important to separate out the irregular component from the other components in order to identify the underlying patterns and trends in the time series, and to make accurate forecasts and predictions.
what is white noise?
In time series analysis, "white noise" refers to a random process where the values at each point in time are independently and identically distributed with a mean of zero and a constant variance.
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the health care provider prescribes cefazolin 550 mg intramuscularly to a client. The nurse dilutes a 2-g vial of cefazolin (Ancef) with 3 mL of diluent to yield a volume of 3.2 mL. How many mL should the nurse administer if the physician orders 550 mg IM? Type the correct answer in the blank.
The nurse should administer 0.88 mL of the cefazolin solution for the 550 mg IM dose.
To determine the number of mL to administer for the 550 mg IM dose of cefazolin, follow these steps:
Determine the concentration of cefazolin per mL:
- You have a 2-g (2000 mg) vial of cefazolin that was diluted with 3 mL of diluent, yielding a total volume of 3.2 mL.
- Divide the total amount of cefazolin (2000 mg) by the total volume (3.2 mL) to find the concentration per mL: 2000 mg / 3.2 mL = 625 mg/mL.
Calculate the volume needed for the 550 mg dose:
- Divide the prescribed dose (550 mg) by the concentration per mL (625 mg/mL):
550 mg / 625 mg/mL = 0.88 mL.
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The nurse should administer 0.88 mL of the cefazolin solution intramuscularly to the client.
To determine the mL to administer for the 550 mg IM order of cefazolin, follow these steps:
1. Calculate the concentration of cefazolin in the solution:
- 2,000 mg (2-g vial) of cefazolin is diluted with 3 mL of diluent, yielding a volume of 3.2 mL.
- Concentration = (2,000 mg) / (3.2 mL) = 625 mg/mL
2. Determine the volume needed for the 550 mg prescribed dose:
- Volume = (Prescribed Dose) / (Concentration)
- Volume = (550 mg) / (625 mg/mL) = 0.88 mL
Cefazolin is an antibiotic used to treat various bacterial infections. The dosage of cefazolin depends on the type and severity of the infection, as well as the patient’s weight, age, and kidney function12. The usual adult dose for mild to moderate infections ranges from 250 mg to 1 g every 6 to 12 hours
The nurse should administer 0.88 mL of the cefazolin solution intramuscularly to the client.
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An initial investment is $14275.
It grows at a rate of 6% a year.
Interest is compounded yearly.
What is the value after 18 years? Round your answer to the nearest
penny.
Answer: $34,828.59
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r)^t
where:
P = the principal (in this case, $14,275)
r = the annual interest rate (6%, or 0.06 as a decimal)
t = the number of years (18)
Plugging in the values we know, we get:
A = $14,275(1 + 0.06)^18
A = $14,275(1.06)^18
A = $34,828.59 (rounded to the nearest penny)
Therefore, the value of the investment after 18 years, rounded to the nearest penny, is $34,828.59
18PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
The exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
sin 30 = a/8 {opposite/hypotenuse}
a = 8 × 1/2 {sin 30 = 1/2}
a = 4
cos 30 = b/8 {adjacent/hypotenuse}
b = 8 × √3/2 {cos 30 = √3/2}
b = 4√3
sin 45 = 4√3/d
d = 4√3 × 2/√2 {sin45 = √2/2}
d = 4√6
cos 45 = c/4√6
c = 4√6 × √2/2
c = 2√12
c = 4√3
Therefore, the exact lengths of the missing sides for the right triangle using trigonometric ratio of the respective angles are: a = 4, b = 4√3, c = 4√3, and d = 4√6
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Question
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
[tex] \frac{36}{12} = \frac{39}{x - 10} [/tex]
[tex] 3 = \frac{39}{x - 10} [/tex]
[tex]3(x - 10) = 39[/tex]
[tex]x - 10 = 13[/tex]
[tex]x = 23[/tex]
[tex]6e/7=48\\[/tex]
The solution of the given equation 6e/7 = 48 is given by, e = 56.
Equation is a mathematical statement where various numerical values, mathematical variables, mathematical operations, exponents or combination of them related via equal sign.
Given the equation is,
6e/7 = 48
We have to solve this equation and have to find the value of 'e' which satisfy this equation.
Solving the given equation we get,
6e = 48*7 [On multiplying 7 with both sides]
6e = 336
e = 336/6 [On dividing 6 from both sides]
e = 56
Hence the solution of the given equation is, e = 56.
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4. Construct a circle with center V. Construct an equilateral triangle RST inscribed within the circle.
A circle with center V and an inscribed equilateral triangle RST.
What is circle?
A circle is a closed two-dimensional shape consisting of all the points that are equidistant from a given point, called the center.
To construct a circle with center V and an inscribed equilateral triangle RST, follow these steps:
Draw point V as the center of the circle.
From point V, draw a radius that will serve as one side of the equilateral triangle RST. Label the endpoint of this radius as point S.
Using a compass, draw a circle with center V and radius VS. This circle will intersect the radius VS at two points, label these points as R and T.
Draw segments RT and RS to complete the equilateral triangle RST.
Your construction should show a circle with center V and an inscribed equilateral triangle RST.
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10. A cone has a Volume of 94.25cm ^ 3 If the radius of the cone is 3 cm, what is the height of the cone?
Answer:
10 cm
Step-by-step explanation:
V =1/3 x π x r² x h
94.25 =1/3 x π x 3² x h
94.25 ÷ 3π =h
so, h= 10 cm
URGENT - Will also give brainliest to simple answer
The area of the sector in terms of pi is: 75π cm²
The Length of arc = 15π cm
What is the Area of a Sector and Length of an Arc of a Circle?Area of a sector = ∅/360 * πr²
Length of arc = ∅/360 * 2πr, where r is the radius and ∅ is the reference angle.
Given the following:
Reference angle (∅) = 270°
Radius of circle (r) = 10 cm
Area of the sector = 270/360 * π * 10²
Area of the sector = 75π cm²
Length of arc = 15π cm
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Angles X and Y are supplementary. Angle X measures 115. 75° and angle Y measures (m − 8)°. Find m∠Y
The measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
What is the supplementary angle?
Two angles are said to be supplementary if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180.
Since angles X and Y are supplementary, their measures add up to 180 degrees. So we have:
X + Y = 180
Substituting the given values, we get:
115.75 + (m - 8) = 180
Simplifying, we get:
m - 8 = 180 - 115.75
m - 8 = 64.25
Adding 8 to both sides, we get:
m = 72.25
Therefore, the measure of angle Y is m - 8 = 72.25 - 8 = 64.25 degrees.
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