The diagonal of a rectangle is 5 units long, and one side is 3 units long. How many units long is the perimeter of the rectangle?
Answers
Answer:
16
Step-by-step explanation:
Perimeter is the total length/ distance around the shape so 3+3=6 5+5=10 6+10=16
Related Questions
Consider the function f defined as: f(x)={
tanx
x
,
2x+1,
−
2
π
0≤x<
2
π
a) Is f continuous at x=
4
π
? Explain. b) Is f differentiable at x=−
4
π
? Explain. c) Is f continuous on the whole interval (−
2
π
,
2
π
) ?
Answers
(a) f(x) is not continuous at x = 4π. b) f(x) is differentiable at x = -4π. c) f(x) is continuous on the whole interval (-2π, 2π).
a) Is f continuous at x = 4π?
To determine the continuity at a specific point, we need to check if the left-hand limit, right-hand limit, and the value of the function at that point are all equal.
For x < 4π:
f(x) = tan(x)
The function tan(x) is continuous for x < 4π, so the left-hand limit exists.
For x > 4π:
f(x) = 2x + 1
The function 2x + 1 is also continuous for x > 4π, so the right-hand limit exists.
Now, let's check the value of the function at x = 4π:
f(4π) = tan(4π)
tan(4π) is undefined because it involves division by zero.
Since the left-hand limit, right-hand limit, and the value of the function at x = 4π are not equal, f(x) is not continuous at x = 4π.
b) Is f differentiable at x = -4π?
To determine differentiability at a specific point, we need to check if the derivative of the function exists at that point.
For x < -4π:
f(x) = tan(x)
The function tan(x) is differentiable for x < -4π, so the derivative exists.
For x > -4π:
f(x) = 2x + 1
The function 2x + 1 is also differentiable for x > -4π, so the derivative exists.
Now, let's check the derivative at x = -4π:
f'(x) = d/dx(tan(x)) = sec^2(x)
f'(-4π) = sec^2(-4π) = sec^2(4π) = 1/(cos^2(4π))
Since cos(4π) = 1, cos^2(4π) = 1, and 1/(cos^2(4π)) = 1/1 = 1, the derivative exists at x = -4π.
Therefore, f(x) is differentiable at x = -4π.
c) Is f continuous on the whole interval (-2π, 2π)?
To determine the continuity on an interval, we need to check if the function is continuous at every point within that interval.
For x < 0:
f(x) = tan(x)
The function tan(x) is continuous for x < 0.
For 0 ≤ x < 2π:
f(x) = 2x + 1
The function 2x + 1 is continuous for 0 ≤ x < 2π.
Since each part of the function is individually continuous for the respective intervals, f(x) is continuous on the whole interval (-2π, 2π).
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6x-3=5x-5
can someone help me
Answers
Answer:
x=-2
Step-by-step explanation:
To find the value of x you will have to isolate the x.
6x-3=5x-5 ------> Add 3 to both sides to get rid of the 3
6x=5x-2 ------> Subtract 5x to both sides to get rid of the 5x
1x=-2
1x is the same as x so
x=-2
a tar heel basketball player makes 80% of his free throw attempts. among 3 attempts he has, the probability that he at least misses one is equal to
Answers
The probability that he at least misses one is equal to 61/125.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given in the question
basketball player makes 80% of his free throw attempts i.e.
P(Success) = 4/5 or 0.8
P(Miss the attempt) = 1 - 0.8 = 0.2 or 1/5
Number of sample (n) = 3
We need to calculate probability that he at least misses one i.e.
P(X > = 1) = 1 - P(X < 1) = 1 - P(X = 0)
Here we will use binomial probability distribution which can be calculated as
P(X = n |N, p)= NCn x (p^n) x (1-p)^(N-n)
P(X > = 1) = 1 - P(X < 1) = 1 - P(X = 0) = 1 - 3C0 x (1/5)^0 x (1 - 1/5)^(3-0)
= 1 - (1 x 1 x 64/125) = 1 - 64/125 = 61/125
Hence, the probability that he at least misses one is equal to 61/125.
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A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is twotailed, separate the values with a comma. Round your answer to three decimal places. A bolt manufacturer is very concerned about the consistency with which his machines produce boits. The bolts should be 0.2 centimeters in diameter. The variance of the boits should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?
Answers
To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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Eva uses 10 tiles to make a mosaic. Five of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Answers
Answer: 1/2
Step-by-step explanation:
From the question, we are informed that Eva uses 10 tiles to make a mosaic and that five of the tiles are blue.
The fraction that represents the tiles that are blue will be:
= Number of blue tiles / Total number of tiles
= 5/10
= 1/2
Help please !!!!!!!!
Answers
Is there a relationship between Column X and Column Y? Perform correlation analysis and summarize your findings.
X Y
10 37
6 10
39 18
24 12
35 11
12 34
33 26
32 9
23 42
10 24
16 40
16 1
35 39
28 24
5 42
22 7
12 17
44 17
15 27
40 47
46 35
35 14
28 38
9 18
9 17
8 22
35 12
15 30
34 18
16 43
19 24
17 45
21 24
Answers
The correlation analysis indicates a moderate positive relationship between Column X and Column Y.
To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.
Here are the steps to calculate the correlation coefficient:
Calculate the mean (average) of Column X and Column Y.
Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375
Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125
Calculate the deviation of each value from the mean for both Column X and Column Y.
Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)
Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)
Calculate the product of the deviations for each pair of values.
Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)
Calculate the sum of the product of deviations.
Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)
Calculate the standard deviation of Column X and Column Y.
StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]
StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]
Calculate the correlation coefficient (r).
r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]
By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.
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Question 6(Multiple Choice Worth 1 points) (02.05 MC) Choose the table that represents g(x) = 4⋅f(x) when f(x) = x − 5. x g(x) 1 −4 2 −3 3 −2 x g(x) 1 −16 2 −12 3 −8 x g(x) 1 −20 2 −18 3 −16 x g(x) 1 −1 2 −2 3 −3
Answers
Answer: (b)
x g(x)
1 -16
2 -12
3 -8
If g(x) is 4*f(x), then we can find g(x) by multiplying 4 by x-5
g(x) = 4(x-5)
= 4x-20
Now we can plug in 1,2, and 3 for x to see which table makes sense.
g(1) = 4(1) - 20
= -16
g(2) = 4(2) - 20
= -12
g(3) = 4(3) - 20
= -8
hope this helps
Answer:
x g(x)
1 -16
2 -12
3 -8
Step-by-step explanation:
PLEASE HELP ME I WILL GIVE BRAINLIEST!!
Which row of Pascal's Triangle should you use to expand the binomial (a + b)^4?
Answers
Answer:
Step-by-step explanation:
a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1
so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6
given a = d and b = -5y
∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +
4x-8-x=7 what is the answer
Answers
Answer:
x=5
Step-by-step explanation:
4x-x = 7 +8
3x = 15
x = 15/3
x = 5
Answer:
5
Step-by-step explanation:
4x - 8 - x =7
3x - 8 =7
3x =7 +8
3x =15
x =15 :3
x =5
what is the distance along the unit circle between any two successive 8th roots of 1?
a. π/8
b. π/6
c. π/4
d. π/2
Answers
The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.
To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.
Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.
Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.
Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.
Therefore, the correct answer is option c. π/4.
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1. Jebrel borrowed $7000 from his friend. He saves $110 each month to pay
him back
a. How much will he have paid off at the beginning of the 1st, 2nd, 3rd, 4th and 5th
months? (Should this chart start with zero or 1)
b. Make a graph to represent the pattern from part a.
Answers
Answer 63
Step-by-step explanation:
it will take around 63 months
Answer:
1. 6890
2. 6790
3. 6670
4. 6560
5. 6450
Step-by-step explanation:
Let W
be a subspace of Rn
spanned by n
non-zero orthogonal vectors. Show that W=Rn
.
Answers
W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.
To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.
Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:
v = c1v1 + c2v2 + ... + cnvn
where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.
To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.
Therefore, if w is any vector in W that is not equal to v, we have:
= = c1 + c2 + ... + cn = 0
since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.
Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.
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How are the properties of exponents used when dividing a polynomial by a monomial?
Answers
Answer:
a couple different obes
Step-by-step explanation:
there are five
what is 60/2000
helphelphelphelphelp
Answers
Answer:
0.03
Step-by-step explanation:
please give me brainliest! :) :) :)
Answer:
The answer is 0.03
Step-by-step explanation:
You are responsible in the customs services of your country; an importer would like to know how to calculate the customs values in the cases of the maritime transport, air and by road. a) What is the basic element for calculating the customs value: When the import is by sea, air and by Road b) How should one calculate the customs duties in these three cases?
Answers
a) The basic element for calculating the customs value in importation by sea, air, and road is the transaction value,b) Customs duties in these three cases are typically calculated based on the customs value of the imported goods.
a) The basic element for calculating the customs value in importation by sea, air, and road is the transaction value. The transaction value is the price actually paid or payable for the imported goods, which typically includes the cost of the goods themselves, any assists (such as packaging or materials provided by the buyer), royalties, license fees, and any other payments made as a condition of sale.
b) To calculate customs duties in these cases, the customs value is used as the basis. The customs value includes the transaction value and certain adjustments, such as the cost of transportation to the place of importation, loading, unloading, and handling charges incurred in transporting the goods to the importing country, as well as the cost of insurance. These adjustments are necessary to determine the value of the goods at the time and place of importation.
Once the customs value is determined, customs duties are applied to this value based on the applicable tariff rates or preferential trade agreements. Customs duties are typically calculated as a percentage of the customs value, although specific duty rates or other calculation methods may also be used depending on the nature of the imported goods and the relevant customs regulations of the country.
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10. A jar contains dimes and quarters. There are 15 more quarters than dimes. The coins total $23. How many
of each coin is in the jar?
What is this question asking you?
Dimes
Quarters
Number of Dimes:
Number of Quarters:
Answers
Answer:
dimes:$8 quarters:$15
Step-by-step explanation:
im still in 6th grade
Answer:
55 dimes and 70 quarters
Step-by-step explanation:
Using a simple strategy of guess and check we know that the quarters will always be 15 more than dimes. From this we know it has to be around the 50s as 40s would bring us numbers too low and 60s too high. 55 happens to be answer for dimes as that brings in $5.50. 23-5.5=17.5 multiply that by 4 as each quarter is only valued at $0.25 you get the answer 70 which just so happens to meet the requirements of being 15 more than 55.
Determine whether the graph of each pair of equations are parrallel, perpendicular, or neither
1. y= 3x +4
y= 3x +7
2. y= -4x+1
4y= x + 3
3. y= 2x - 5
y = 5x -5
4. y= -1/3x +2
y = 3x - 5
5. y = 3/5x - 3
5y=3x-10
Answers
Answer: 1: parrallel
2:perpendicular
3; neither
4; perpendicular. 5: parrallel
Step-by-step explanation:
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Answers
The statement that is true about the quadratic functions is:
g(x) > h(x) for x = -1.
Which statements are true for functions g(x) and g(x)?Here we have the two quadratic functions:
g(x) = x^2
h(x) = -x^2
Notice that h(x) = -g(x).
Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.
g(0) = 0^2 = -0^2 = h(0)
Then the statement that is true is
g(x) > h(x) for x = -1.
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What is 1 10/21 + 4 5/7 these are fractions btw
Answers
Answer:
Exact form:
130/21
Decimal form:
6.190476 (repeating decimal)
Mixed number form:
6 4/21
the guy took 15 pieses and there is 4 left
Answers
The number of pieces in the bowl before she added the 20 is 8 pieces of candy
Here, we want to get the number of pieces in the bowl before the addition of the 20 pieces
Let the number of pieces before the addition be n
she added 20 pieces to what is there initially, this brings the total to;
\(n\text{ + 20}\)Now, two days after the addition, half of the above is gone
Half of the above is;
\(\frac{n+20}{2}\)Now, the difference between the number of pieces in the bowl after the addition of the 20 and the half gone is 14; we have the equation as thus;
\(\begin{gathered} n\text{ + 20 - (}\frac{n+20}{2})\text{ = 14} \\ \\ 2(n+20)-(n+20)\text{ = 28} \\ n\text{ +20 = 28} \\ n\text{ = 28-20} \\ n\text{ = 8} \end{gathered}\)Find the values of x and y. Leave answer in simplest radical form
Answers
Answer:
x = 4/√2
y = 4/√2
Step-by-step explanation:
Hypotenuse = 4
θ = 45°
x = Opposite side
y = Adjacent Side
a) Solving for x = Opposite side
We solve using Trigonometry function of Sine
sin θ = Opposite/Hypotenuse
sin 45 = x/4
Cross Multiply
x = sin 45 × 4
Note that : sin 45 = 1/√2
x = 1/√2 × 4
x = 4/√2
b) Solving for y
We solve using Trigonometric function of Cosine
cos θ = Adjacent/Hypotenuse
cos 45 = x/4
Cross Multiply
x = cos 45 × 4
Note that : cos 45 = 1/√2
x = 1/√2 × 4
y = 4/√2
What is 4 1/5 multiplied by 3/10
Answers
Answer:
1 13/50
Step-by-step explanation:
4 1/5 * 3/10
Change the mixed number to an improper fraction
4 1/5 = (5*4+1)/5 = 21/5
21/5 *3/10
63/50
Changing back to a mixed number
1 13/50
Answer:
1 13/50
Step-by-step explanation:
4⅕ × 3/10
21/5 × 3/10
63/50
1 13/50
what is 6/14 x 21/30 ?
Answers
what is 6/14 x 21/30 ?
it's 0.3
Trapezoid ABCD was dilated to create trapezoid A’B’C’D’. Which statements are true about the trapezoids? Select three options
Answers
The 3 options--1, 2, and 4.
Answer:A, B, E
Step-by-step explanation:
edgenunity
What is the 7th term of the geometric sequence below? 7, -14,28, -56, А -448 b b -896 с 448 D 896
Answers
Given the sequence:
7, -14, 28, -56,
To find the 7th term of the geometric sequence, use the formula below:
\(a_n=ar^{(n-1)}\)where,
a is the first term = 7
n is the number of terms = 7
r = common ratio =
\(r\text{ = }\frac{\sec ond\text{ term}}{\text{first term}}\text{ = }\frac{-14}{7}=\text{ -2}\)Thus, we have:
\(\begin{gathered} a_7=\text{ 7(}-2^{(7-1)}) \\ \\ \text{ = 7 }(-2^6) \\ \\ \text{ = }7(-64) \\ \\ \text{ = }-448 \end{gathered}\)The 7th term is -448
ANSWER:
A) -448
What is -5 1/4 - (-7 1/2)
Answers
Answer: 9/4 or 2 1/4
Step-by-step explanation:
How do you solve a system of equations step by step?
Answers
A system of equations can be solved by graphing or substitution or elimination methods.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Solve by graphing:
1) Graph the first equation
2) Then graph the second equation in the same coordinate system
3) Identify the intersection point of the equations.
4) The solution of equations is the intersection.
Solving by substitution:
1) Solve the first equation for y.
2) Put the value of y that got from the first equation in the second equation.
3) Solve the equation for x.
4) Put the value of x in the first equation.
5) The value of x and y is the solution of the system of equations.
Solving by elimination:
1) Multiply both equations by a number such that the coefficient of x or y will be the same.
2) Then subtract the equations to eliminate x or y.
3) Then calculate the value of x or y.
4) Substitute the value of x or y in the first equation and find the value y or x.
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NEED HELP ASAP
Rectangular pyramids X and Y have equal volumes.
20 cm
h
12 cm
10 cm
13 cm
12 cm
Pyramid x
Pyramid Y
Which is the height, h, of pyramid Y?
O A. 17 cm
OB. 20 cm
O c. 23 cm
OD. 26 cm
Answers
Step-by-step explanation:
10/12=x/20
10×20=12x
200=12x
x=200/12
x=17
what is (fxg)(x)
f(x)=x^3-4x+2
g(x)=x^2+2
Answers
Answer: x^6+6x^4+8x^2+2
Step-by-step explanation:
Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in
(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2